Special cases: *
value.
*/
CesiumMath.sinh = function(value) {
var part1 = Math.pow(Math.E, value);
var part2 = Math.pow(Math.E, -1.0 * value);
return (part1 - part2) * 0.5;
};
/**
* Returns the hyperbolic cosine of a number.
* The hyperbolic cosine of value is defined to be
* (ex + e-x)/2.0
* where e is Euler's number, approximately 2.71828183.
*
* Special cases: *
value.
*/
CesiumMath.cosh = function(value) {
var part1 = Math.pow(Math.E, value);
var part2 = Math.pow(Math.E, -1.0 * value);
return (part1 + part2) * 0.5;
};
/**
* Computes the linear interpolation of two values.
*
* @param {Number} p The start value to interpolate.
* @param {Number} q The end value to interpolate.
* @param {Number} time The time of interpolation generally in the range [0.0, 1.0].
* @returns {Number} The linearly interpolated value.
*
* @example
* var n = Cesium.Math.lerp(0.0, 2.0, 0.5); // returns 1.0
*/
CesiumMath.lerp = function(p, q, time) {
return ((1.0 - time) * p) + (time * q);
};
/**
* pi
*
* @type {Number}
* @constant
*/
CesiumMath.PI = Math.PI;
/**
* 1/pi
*
* @type {Number}
* @constant
*/
CesiumMath.ONE_OVER_PI = 1.0 / Math.PI;
/**
* pi/2
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_TWO = Math.PI * 0.5;
/**
* pi/3
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_THREE = Math.PI / 3.0;
/**
* pi/4
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_FOUR = Math.PI / 4.0;
/**
* pi/6
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_SIX = Math.PI / 6.0;
/**
* 3pi/2
*
* @type {Number}
* @constant
*/
CesiumMath.THREE_PI_OVER_TWO = (3.0 * Math.PI) * 0.5;
/**
* 2pi
*
* @type {Number}
* @constant
*/
CesiumMath.TWO_PI = 2.0 * Math.PI;
/**
* 1/2pi
*
* @type {Number}
* @constant
*/
CesiumMath.ONE_OVER_TWO_PI = 1.0 / (2.0 * Math.PI);
/**
* The number of radians in a degree.
*
* @type {Number}
* @constant
* @default Math.PI / 180.0
*/
CesiumMath.RADIANS_PER_DEGREE = Math.PI / 180.0;
/**
* The number of degrees in a radian.
*
* @type {Number}
* @constant
* @default 180.0 / Math.PI
*/
CesiumMath.DEGREES_PER_RADIAN = 180.0 / Math.PI;
/**
* The number of radians in an arc second.
*
* @type {Number}
* @constant
* @default {@link CesiumMath.RADIANS_PER_DEGREE} / 3600.0
*/
CesiumMath.RADIANS_PER_ARCSECOND = CesiumMath.RADIANS_PER_DEGREE / 3600.0;
/**
* Converts degrees to radians.
* @param {Number} degrees The angle to convert in degrees.
* @returns {Number} The corresponding angle in radians.
*/
CesiumMath.toRadians = function(degrees) {
if (!defined(degrees)) {
throw new DeveloperError('degrees is required.');
}
return degrees * CesiumMath.RADIANS_PER_DEGREE;
};
/**
* Converts radians to degrees.
* @param {Number} radians The angle to convert in radians.
* @returns {Number} The corresponding angle in degrees.
*/
CesiumMath.toDegrees = function(radians) {
if (!defined(radians)) {
throw new DeveloperError('radians is required.');
}
return radians * CesiumMath.DEGREES_PER_RADIAN;
};
/**
* Converts a longitude value, in radians, to the range [-Math.PI, Math.PI).
*
* @param {Number} angle The longitude value, in radians, to convert to the range [-Math.PI, Math.PI).
* @returns {Number} The equivalent longitude value in the range [-Math.PI, Math.PI).
*
* @example
* // Convert 270 degrees to -90 degrees longitude
* var longitude = Cesium.Math.convertLongitudeRange(Cesium.Math.toRadians(270.0));
*/
CesiumMath.convertLongitudeRange = function(angle) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
var twoPi = CesiumMath.TWO_PI;
var simplified = angle - Math.floor(angle / twoPi) * twoPi;
if (simplified < -Math.PI) {
return simplified + twoPi;
}
if (simplified >= Math.PI) {
return simplified - twoPi;
}
return simplified;
};
/**
* Convenience function that clamps a latitude value, in radians, to the range [-Math.PI/2, Math.PI/2).
* Useful for sanitizing data before use in objects requiring correct range.
*
* @param {Number} angle The latitude value, in radians, to clamp to the range [-Math.PI/2, Math.PI/2).
* @returns {Number} The latitude value clamped to the range [-Math.PI/2, Math.PI/2).
*
* @example
* // Clamp 108 degrees latitude to 90 degrees latitude
* var latitude = Cesium.Math.clampToLatitudeRange(Cesium.Math.toRadians(108.0));
*/
CesiumMath.clampToLatitudeRange = function(angle) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
return CesiumMath.clamp(angle, -1*CesiumMath.PI_OVER_TWO, CesiumMath.PI_OVER_TWO);
};
/**
* Produces an angle in the range -Pi <= angle <= Pi which is equivalent to the provided angle.
*
* @param {Number} angle in radians
* @returns {Number} The angle in the range [-CesiumMath.PI, CesiumMath.PI].
*/
CesiumMath.negativePiToPi = function(x) {
if (!defined(x)) {
throw new DeveloperError('x is required.');
}
return CesiumMath.zeroToTwoPi(x + CesiumMath.PI) - CesiumMath.PI;
};
/**
* Produces an angle in the range 0 <= angle <= 2Pi which is equivalent to the provided angle.
*
* @param {Number} angle in radians
* @returns {Number} The angle in the range [0, CesiumMath.TWO_PI].
*/
CesiumMath.zeroToTwoPi = function(x) {
if (!defined(x)) {
throw new DeveloperError('x is required.');
}
var mod = CesiumMath.mod(x, CesiumMath.TWO_PI);
if (Math.abs(mod) < CesiumMath.EPSILON14 && Math.abs(x) > CesiumMath.EPSILON14) {
return CesiumMath.TWO_PI;
}
return mod;
};
/**
* The modulo operation that also works for negative dividends.
*
* @param {Number} m The dividend.
* @param {Number} n The divisor.
* @returns {Number} The remainder.
*/
CesiumMath.mod = function(m, n) {
if (!defined(m)) {
throw new DeveloperError('m is required.');
}
if (!defined(n)) {
throw new DeveloperError('n is required.');
}
return ((m % n) + n) % n;
};
/**
* Determines if two values are equal using an absolute or relative tolerance test. This is useful
* to avoid problems due to roundoff error when comparing floating-point values directly. The values are
* first compared using an absolute tolerance test. If that fails, a relative tolerance test is performed.
* Use this test if you are unsure of the magnitudes of left and right.
*
* @param {Number} left The first value to compare.
* @param {Number} right The other value to compare.
* @param {Number} relativeEpsilon The maximum inclusive delta between left and right for the relative tolerance test.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The maximum inclusive delta between left and right for the absolute tolerance test.
* @returns {Boolean} true if the values are equal within the epsilon; otherwise, false.
*
* @example
* var a = Cesium.Math.equalsEpsilon(0.0, 0.01, Cesium.Math.EPSILON2); // true
* var b = Cesium.Math.equalsEpsilon(0.0, 0.1, Cesium.Math.EPSILON2); // false
* var c = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON7); // true
* var d = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON9); // false
*/
CesiumMath.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(relativeEpsilon)) {
throw new DeveloperError('relativeEpsilon is required.');
}
absoluteEpsilon = defaultValue(absoluteEpsilon, relativeEpsilon);
var absDiff = Math.abs(left - right);
return absDiff <= absoluteEpsilon || absDiff <= relativeEpsilon * Math.max(Math.abs(left), Math.abs(right));
};
var factorials = [1];
/**
* Computes the factorial of the provided number.
*
* @param {Number} n The number whose factorial is to be computed.
* @returns {Number} The factorial of the provided number or undefined if the number is less than 0.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
*
* @example
* //Compute 7!, which is equal to 5040
* var computedFactorial = Cesium.Math.factorial(7);
*
* @see {@link http://en.wikipedia.org/wiki/Factorial|Factorial on Wikipedia}
*/
CesiumMath.factorial = function(n) {
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
var length = factorials.length;
if (n >= length) {
var sum = factorials[length - 1];
for (var i = length; i <= n; i++) {
factorials.push(sum * i);
}
}
return factorials[n];
};
/**
* Increments a number with a wrapping to a minimum value if the number exceeds the maximum value.
*
* @param {Number} [n] The number to be incremented.
* @param {Number} [maximumValue] The maximum incremented value before rolling over to the minimum value.
* @param {Number} [minimumValue=0.0] The number reset to after the maximum value has been exceeded.
* @returns {Number} The incremented number.
*
* @exception {DeveloperError} Maximum value must be greater than minimum value.
*
* @example
* var n = Cesium.Math.incrementWrap(5, 10, 0); // returns 6
* var n = Cesium.Math.incrementWrap(10, 10, 0); // returns 0
*/
CesiumMath.incrementWrap = function(n, maximumValue, minimumValue) {
minimumValue = defaultValue(minimumValue, 0.0);
if (!defined(n)) {
throw new DeveloperError('n is required.');
}
if (maximumValue <= minimumValue) {
throw new DeveloperError('maximumValue must be greater than minimumValue.');
}
++n;
if (n > maximumValue) {
n = minimumValue;
}
return n;
};
/**
* Determines if a positive integer is a power of two.
*
* @param {Number} n The positive integer to test.
* @returns {Boolean} true if the number if a power of two; otherwise, false.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
* @example
* var t = Cesium.Math.isPowerOfTwo(16); // true
* var f = Cesium.Math.isPowerOfTwo(20); // false
*/
CesiumMath.isPowerOfTwo = function(n) {
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
return (n !== 0) && ((n & (n - 1)) === 0);
};
/**
* Computes the next power-of-two integer greater than or equal to the provided positive integer.
*
* @param {Number} n The positive integer to test.
* @returns {Number} The next power-of-two integer.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
* @example
* var n = Cesium.Math.nextPowerOfTwo(29); // 32
* var m = Cesium.Math.nextPowerOfTwo(32); // 32
*/
CesiumMath.nextPowerOfTwo = function(n) {
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
// From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
--n;
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
++n;
return n;
};
/**
* Constraint a value to lie between two values.
*
* @param {Number} value The value to constrain.
* @param {Number} min The minimum value.
* @param {Number} max The maximum value.
* @returns {Number} The value clamped so that min <= value <= max.
*/
CesiumMath.clamp = function(value, min, max) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(min)) {
throw new DeveloperError('min is required.');
}
if (!defined(max)) {
throw new DeveloperError('max is required.');
}
return value < min ? min : value > max ? max : value;
};
var randomNumberGenerator = new MersenneTwister();
/**
* Sets the seed used by the random number generator
* in {@link CesiumMath#nextRandomNumber}.
*
* @param {Number} seed An integer used as the seed.
*/
CesiumMath.setRandomNumberSeed = function(seed) {
if (!defined(seed)) {
throw new DeveloperError('seed is required.');
}
randomNumberGenerator = new MersenneTwister(seed);
};
/**
* Generates a random number in the range of [0.0, 1.0)
* using a Mersenne twister.
*
* @returns {Number} A random number in the range of [0.0, 1.0).
*
* @see CesiumMath.setRandomNumberSeed
* @see {@link http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne twister on Wikipedia}
*/
CesiumMath.nextRandomNumber = function() {
return randomNumberGenerator.random();
};
/**
* Computes Math.acos(value), but first clamps value to the range [-1.0, 1.0]
* so that the function will never return NaN.
*
* @param {Number} value The value for which to compute acos.
* @returns {Number} The acos of the value if the value is in the range [-1.0, 1.0], or the acos of -1.0 or 1.0,
* whichever is closer, if the value is outside the range.
*/
CesiumMath.acosClamped = function(value) {
if (!defined(value)) {
throw new DeveloperError('value is required.');
}
return Math.acos(CesiumMath.clamp(value, -1.0, 1.0));
};
/**
* Computes Math.asin(value), but first clamps value to the range [-1.0, 1.0]
* so that the function will never return NaN.
*
* @param {Number} value The value for which to compute asin.
* @returns {Number} The asin of the value if the value is in the range [-1.0, 1.0], or the asin of -1.0 or 1.0,
* whichever is closer, if the value is outside the range.
*/
CesiumMath.asinClamped = function(value) {
if (!defined(value)) {
throw new DeveloperError('value is required.');
}
return Math.asin(CesiumMath.clamp(value, -1.0, 1.0));
};
/**
* Finds the chord length between two points given the circle's radius and the angle between the points.
*
* @param {Number} angle The angle between the two points.
* @param {Number} radius The radius of the circle.
* @returns {Number} The chord length.
*/
CesiumMath.chordLength = function(angle, radius) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
if (!defined(radius)) {
throw new DeveloperError('radius is required.');
}
return 2.0 * radius * Math.sin(angle * 0.5);
};
/**
* Finds the logarithm of a number to a base.
*
* @param {Number} number The number.
* @param {Number} base The base.
* @returns {Number} The result.
*/
CesiumMath.logBase = function(number, base) {
if (!defined(number)) {
throw new DeveloperError('number is required.');
}
if (!defined(base)) {
throw new DeveloperError('base is required.');
}
return Math.log(number) / Math.log(base);
};
/**
* @private
*/
CesiumMath.fog = function(distanceToCamera, density) {
var scalar = distanceToCamera * density;
return 1.0 - Math.exp(-(scalar * scalar));
};
return CesiumMath;
});
/*global define*/
define('Core/Cartesian3',[
'./Check',
'./defaultValue',
'./defined',
'./DeveloperError',
'./freezeObject',
'./Math'
], function(
Check,
defaultValue,
defined,
DeveloperError,
freezeObject,
CesiumMath) {
'use strict';
/**
* A 3D Cartesian point.
* @alias Cartesian3
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
*
* @see Cartesian2
* @see Cartesian4
* @see Packable
*/
function Cartesian3(x, y, z) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = defaultValue(z, 0.0);
}
/**
* Converts the provided Spherical into Cartesian3 coordinates.
*
* @param {Spherical} spherical The Spherical to be converted to Cartesian3.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromSpherical = function(spherical, result) {
Check.typeOf.object(spherical, 'spherical');
if (!defined(result)) {
result = new Cartesian3();
}
var clock = spherical.clock;
var cone = spherical.cone;
var magnitude = defaultValue(spherical.magnitude, 1.0);
var radial = magnitude * Math.sin(cone);
result.x = radial * Math.cos(clock);
result.y = radial * Math.sin(clock);
result.z = magnitude * Math.cos(cone);
return result;
};
/**
* Creates a Cartesian3 instance from x, y and z coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Number} z The z coordinate.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromElements = function(x, y, z, result) {
if (!defined(result)) {
return new Cartesian3(x, y, z);
}
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Duplicates a Cartesian3 instance.
*
* @param {Cartesian3} cartesian The Cartesian to duplicate.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian3.clone = function(cartesian, result) {
if (!defined(cartesian)) {
return undefined;
}
if (!defined(result)) {
return new Cartesian3(cartesian.x, cartesian.y, cartesian.z);
}
result.x = cartesian.x;
result.y = cartesian.y;
result.z = cartesian.z;
return result;
};
/**
* Creates a Cartesian3 instance from an existing Cartesian4. This simply takes the
* x, y, and z properties of the Cartesian4 and drops w.
* @function
*
* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromCartesian4 = Cartesian3.clone;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian3.packedLength = 3;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian3} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian3.pack = function(value, array, startingIndex) {
Check.typeOf.object(value, 'value');
Check.defined(array, 'array');
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex] = value.z;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian3} [result] The object into which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.unpack = function(array, startingIndex, result) {
Check.defined(array, 'array');
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Cartesian3();
}
result.x = array[startingIndex++];
result.y = array[startingIndex++];
result.z = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian3s into an array of components.
*
* @param {Cartesian3[]} array The array of cartesians to pack.
* @param {Number[]} result The array onto which to store the result.
* @returns {Number[]} The packed array.
*/
Cartesian3.packArray = function(array, result) {
Check.defined(array, 'array');
var length = array.length;
if (!defined(result)) {
result = new Array(length * 3);
} else {
result.length = length * 3;
}
for (var i = 0; i < length; ++i) {
Cartesian3.pack(array[i], result, i * 3);
}
return result;
};
/**
* Unpacks an array of cartesian components into an array of Cartesian3s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian3[]} result The array onto which to store the result.
* @returns {Cartesian3[]} The unpacked array.
*/
Cartesian3.unpackArray = function(array, result) {
Check.defined(array, 'array');
Check.numeric.minimum(array.length, 3);
if (array.length % 3 !== 0) {
throw new DeveloperError('array length must be a multiple of 3.');
}
var length = array.length;
if (!defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var index = i / 3;
result[index] = Cartesian3.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian3 from three consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*
* @example
* // Create a Cartesian3 with (1.0, 2.0, 3.0)
* var v = [1.0, 2.0, 3.0];
* var p = Cesium.Cartesian3.fromArray(v);
*
* // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 2.0, 3.0];
* var p2 = Cesium.Cartesian3.fromArray(v2, 2);
*/
Cartesian3.fromArray = Cartesian3.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian3} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian3.maximumComponent = function(cartesian) {
Check.typeOf.object(cartesian, 'cartesian');
return Math.max(cartesian.x, cartesian.y, cartesian.z);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian3} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian3.minimumComponent = function(cartesian) {
Check.typeOf.object(cartesian, 'cartesian');
return Math.min(cartesian.x, cartesian.y, cartesian.z);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian3} first A cartesian to compare.
* @param {Cartesian3} second A cartesian to compare.
* @param {Cartesian3} result The object into which to store the result.
* @returns {Cartesian3} A cartesian with the minimum components.
*/
Cartesian3.minimumByComponent = function(first, second, result) {
Check.typeOf.object(first, 'first');
Check.typeOf.object(second, 'second');
Check.typeOf.object(result, 'result');
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
result.z = Math.min(first.z, second.z);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian3} first A cartesian to compare.
* @param {Cartesian3} second A cartesian to compare.
* @param {Cartesian3} result The object into which to store the result.
* @returns {Cartesian3} A cartesian with the maximum components.
*/
Cartesian3.maximumByComponent = function(first, second, result) {
Check.typeOf.object(first, 'first');
Check.typeOf.object(second, 'second');
Check.typeOf.object(result, 'result');
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
result.z = Math.max(first.z, second.z);
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian3.magnitudeSquared = function(cartesian) {
Check.typeOf.object(cartesian, 'cartesian');
return cartesian.x * cartesian.x + cartesian.y * cartesian.y + cartesian.z * cartesian.z;
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian3.magnitude = function(cartesian) {
return Math.sqrt(Cartesian3.magnitudeSquared(cartesian));
};
var distanceScratch = new Cartesian3();
/**
* Computes the distance between two points.
*
* @param {Cartesian3} left The first point to compute the distance from.
* @param {Cartesian3} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* var d = Cesium.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0));
*/
Cartesian3.distance = function(left, right) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Cartesian3.subtract(left, right, distanceScratch);
return Cartesian3.magnitude(distanceScratch);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian3#distance}.
*
* @param {Cartesian3} left The first point to compute the distance from.
* @param {Cartesian3} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* var d = Cesium.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0));
*/
Cartesian3.distanceSquared = function(left, right) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Cartesian3.subtract(left, right, distanceScratch);
return Cartesian3.magnitudeSquared(distanceScratch);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian to be normalized.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.normalize = function(cartesian, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.object(result, 'result');
var magnitude = Cartesian3.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
result.z = cartesian.z / magnitude;
if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {
throw new DeveloperError('normalized result is not a number');
}
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian3.dot = function(left, right) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
return left.x * right.x + left.y * right.y + left.z * right.z;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.multiplyComponents = function(left, right, result) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Check.typeOf.object(result, 'result');
result.x = left.x * right.x;
result.y = left.y * right.y;
result.z = left.z * right.z;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.divideComponents = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x / right.x;
result.y = left.y / right.y;
result.z = left.z / right.z;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.add = function(left, right, result) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Check.typeOf.object(result, 'result');
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.subtract = function(left, right, result) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Check.typeOf.object(result, 'result');
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian3} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.multiplyByScalar = function(cartesian, scalar, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.number(scalar, 'scalar');
Check.typeOf.object(result, 'result');
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
result.z = cartesian.z * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian3} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.divideByScalar = function(cartesian, scalar, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.number(scalar, 'scalar');
Check.typeOf.object(result, 'result');
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
result.z = cartesian.z / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian to be negated.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.negate = function(cartesian, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.object(result, 'result');
result.x = -cartesian.x;
result.y = -cartesian.y;
result.z = -cartesian.z;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.abs = function(cartesian, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.object(result, 'result');
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
result.z = Math.abs(cartesian.z);
return result;
};
var lerpScratch = new Cartesian3();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian3} start The value corresponding to t at 0.0.
* @param {Cartesian3} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.lerp = function(start, end, t, result) {
Check.typeOf.object(start, 'start');
Check.typeOf.object(end, 'end');
Check.typeOf.number(t, 't');
Check.typeOf.object(result, 'result');
Cartesian3.multiplyByScalar(end, t, lerpScratch);
result = Cartesian3.multiplyByScalar(start, 1.0 - t, result);
return Cartesian3.add(lerpScratch, result, result);
};
var angleBetweenScratch = new Cartesian3();
var angleBetweenScratch2 = new Cartesian3();
/**
* Returns the angle, in radians, between the provided Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @returns {Number} The angle between the Cartesians.
*/
Cartesian3.angleBetween = function(left, right) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Cartesian3.normalize(left, angleBetweenScratch);
Cartesian3.normalize(right, angleBetweenScratch2);
var cosine = Cartesian3.dot(angleBetweenScratch, angleBetweenScratch2);
var sine = Cartesian3.magnitude(Cartesian3.cross(angleBetweenScratch, angleBetweenScratch2, angleBetweenScratch));
return Math.atan2(sine, cosine);
};
var mostOrthogonalAxisScratch = new Cartesian3();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The most orthogonal axis.
*/
Cartesian3.mostOrthogonalAxis = function(cartesian, result) {
Check.typeOf.object(cartesian, 'cartesian');
Check.typeOf.object(result, 'result');
var f = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch);
Cartesian3.abs(f, f);
if (f.x <= f.y) {
if (f.x <= f.z) {
result = Cartesian3.clone(Cartesian3.UNIT_X, result);
} else {
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
}
} else {
if (f.y <= f.z) {
result = Cartesian3.clone(Cartesian3.UNIT_Y, result);
} else {
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
}
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian3.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.x === right.x) &&
(left.y === right.y) &&
(left.z === right.z));
};
/**
* @private
*/
Cartesian3.equalsArray = function(cartesian, array, offset) {
return cartesian.x === array[offset] &&
cartesian.y === array[offset + 1] &&
cartesian.z === array[offset + 2];
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian3.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
return (left === right) ||
(defined(left) &&
defined(right) &&
CesiumMath.equalsEpsilon(left.x, right.x, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.y, right.y, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.z, right.z, relativeEpsilon, absoluteEpsilon));
};
/**
* Computes the cross (outer) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The cross product.
*/
Cartesian3.cross = function(left, right, result) {
Check.typeOf.object(left, 'left');
Check.typeOf.object(right, 'right');
Check.typeOf.object(result, 'result');
var leftX = left.x;
var leftY = left.y;
var leftZ = left.z;
var rightX = right.x;
var rightY = right.y;
var rightZ = right.z;
var x = leftY * rightZ - leftZ * rightY;
var y = leftZ * rightX - leftX * rightZ;
var z = leftX * rightY - leftY * rightX;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Returns a Cartesian3 position from longitude and latitude values given in degrees.
*
* @param {Number} longitude The longitude, in degrees
* @param {Number} latitude The latitude, in degrees
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* var position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
*/
Cartesian3.fromDegrees = function(longitude, latitude, height, ellipsoid, result) {
Check.typeOf.number(longitude, 'longitude');
Check.typeOf.number(latitude, 'latitude');
longitude = CesiumMath.toRadians(longitude);
latitude = CesiumMath.toRadians(latitude);
return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);
};
var scratchN = new Cartesian3();
var scratchK = new Cartesian3();
var wgs84RadiiSquared = new Cartesian3(6378137.0 * 6378137.0, 6378137.0 * 6378137.0, 6356752.3142451793 * 6356752.3142451793);
/**
* Returns a Cartesian3 position from longitude and latitude values given in radians.
*
* @param {Number} longitude The longitude, in radians
* @param {Number} latitude The latitude, in radians
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* var position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
*/
Cartesian3.fromRadians = function(longitude, latitude, height, ellipsoid, result) {
Check.typeOf.number(longitude, 'longitude');
Check.typeOf.number(latitude, 'latitude');
height = defaultValue(height, 0.0);
var radiiSquared = defined(ellipsoid) ? ellipsoid.radiiSquared : wgs84RadiiSquared;
var cosLatitude = Math.cos(latitude);
scratchN.x = cosLatitude * Math.cos(longitude);
scratchN.y = cosLatitude * Math.sin(longitude);
scratchN.z = Math.sin(latitude);
scratchN = Cartesian3.normalize(scratchN, scratchN);
Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
var gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));
scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);
scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);
if (!defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(scratchK, scratchN, result);
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
*/
Cartesian3.fromDegreesArray = function(coordinates, ellipsoid, result) {
Check.defined(coordinates, 'coordinates');
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new DeveloperError('the number of coordinates must be a multiple of 2 and at least 2');
}
var length = coordinates.length;
if (!defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var index = i / 2;
result[index] = Cartesian3.fromDegrees(longitude, latitude, 0, ellipsoid, result[index]);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
*/
Cartesian3.fromRadiansArray = function(coordinates, ellipsoid, result) {
Check.defined(coordinates, 'coordinates');
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new DeveloperError('the number of coordinates must be a multiple of 2 and at least 2');
}
var length = coordinates.length;
if (!defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var index = i / 2;
result[index] = Cartesian3.fromRadians(longitude, latitude, 0, ellipsoid, result[index]);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
*/
Cartesian3.fromDegreesArrayHeights = function(coordinates, ellipsoid, result) {
Check.defined(coordinates, 'coordinates');
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new DeveloperError('the number of coordinates must be a multiple of 3 and at least 3');
}
var length = coordinates.length;
if (!defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var height = coordinates[i + 2];
var index = i / 3;
result[index] = Cartesian3.fromDegrees(longitude, latitude, height, ellipsoid, result[index]);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
*/
Cartesian3.fromRadiansArrayHeights = function(coordinates, ellipsoid, result) {
Check.defined(coordinates, 'coordinates');
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new DeveloperError('the number of coordinates must be a multiple of 3 and at least 3');
}
var length = coordinates.length;
if (!defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var height = coordinates[i + 2];
var index = i / 3;
result[index] = Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result[index]);
}
return result;
};
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.ZERO = freezeObject(new Cartesian3(0.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_X = freezeObject(new Cartesian3(1.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Y = freezeObject(new Cartesian3(0.0, 1.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Z = freezeObject(new Cartesian3(0.0, 0.0, 1.0));
/**
* Duplicates this Cartesian3 instance.
*
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.prototype.clone = function(result) {
return Cartesian3.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian3.prototype.equals = function(right) {
return Cartesian3.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian3.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
return Cartesian3.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
};
/**
* Creates a string representing this Cartesian in the format '(x, y, z)'.
*
* @returns {String} A string representing this Cartesian in the format '(x, y, z)'.
*/
Cartesian3.prototype.toString = function() {
return '(' + this.x + ', ' + this.y + ', ' + this.z + ')';
};
return Cartesian3;
});
/*global define*/
define('Core/scaleToGeodeticSurface',[
'./Cartesian3',
'./defined',
'./DeveloperError',
'./Math'
], function(
Cartesian3,
defined,
DeveloperError,
CesiumMath) {
'use strict';
var scaleToGeodeticSurfaceIntersection = new Cartesian3();
var scaleToGeodeticSurfaceGradient = new Cartesian3();
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.
* @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
* @param {Number} centerToleranceSquared Tolerance for closeness to the center.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*
* @exports scaleToGeodeticSurface
*
* @private
*/
function scaleToGeodeticSurface(cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
if (!defined(oneOverRadii)) {
throw new DeveloperError('oneOverRadii is required.');
}
if (!defined(oneOverRadiiSquared)) {
throw new DeveloperError('oneOverRadiiSquared is required.');
}
if (!defined(centerToleranceSquared)) {
throw new DeveloperError('centerToleranceSquared is required.');
}
var positionX = cartesian.x;
var positionY = cartesian.y;
var positionZ = cartesian.z;
var oneOverRadiiX = oneOverRadii.x;
var oneOverRadiiY = oneOverRadii.y;
var oneOverRadiiZ = oneOverRadii.z;
var x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
var y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
var z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;
// Compute the squared ellipsoid norm.
var squaredNorm = x2 + y2 + z2;
var ratio = Math.sqrt(1.0 / squaredNorm);
// As an initial approximation, assume that the radial intersection is the projection point.
var intersection = Cartesian3.multiplyByScalar(cartesian, ratio, scaleToGeodeticSurfaceIntersection);
// If the position is near the center, the iteration will not converge.
if (squaredNorm < centerToleranceSquared) {
return !isFinite(ratio) ? undefined : Cartesian3.clone(intersection, result);
}
var oneOverRadiiSquaredX = oneOverRadiiSquared.x;
var oneOverRadiiSquaredY = oneOverRadiiSquared.y;
var oneOverRadiiSquaredZ = oneOverRadiiSquared.z;
// Use the gradient at the intersection point in place of the true unit normal.
// The difference in magnitude will be absorbed in the multiplier.
var gradient = scaleToGeodeticSurfaceGradient;
gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;
// Compute the initial guess at the normal vector multiplier, lambda.
var lambda = (1.0 - ratio) * Cartesian3.magnitude(cartesian) / (0.5 * Cartesian3.magnitude(gradient));
var correction = 0.0;
var func;
var denominator;
var xMultiplier;
var yMultiplier;
var zMultiplier;
var xMultiplier2;
var yMultiplier2;
var zMultiplier2;
var xMultiplier3;
var yMultiplier3;
var zMultiplier3;
do {
lambda -= correction;
xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);
xMultiplier2 = xMultiplier * xMultiplier;
yMultiplier2 = yMultiplier * yMultiplier;
zMultiplier2 = zMultiplier * zMultiplier;
xMultiplier3 = xMultiplier2 * xMultiplier;
yMultiplier3 = yMultiplier2 * yMultiplier;
zMultiplier3 = zMultiplier2 * zMultiplier;
func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;
// "denominator" here refers to the use of this expression in the velocity and acceleration
// computations in the sections to follow.
denominator = x2 * xMultiplier3 * oneOverRadiiSquaredX + y2 * yMultiplier3 * oneOverRadiiSquaredY + z2 * zMultiplier3 * oneOverRadiiSquaredZ;
var derivative = -2.0 * denominator;
correction = func / derivative;
} while (Math.abs(func) > CesiumMath.EPSILON12);
if (!defined(result)) {
return new Cartesian3(positionX * xMultiplier, positionY * yMultiplier, positionZ * zMultiplier);
}
result.x = positionX * xMultiplier;
result.y = positionY * yMultiplier;
result.z = positionZ * zMultiplier;
return result;
}
return scaleToGeodeticSurface;
});
/*global define*/
define('Core/Cartographic',[
'./Cartesian3',
'./defaultValue',
'./defined',
'./DeveloperError',
'./freezeObject',
'./Math',
'./scaleToGeodeticSurface'
], function(
Cartesian3,
defaultValue,
defined,
DeveloperError,
freezeObject,
CesiumMath,
scaleToGeodeticSurface) {
'use strict';
/**
* A position defined by longitude, latitude, and height.
* @alias Cartographic
* @constructor
*
* @param {Number} [longitude=0.0] The longitude, in radians.
* @param {Number} [latitude=0.0] The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
*
* @see Ellipsoid
*/
function Cartographic(longitude, latitude, height) {
/**
* The longitude, in radians.
* @type {Number}
* @default 0.0
*/
this.longitude = defaultValue(longitude, 0.0);
/**
* The latitude, in radians.
* @type {Number}
* @default 0.0
*/
this.latitude = defaultValue(latitude, 0.0);
/**
* The height, in meters, above the ellipsoid.
* @type {Number}
* @default 0.0
*/
this.height = defaultValue(height, 0.0);
}
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in radians.
*
* @param {Number} longitude The longitude, in radians.
* @param {Number} latitude The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromRadians = function(longitude, latitude, height, result) {
if (!defined(longitude)) {
throw new DeveloperError('longitude is required.');
}
if (!defined(latitude)) {
throw new DeveloperError('latitude is required.');
}
height = defaultValue(height, 0.0);
if (!defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in degrees. The values in the resulting object will
* be in radians.
*
* @param {Number} longitude The longitude, in degrees.
* @param {Number} latitude The latitude, in degrees.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromDegrees = function(longitude, latitude, height, result) {
if (!defined(longitude)) {
throw new DeveloperError('longitude is required.');
}
if (!defined(latitude)) {
throw new DeveloperError('latitude is required.');
}
longitude = CesiumMath.toRadians(longitude);
latitude = CesiumMath.toRadians(latitude);
return Cartographic.fromRadians(longitude, latitude, height, result);
};
var cartesianToCartographicN = new Cartesian3();
var cartesianToCartographicP = new Cartesian3();
var cartesianToCartographicH = new Cartesian3();
var wgs84OneOverRadii = new Cartesian3(1.0 / 6378137.0, 1.0 / 6378137.0, 1.0 / 6356752.3142451793);
var wgs84OneOverRadiiSquared = new Cartesian3(1.0 / (6378137.0 * 6378137.0), 1.0 / (6378137.0 * 6378137.0), 1.0 / (6356752.3142451793 * 6356752.3142451793));
var wgs84CenterToleranceSquared = CesiumMath.EPSILON1;
/**
* Creates a new Cartographic instance from a Cartesian position. The values in the
* resulting object will be in radians.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*/
Cartographic.fromCartesian = function(cartesian, ellipsoid, result) {
var oneOverRadii = defined(ellipsoid) ? ellipsoid.oneOverRadii : wgs84OneOverRadii;
var oneOverRadiiSquared = defined(ellipsoid) ? ellipsoid.oneOverRadiiSquared : wgs84OneOverRadiiSquared;
var centerToleranceSquared = defined(ellipsoid) ? ellipsoid._centerToleranceSquared : wgs84CenterToleranceSquared;
//`cartesian is required.` is thrown from scaleToGeodeticSurface
var p = scaleToGeodeticSurface(cartesian, oneOverRadii, oneOverRadiiSquared, centerToleranceSquared, cartesianToCartographicP);
if (!defined(p)) {
return undefined;
}
var n = Cartesian3.multiplyComponents(p, oneOverRadiiSquared, cartesianToCartographicN);
n = Cartesian3.normalize(n, n);
var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
var longitude = Math.atan2(n.y, n.x);
var latitude = Math.asin(n.z);
var height = CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Duplicates a Cartographic instance.
*
* @param {Cartographic} cartographic The cartographic to duplicate.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)
*/
Cartographic.clone = function(cartographic, result) {
if (!defined(cartographic)) {
return undefined;
}
if (!defined(result)) {
return new Cartographic(cartographic.longitude, cartographic.latitude, cartographic.height);
}
result.longitude = cartographic.longitude;
result.latitude = cartographic.latitude;
result.height = cartographic.height;
return result;
};
/**
* Compares the provided cartographics componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartographic.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.longitude === right.longitude) &&
(left.latitude === right.latitude) &&
(left.height === right.height));
};
/**
* Compares the provided cartographics componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartographic.equalsEpsilon = function(left, right, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon is required and must be a number.');
}
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(Math.abs(left.longitude - right.longitude) <= epsilon) &&
(Math.abs(left.latitude - right.latitude) <= epsilon) &&
(Math.abs(left.height - right.height) <= epsilon));
};
/**
* An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartographic}
* @constant
*/
Cartographic.ZERO = freezeObject(new Cartographic(0.0, 0.0, 0.0));
/**
* Duplicates this instance.
*
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.prototype.clone = function(result) {
return Cartographic.clone(this, result);
};
/**
* Compares the provided against this cartographic componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartographic.prototype.equals = function(right) {
return Cartographic.equals(this, right);
};
/**
* Compares the provided against this cartographic componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartographic.prototype.equalsEpsilon = function(right, epsilon) {
return Cartographic.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this cartographic in the format '(longitude, latitude, height)'.
*
* @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.
*/
Cartographic.prototype.toString = function() {
return '(' + this.longitude + ', ' + this.latitude + ', ' + this.height + ')';
};
return Cartographic;
});
/*global define*/
define('Core/defineProperties',[
'./defined'
], function(
defined) {
'use strict';
var definePropertyWorks = (function() {
try {
return 'x' in Object.defineProperty({}, 'x', {});
} catch (e) {
return false;
}
})();
/**
* Defines properties on an object, using Object.defineProperties if available,
* otherwise returns the object unchanged. This function should be used in
* setup code to prevent errors from completely halting JavaScript execution
* in legacy browsers.
*
* @private
*
* @exports defineProperties
*/
var defineProperties = Object.defineProperties;
if (!definePropertyWorks || !defined(defineProperties)) {
defineProperties = function(o) {
return o;
};
}
return defineProperties;
});
/*global define*/
define('Core/Ellipsoid',[
'./Cartesian3',
'./Cartographic',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./freezeObject',
'./Math',
'./scaleToGeodeticSurface'
], function(
Cartesian3,
Cartographic,
defaultValue,
defined,
defineProperties,
DeveloperError,
freezeObject,
CesiumMath,
scaleToGeodeticSurface) {
'use strict';
function initialize(ellipsoid, x, y, z) {
x = defaultValue(x, 0.0);
y = defaultValue(y, 0.0);
z = defaultValue(z, 0.0);
if (x < 0.0 || y < 0.0 || z < 0.0) {
throw new DeveloperError('All radii components must be greater than or equal to zero.');
}
ellipsoid._radii = new Cartesian3(x, y, z);
ellipsoid._radiiSquared = new Cartesian3(x * x,
y * y,
z * z);
ellipsoid._radiiToTheFourth = new Cartesian3(x * x * x * x,
y * y * y * y,
z * z * z * z);
ellipsoid._oneOverRadii = new Cartesian3(x === 0.0 ? 0.0 : 1.0 / x,
y === 0.0 ? 0.0 : 1.0 / y,
z === 0.0 ? 0.0 : 1.0 / z);
ellipsoid._oneOverRadiiSquared = new Cartesian3(x === 0.0 ? 0.0 : 1.0 / (x * x),
y === 0.0 ? 0.0 : 1.0 / (y * y),
z === 0.0 ? 0.0 : 1.0 / (z * z));
ellipsoid._minimumRadius = Math.min(x, y, z);
ellipsoid._maximumRadius = Math.max(x, y, z);
ellipsoid._centerToleranceSquared = CesiumMath.EPSILON1;
if (ellipsoid._radiiSquared.z !== 0) {
ellipsoid._sqauredXOverSquaredZ = ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
}
}
/**
* A quadratic surface defined in Cartesian coordinates by the equation
* (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used
* by Cesium to represent the shape of planetary bodies.
*
* Rather than constructing this object directly, one of the provided
* constants is normally used.
* @alias Ellipsoid
* @constructor
*
* @param {Number} [x=0] The radius in the x direction.
* @param {Number} [y=0] The radius in the y direction.
* @param {Number} [z=0] The radius in the z direction.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.fromCartesian3
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
function Ellipsoid(x, y, z) {
this._radii = undefined;
this._radiiSquared = undefined;
this._radiiToTheFourth = undefined;
this._oneOverRadii = undefined;
this._oneOverRadiiSquared = undefined;
this._minimumRadius = undefined;
this._maximumRadius = undefined;
this._centerToleranceSquared = undefined;
this._sqauredXOverSquaredZ = undefined;
initialize(this, x, y, z);
}
defineProperties(Ellipsoid.prototype, {
/**
* Gets the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radii : {
get: function() {
return this._radii;
}
},
/**
* Gets the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiSquared : {
get : function() {
return this._radiiSquared;
}
},
/**
* Gets the radii of the ellipsoid raise to the fourth power.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiToTheFourth : {
get : function() {
return this._radiiToTheFourth;
}
},
/**
* Gets one over the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadii : {
get : function() {
return this._oneOverRadii;
}
},
/**
* Gets one over the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadiiSquared : {
get : function() {
return this._oneOverRadiiSquared;
}
},
/**
* Gets the minimum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
minimumRadius : {
get : function() {
return this._minimumRadius;
}
},
/**
* Gets the maximum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
maximumRadius : {
get : function() {
return this._maximumRadius;
}
}
});
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
*/
Ellipsoid.clone = function(ellipsoid, result) {
if (!defined(ellipsoid)) {
return undefined;
}
var radii = ellipsoid._radii;
if (!defined(result)) {
return new Ellipsoid(radii.x, radii.y, radii.z);
}
Cartesian3.clone(radii, result._radii);
Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
result._minimumRadius = ellipsoid._minimumRadius;
result._maximumRadius = ellipsoid._maximumRadius;
result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
return result;
};
/**
* Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
*
* @param {Cartesian3} [radii=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
* @returns {Ellipsoid} A new Ellipsoid instance.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
Ellipsoid.fromCartesian3 = function(cartesian, result) {
if (!defined(result)) {
result = new Ellipsoid();
}
if (!defined(cartesian)) {
return result;
}
initialize(result, cartesian.x, cartesian.y, cartesian.z);
return result;
};
/**
* An Ellipsoid instance initialized to the WGS84 standard.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.WGS84 = freezeObject(new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793));
/**
* An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.UNIT_SPHERE = freezeObject(new Ellipsoid(1.0, 1.0, 1.0));
/**
* An Ellipsoid instance initialized to a sphere with the lunar radius.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.MOON = freezeObject(new Ellipsoid(CesiumMath.LUNAR_RADIUS, CesiumMath.LUNAR_RADIUS, CesiumMath.LUNAR_RADIUS));
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid.
*/
Ellipsoid.prototype.clone = function(result) {
return Ellipsoid.clone(this, result);
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Ellipsoid.packedLength = Cartesian3.packedLength;
/**
* Stores the provided instance into the provided array.
*
* @param {Ellipsoid} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Ellipsoid.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
Cartesian3.pack(value._radii, array, startingIndex);
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Ellipsoid} [result] The object into which to store the result.
* @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
*/
Ellipsoid.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
var radii = Cartesian3.unpack(array, startingIndex);
return Ellipsoid.fromCartesian3(radii, result);
};
/**
* Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
* @function
*
* @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function(cartographic, result) {
if (!defined(cartographic)) {
throw new DeveloperError('cartographic is required.');
}
var longitude = cartographic.longitude;
var latitude = cartographic.latitude;
var cosLatitude = Math.cos(latitude);
var x = cosLatitude * Math.cos(longitude);
var y = cosLatitude * Math.sin(longitude);
var z = Math.sin(latitude);
if (!defined(result)) {
result = new Cartesian3();
}
result.x = x;
result.y = y;
result.z = z;
return Cartesian3.normalize(result, result);
};
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geodeticSurfaceNormal = function(cartesian, result) {
if (!defined(result)) {
result = new Cartesian3();
}
result = Cartesian3.multiplyComponents(cartesian, this._oneOverRadiiSquared, result);
return Cartesian3.normalize(result, result);
};
var cartographicToCartesianNormal = new Cartesian3();
var cartographicToCartesianK = new Cartesian3();
/**
* Converts the provided cartographic to Cartesian representation.
*
* @param {Cartographic} cartographic The cartographic position.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*
* @example
* //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
* var position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
* var cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
*/
Ellipsoid.prototype.cartographicToCartesian = function(cartographic, result) {
//`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
var n = cartographicToCartesianNormal;
var k = cartographicToCartesianK;
this.geodeticSurfaceNormalCartographic(cartographic, n);
Cartesian3.multiplyComponents(this._radiiSquared, n, k);
var gamma = Math.sqrt(Cartesian3.dot(n, k));
Cartesian3.divideByScalar(k, gamma, k);
Cartesian3.multiplyByScalar(n, cartographic.height, n);
if (!defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(k, n, result);
};
/**
* Converts the provided array of cartographics to an array of Cartesians.
*
* @param {Cartographic[]} cartographics An array of cartographic positions.
* @param {Cartesian3[]} [result] The object onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
* var positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
* var cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
*/
Ellipsoid.prototype.cartographicArrayToCartesianArray = function(cartographics, result) {
if (!defined(cartographics)) {
throw new DeveloperError('cartographics is required.');
}
var length = cartographics.length;
if (!defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for ( var i = 0; i < length; i++) {
result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
}
return result;
};
var cartesianToCartographicN = new Cartesian3();
var cartesianToCartographicP = new Cartesian3();
var cartesianToCartographicH = new Cartesian3();
/**
* Converts the provided cartesian to cartographic representation.
* The cartesian is undefined at the center of the ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*
* @example
* //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
* var position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
* var cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
*/
Ellipsoid.prototype.cartesianToCartographic = function(cartesian, result) {
//`cartesian is required.` is thrown from scaleToGeodeticSurface
var p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
if (!defined(p)) {
return undefined;
}
var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
var longitude = Math.atan2(n.y, n.x);
var latitude = Math.asin(n.z);
var height = CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Converts the provided array of cartesians to an array of cartographics.
*
* @param {Cartesian3[]} cartesians An array of Cartesian positions.
* @param {Cartographic[]} [result] The object onto which to store the result.
* @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
* var positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
* new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
* new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
* var cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
*/
Ellipsoid.prototype.cartesianArrayToCartographicArray = function(cartesians, result) {
if (!defined(cartesians)) {
throw new DeveloperError('cartesians is required.');
}
var length = cartesians.length;
if (!defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for ( var i = 0; i < length; ++i) {
result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
}
return result;
};
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*/
Ellipsoid.prototype.scaleToGeodeticSurface = function(cartesian, result) {
return scaleToGeodeticSurface(cartesian, this._oneOverRadii, this._oneOverRadiiSquared, this._centerToleranceSquared, result);
};
/**
* Scales the provided Cartesian position along the geocentric surface normal
* so that it is on the surface of this ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.scaleToGeocentricSurface = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
if (!defined(result)) {
result = new Cartesian3();
}
var positionX = cartesian.x;
var positionY = cartesian.y;
var positionZ = cartesian.z;
var oneOverRadiiSquared = this._oneOverRadiiSquared;
var beta = 1.0 / Math.sqrt((positionX * positionX) * oneOverRadiiSquared.x +
(positionY * positionY) * oneOverRadiiSquared.y +
(positionZ * positionZ) * oneOverRadiiSquared.z);
return Cartesian3.multiplyByScalar(cartesian, beta, result);
};
/**
* Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#oneOverRadii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionToScaledSpace = function(position, result) {
if (!defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
};
/**
* Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#radii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionFromScaledSpace = function(position, result) {
if (!defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._radii, result);
};
/**
* Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Ellipsoid} [right] The other Ellipsoid.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Ellipsoid.prototype.equals = function(right) {
return (this === right) ||
(defined(right) &&
Cartesian3.equals(this._radii, right._radii));
};
/**
* Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*
* @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*/
Ellipsoid.prototype.toString = function() {
return this._radii.toString();
};
/**
* Computes a point which is the intersection of the surface normal with the z-axis.
*
* @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
* @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
* In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
* In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
* Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
* @param {Cartesian} [result] The cartesian to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
*
* @exception {DeveloperError} position is required.
* @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
* @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
*/
Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function(position, buffer, result) {
if (!defined(position)) {
throw new DeveloperError('position is required.');
}
if (!CesiumMath.equalsEpsilon(this._radii.x, this._radii.y, CesiumMath.EPSILON15)) {
throw new DeveloperError('Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)');
}
if (this._radii.z === 0) {
throw new DeveloperError('Ellipsoid.radii.z must be greater than 0');
}
buffer = defaultValue(buffer, 0.0);
var sqauredXOverSquaredZ = this._sqauredXOverSquaredZ;
if (!defined(result)) {
result = new Cartesian3();
}
result.x = 0.0;
result.y = 0.0;
result.z = position.z * (1 - sqauredXOverSquaredZ);
if (Math.abs(result.z) >= this._radii.z - buffer) {
return undefined;
}
return result;
};
return Ellipsoid;
});
/*global define*/
define('Core/Rectangle',[
'./Cartographic',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./Ellipsoid',
'./freezeObject',
'./Math'
], function(
Cartographic,
defaultValue,
defined,
defineProperties,
DeveloperError,
Ellipsoid,
freezeObject,
CesiumMath) {
'use strict';
/**
* A two dimensional region specified as longitude and latitude coordinates.
*
* @alias Rectangle
* @constructor
*
* @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].
* @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].
*
* @see Packable
*/
function Rectangle(west, south, east, north) {
/**
* The westernmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.west = defaultValue(west, 0.0);
/**
* The southernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.south = defaultValue(south, 0.0);
/**
* The easternmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.east = defaultValue(east, 0.0);
/**
* The northernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.north = defaultValue(north, 0.0);
}
defineProperties(Rectangle.prototype, {
/**
* Gets the width of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
*/
width : {
get : function() {
return Rectangle.computeWidth(this);
}
},
/**
* Gets the height of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
*/
height : {
get : function() {
return Rectangle.computeHeight(this);
}
}
});
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Rectangle.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Rectangle} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Rectangle.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.west;
array[startingIndex++] = value.south;
array[startingIndex++] = value.east;
array[startingIndex] = value.north;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Rectangle} [result] The object into which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Rectangle();
}
result.west = array[startingIndex++];
result.south = array[startingIndex++];
result.east = array[startingIndex++];
result.north = array[startingIndex];
return result;
};
/**
* Computes the width of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the width of.
* @returns {Number} The width.
*/
Rectangle.computeWidth = function(rectangle) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required.');
}
var east = rectangle.east;
var west = rectangle.west;
if (east < west) {
east += CesiumMath.TWO_PI;
}
return east - west;
};
/**
* Computes the height of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the height of.
* @returns {Number} The height.
*/
Rectangle.computeHeight = function(rectangle) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required.');
}
return rectangle.north - rectangle.south;
};
/**
* Creates an rectangle given the boundary longitude and latitude in degrees.
*
* @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*
* @example
* var rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);
*/
Rectangle.fromDegrees = function(west, south, east, north, result) {
west = CesiumMath.toRadians(defaultValue(west, 0.0));
south = CesiumMath.toRadians(defaultValue(south, 0.0));
east = CesiumMath.toRadians(defaultValue(east, 0.0));
north = CesiumMath.toRadians(defaultValue(north, 0.0));
if (!defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartographic[]} cartographics The list of Cartographic instances.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartographicArray = function(cartographics, result) {
if (!defined(cartographics)) {
throw new DeveloperError('cartographics is required.');
}
var west = Number.MAX_VALUE;
var east = -Number.MAX_VALUE;
var westOverIDL = Number.MAX_VALUE;
var eastOverIDL = -Number.MAX_VALUE;
var south = Number.MAX_VALUE;
var north = -Number.MAX_VALUE;
for ( var i = 0, len = cartographics.length; i < len; i++) {
var position = cartographics[i];
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
var lonAdjusted = position.longitude >= 0 ? position.longitude : position.longitude + CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if(east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > CesiumMath.PI) {
east = east - CesiumMath.TWO_PI;
}
if (west > CesiumMath.PI) {
west = west - CesiumMath.TWO_PI;
}
}
if (!defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartesian[]} cartesians The list of Cartesian instances.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartesianArray = function(cartesians, ellipsoid, result) {
if (!defined(cartesians)) {
throw new DeveloperError('cartesians is required.');
}
var west = Number.MAX_VALUE;
var east = -Number.MAX_VALUE;
var westOverIDL = Number.MAX_VALUE;
var eastOverIDL = -Number.MAX_VALUE;
var south = Number.MAX_VALUE;
var north = -Number.MAX_VALUE;
for ( var i = 0, len = cartesians.length; i < len; i++) {
var position = ellipsoid.cartesianToCartographic(cartesians[i]);
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
var lonAdjusted = position.longitude >= 0 ? position.longitude : position.longitude + CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if(east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > CesiumMath.PI) {
east = east - CesiumMath.TWO_PI;
}
if (west > CesiumMath.PI) {
west = west - CesiumMath.TWO_PI;
}
}
if (!defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Duplicates an Rectangle.
*
* @param {Rectangle} rectangle The rectangle to clone.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)
*/
Rectangle.clone = function(rectangle, result) {
if (!defined(rectangle)) {
return undefined;
}
if (!defined(result)) {
return new Rectangle(rectangle.west, rectangle.south, rectangle.east, rectangle.north);
}
result.west = rectangle.west;
result.south = rectangle.south;
result.east = rectangle.east;
result.north = rectangle.north;
return result;
};
/**
* Duplicates this Rectangle.
*
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.prototype.clone = function(result) {
return Rectangle.clone(this, result);
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @returns {Boolean} true if the Rectangles are equal, false otherwise.
*/
Rectangle.prototype.equals = function(other) {
return Rectangle.equals(this, other);
};
/**
* Compares the provided rectangles and returns true if they are equal,
* false otherwise.
*
* @param {Rectangle} [left] The first Rectangle.
* @param {Rectangle} [right] The second Rectangle.
* @returns {Boolean} true if left and right are equal; otherwise false.
*/
Rectangle.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.west === right.west) &&
(left.south === right.south) &&
(left.east === right.east) &&
(left.north === right.north));
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if the Rectangles are within the provided epsilon, false otherwise.
*/
Rectangle.prototype.equalsEpsilon = function(other, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon is required and must be a number.');
}
return defined(other) &&
(Math.abs(this.west - other.west) <= epsilon) &&
(Math.abs(this.south - other.south) <= epsilon) &&
(Math.abs(this.east - other.east) <= epsilon) &&
(Math.abs(this.north - other.north) <= epsilon);
};
/**
* Checks an Rectangle's properties and throws if they are not in valid ranges.
*
* @param {Rectangle} rectangle The rectangle to validate
*
* @exception {DeveloperError} north must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} south must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} east must be in the interval [-Pi, Pi].
* @exception {DeveloperError} west must be in the interval [-Pi, Pi].
*/
Rectangle.validate = function(rectangle) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
var north = rectangle.north;
if (typeof north !== 'number') {
throw new DeveloperError('north is required to be a number.');
}
if (north < -CesiumMath.PI_OVER_TWO || north > CesiumMath.PI_OVER_TWO) {
throw new DeveloperError('north must be in the interval [-Pi/2, Pi/2].');
}
var south = rectangle.south;
if (typeof south !== 'number') {
throw new DeveloperError('south is required to be a number.');
}
if (south < -CesiumMath.PI_OVER_TWO || south > CesiumMath.PI_OVER_TWO) {
throw new DeveloperError('south must be in the interval [-Pi/2, Pi/2].');
}
var west = rectangle.west;
if (typeof west !== 'number') {
throw new DeveloperError('west is required to be a number.');
}
if (west < -Math.PI || west > Math.PI) {
throw new DeveloperError('west must be in the interval [-Pi, Pi].');
}
var east = rectangle.east;
if (typeof east !== 'number') {
throw new DeveloperError('east is required to be a number.');
}
if (east < -Math.PI || east > Math.PI) {
throw new DeveloperError('east must be in the interval [-Pi, Pi].');
}
};
/**
* Computes the southwest corner of an rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southwest = function(rectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(result)) {
return new Cartographic(rectangle.west, rectangle.south);
}
result.longitude = rectangle.west;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the northwest corner of an rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northwest = function(rectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(result)) {
return new Cartographic(rectangle.west, rectangle.north);
}
result.longitude = rectangle.west;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the northeast corner of an rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northeast = function(rectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(result)) {
return new Cartographic(rectangle.east, rectangle.north);
}
result.longitude = rectangle.east;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the southeast corner of an rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southeast = function(rectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(result)) {
return new Cartographic(rectangle.east, rectangle.south);
}
result.longitude = rectangle.east;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the center of an rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the center
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.center = function(rectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
var east = rectangle.east;
var west = rectangle.west;
if (east < west) {
east += CesiumMath.TWO_PI;
}
var longitude = CesiumMath.negativePiToPi((west + east) * 0.5);
var latitude = (rectangle.south + rectangle.north) * 0.5;
if (!defined(result)) {
return new Cartographic(longitude, latitude);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = 0.0;
return result;
};
/**
* Computes the intersection of two rectangles. This function assumes that the rectangle's coordinates are
* latitude and longitude in radians and produces a correct intersection, taking into account the fact that
* the same angle can be represented with multiple values as well as the wrapping of longitude at the
* anti-meridian. For a simple intersection that ignores these factors and can be used with projected
* coordinates, see {@link Rectangle.simpleIntersection}.
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.intersection = function(rectangle, otherRectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(otherRectangle)) {
throw new DeveloperError('otherRectangle is required.');
}
var rectangleEast = rectangle.east;
var rectangleWest = rectangle.west;
var otherRectangleEast = otherRectangle.east;
var otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += CesiumMath.TWO_PI;
}
var west = CesiumMath.negativePiToPi(Math.max(rectangleWest, otherRectangleWest));
var east = CesiumMath.negativePiToPi(Math.min(rectangleEast, otherRectangleEast));
if ((rectangle.west < rectangle.east || otherRectangle.west < otherRectangle.east) && east <= west) {
return undefined;
}
var south = Math.max(rectangle.south, otherRectangle.south);
var north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north) {
return undefined;
}
if (!defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a simple intersection of two rectangles. Unlike {@link Rectangle.intersection}, this function
* does not attempt to put the angular coordinates into a consistent range or to account for crossing the
* anti-meridian. As such, it can be used for rectangles where the coordinates are not simply latitude
* and longitude (i.e. projected coordinates).
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.simpleIntersection = function(rectangle, otherRectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(otherRectangle)) {
throw new DeveloperError('otherRectangle is required.');
}
var west = Math.max(rectangle.west, otherRectangle.west);
var south = Math.max(rectangle.south, otherRectangle.south);
var east = Math.min(rectangle.east, otherRectangle.east);
var north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north || west >= east) {
return undefined;
}
if (!defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a rectangle that is the union of two rectangles.
*
* @param {Rectangle} rectangle A rectangle to enclose in rectangle.
* @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.union = function(rectangle, otherRectangle, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(otherRectangle)) {
throw new DeveloperError('otherRectangle is required.');
}
if (!defined(result)) {
result = new Rectangle();
}
var rectangleEast = rectangle.east;
var rectangleWest = rectangle.west;
var otherRectangleEast = otherRectangle.east;
var otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += CesiumMath.TWO_PI;
}
var west = CesiumMath.convertLongitudeRange(Math.min(rectangleWest, otherRectangleWest));
var east = CesiumMath.convertLongitudeRange(Math.max(rectangleEast, otherRectangleEast));
result.west = west;
result.south = Math.min(rectangle.south, otherRectangle.south);
result.east = east;
result.north = Math.max(rectangle.north, otherRectangle.north);
return result;
};
/**
* Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.
*
* @param {Rectangle} rectangle A rectangle to expand.
* @param {Cartographic} cartographic A cartographic to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.expand = function(rectangle, cartographic, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required.');
}
if (!defined(cartographic)) {
throw new DeveloperError('cartographic is required.');
}
if (!defined(result)) {
result = new Rectangle();
}
result.west = Math.min(rectangle.west, cartographic.longitude);
result.south = Math.min(rectangle.south, cartographic.latitude);
result.east = Math.max(rectangle.east, cartographic.longitude);
result.north = Math.max(rectangle.north, cartographic.latitude);
return result;
};
/**
* Returns true if the cartographic is on or inside the rectangle, false otherwise.
*
* @param {Rectangle} rectangle The rectangle
* @param {Cartographic} cartographic The cartographic to test.
* @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.
*/
Rectangle.contains = function(rectangle, cartographic) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
if (!defined(cartographic)) {
throw new DeveloperError('cartographic is required.');
}
var longitude = cartographic.longitude;
var latitude = cartographic.latitude;
var west = rectangle.west;
var east = rectangle.east;
if (east < west) {
east += CesiumMath.TWO_PI;
if (longitude < 0.0) {
longitude += CesiumMath.TWO_PI;
}
}
return (longitude > west || CesiumMath.equalsEpsilon(longitude, west, CesiumMath.EPSILON14)) &&
(longitude < east || CesiumMath.equalsEpsilon(longitude, east, CesiumMath.EPSILON14)) &&
latitude >= rectangle.south &&
latitude <= rectangle.north;
};
var subsampleLlaScratch = new Cartographic();
/**
* Samples an rectangle so that it includes a list of Cartesian points suitable for passing to
* {@link BoundingSphere#fromPoints}. Sampling is necessary to account
* for rectangles that cover the poles or cross the equator.
*
* @param {Rectangle} rectangle The rectangle to subsample.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use.
* @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid.
* @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided.
*/
Rectangle.subsample = function(rectangle, ellipsoid, surfaceHeight, result) {
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required');
}
ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
surfaceHeight = defaultValue(surfaceHeight, 0.0);
if (!defined(result)) {
result = [];
}
var length = 0;
var north = rectangle.north;
var south = rectangle.south;
var east = rectangle.east;
var west = rectangle.west;
var lla = subsampleLlaScratch;
lla.height = surfaceHeight;
lla.longitude = west;
lla.latitude = north;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.latitude = south;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
if (north < 0.0) {
lla.latitude = north;
} else if (south > 0.0) {
lla.latitude = south;
} else {
lla.latitude = 0.0;
}
for ( var i = 1; i < 8; ++i) {
lla.longitude = -Math.PI + i * CesiumMath.PI_OVER_TWO;
if (Rectangle.contains(rectangle, lla)) {
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
}
if (lla.latitude === 0.0) {
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
result.length = length;
return result;
};
/**
* The largest possible rectangle.
*
* @type {Rectangle}
* @constant
*/
Rectangle.MAX_VALUE = freezeObject(new Rectangle(-Math.PI, -CesiumMath.PI_OVER_TWO, Math.PI, CesiumMath.PI_OVER_TWO));
return Rectangle;
});
/*global define*/
define('Core/GeographicProjection',[
'./Cartesian3',
'./Cartographic',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./Ellipsoid'
], function(
Cartesian3,
Cartographic,
defaultValue,
defined,
defineProperties,
DeveloperError,
Ellipsoid) {
'use strict';
/**
* A simple map projection where longitude and latitude are linearly mapped to X and Y by multiplying
* them by the {@link Ellipsoid#maximumRadius}. This projection
* is commonly known as geographic, equirectangular, equidistant cylindrical, or plate carrée. It
* is also known as EPSG:4326.
*
* @alias GeographicProjection
* @constructor
*
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid.
*
* @see WebMercatorProjection
*/
function GeographicProjection(ellipsoid) {
this._ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
this._semimajorAxis = this._ellipsoid.maximumRadius;
this._oneOverSemimajorAxis = 1.0 / this._semimajorAxis;
}
defineProperties(GeographicProjection.prototype, {
/**
* Gets the {@link Ellipsoid}.
*
* @memberof GeographicProjection.prototype
*
* @type {Ellipsoid}
* @readonly
*/
ellipsoid : {
get : function() {
return this._ellipsoid;
}
}
});
/**
* Projects a set of {@link Cartographic} coordinates, in radians, to map coordinates, in meters.
* X and Y are the longitude and latitude, respectively, multiplied by the maximum radius of the
* ellipsoid. Z is the unmodified height.
*
* @param {Cartographic} cartographic The coordinates to project.
* @param {Cartesian3} [result] An instance into which to copy the result. If this parameter is
* undefined, a new instance is created and returned.
* @returns {Cartesian3} The projected coordinates. If the result parameter is not undefined, the
* coordinates are copied there and that instance is returned. Otherwise, a new instance is
* created and returned.
*/
GeographicProjection.prototype.project = function(cartographic, result) {
// Actually this is the special case of equidistant cylindrical called the plate carree
var semimajorAxis = this._semimajorAxis;
var x = cartographic.longitude * semimajorAxis;
var y = cartographic.latitude * semimajorAxis;
var z = cartographic.height;
if (!defined(result)) {
return new Cartesian3(x, y, z);
}
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Unprojects a set of projected {@link Cartesian3} coordinates, in meters, to {@link Cartographic}
* coordinates, in radians. Longitude and Latitude are the X and Y coordinates, respectively,
* divided by the maximum radius of the ellipsoid. Height is the unmodified Z coordinate.
*
* @param {Cartesian3} cartesian The Cartesian position to unproject with height (z) in meters.
* @param {Cartographic} [result] An instance into which to copy the result. If this parameter is
* undefined, a new instance is created and returned.
* @returns {Cartographic} The unprojected coordinates. If the result parameter is not undefined, the
* coordinates are copied there and that instance is returned. Otherwise, a new instance is
* created and returned.
*/
GeographicProjection.prototype.unproject = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
var oneOverEarthSemimajorAxis = this._oneOverSemimajorAxis;
var longitude = cartesian.x * oneOverEarthSemimajorAxis;
var latitude = cartesian.y * oneOverEarthSemimajorAxis;
var height = cartesian.z;
if (!defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
return GeographicProjection;
});
/*global define*/
define('Core/Intersect',[
'./freezeObject'
], function(
freezeObject) {
'use strict';
/**
* This enumerated type is used in determining where, relative to the frustum, an
* object is located. The object can either be fully contained within the frustum (INSIDE),
* partially inside the frustum and partially outside (INTERSECTING), or somwhere entirely
* outside of the frustum's 6 planes (OUTSIDE).
*
* @exports Intersect
*/
var Intersect = {
/**
* Represents that an object is not contained within the frustum.
*
* @type {Number}
* @constant
*/
OUTSIDE : -1,
/**
* Represents that an object intersects one of the frustum's planes.
*
* @type {Number}
* @constant
*/
INTERSECTING : 0,
/**
* Represents that an object is fully within the frustum.
*
* @type {Number}
* @constant
*/
INSIDE : 1
};
return freezeObject(Intersect);
});
/*global define*/
define('Core/Interval',[
'./defaultValue'
], function(
defaultValue) {
'use strict';
/**
* Represents the closed interval [start, stop].
* @alias Interval
* @constructor
*
* @param {Number} [start=0.0] The beginning of the interval.
* @param {Number} [stop=0.0] The end of the interval.
*/
function Interval(start, stop) {
/**
* The beginning of the interval.
* @type {Number}
* @default 0.0
*/
this.start = defaultValue(start, 0.0);
/**
* The end of the interval.
* @type {Number}
* @default 0.0
*/
this.stop = defaultValue(stop, 0.0);
}
return Interval;
});
/*global define*/
define('Core/Matrix3',[
'./Cartesian3',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./freezeObject',
'./Math'
], function(
Cartesian3,
defaultValue,
defined,
defineProperties,
DeveloperError,
freezeObject,
CesiumMath) {
'use strict';
/**
* A 3x3 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix3
* @constructor
*
* @param {Number} [column0Row0=0.0] The value for column 0, row 0.
* @param {Number} [column1Row0=0.0] The value for column 1, row 0.
* @param {Number} [column2Row0=0.0] The value for column 2, row 0.
* @param {Number} [column0Row1=0.0] The value for column 0, row 1.
* @param {Number} [column1Row1=0.0] The value for column 1, row 1.
* @param {Number} [column2Row1=0.0] The value for column 2, row 1.
* @param {Number} [column0Row2=0.0] The value for column 0, row 2.
* @param {Number} [column1Row2=0.0] The value for column 1, row 2.
* @param {Number} [column2Row2=0.0] The value for column 2, row 2.
*
* @see Matrix3.fromColumnMajorArray
* @see Matrix3.fromRowMajorArray
* @see Matrix3.fromQuaternion
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix2
* @see Matrix4
*/
function Matrix3(column0Row0, column1Row0, column2Row0,
column0Row1, column1Row1, column2Row1,
column0Row2, column1Row2, column2Row2) {
this[0] = defaultValue(column0Row0, 0.0);
this[1] = defaultValue(column0Row1, 0.0);
this[2] = defaultValue(column0Row2, 0.0);
this[3] = defaultValue(column1Row0, 0.0);
this[4] = defaultValue(column1Row1, 0.0);
this[5] = defaultValue(column1Row2, 0.0);
this[6] = defaultValue(column2Row0, 0.0);
this[7] = defaultValue(column2Row1, 0.0);
this[8] = defaultValue(column2Row2, 0.0);
}
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Matrix3.packedLength = 9;
/**
* Stores the provided instance into the provided array.
*
* @param {Matrix3} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Matrix3.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value[0];
array[startingIndex++] = value[1];
array[startingIndex++] = value[2];
array[startingIndex++] = value[3];
array[startingIndex++] = value[4];
array[startingIndex++] = value[5];
array[startingIndex++] = value[6];
array[startingIndex++] = value[7];
array[startingIndex++] = value[8];
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Matrix3} [result] The object into which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
Matrix3.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Matrix3();
}
result[0] = array[startingIndex++];
result[1] = array[startingIndex++];
result[2] = array[startingIndex++];
result[3] = array[startingIndex++];
result[4] = array[startingIndex++];
result[5] = array[startingIndex++];
result[6] = array[startingIndex++];
result[7] = array[startingIndex++];
result[8] = array[startingIndex++];
return result;
};
/**
* Duplicates a Matrix3 instance.
*
* @param {Matrix3} matrix The matrix to duplicate.
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
*/
Matrix3.clone = function(values, result) {
if (!defined(values)) {
return undefined;
}
if (!defined(result)) {
return new Matrix3(values[0], values[3], values[6],
values[1], values[4], values[7],
values[2], values[5], values[8]);
}
result[0] = values[0];
result[1] = values[1];
result[2] = values[2];
result[3] = values[3];
result[4] = values[4];
result[5] = values[5];
result[6] = values[6];
result[7] = values[7];
result[8] = values[8];
return result;
};
/**
* Creates a Matrix3 from 9 consecutive elements in an array.
*
* @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*
* @example
* // Create the Matrix3:
* // [1.0, 2.0, 3.0]
* // [1.0, 2.0, 3.0]
* // [1.0, 2.0, 3.0]
*
* var v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
* var m = Cesium.Matrix3.fromArray(v);
*
* // Create same Matrix3 with using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
* var m2 = Cesium.Matrix3.fromArray(v2, 2);
*/
Matrix3.fromArray = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Matrix3();
}
result[0] = array[startingIndex];
result[1] = array[startingIndex + 1];
result[2] = array[startingIndex + 2];
result[3] = array[startingIndex + 3];
result[4] = array[startingIndex + 4];
result[5] = array[startingIndex + 5];
result[6] = array[startingIndex + 6];
result[7] = array[startingIndex + 7];
result[8] = array[startingIndex + 8];
return result;
};
/**
* Creates a Matrix3 instance from a column-major order array.
*
* @param {Number[]} values The column-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
Matrix3.fromColumnMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values parameter is required');
}
return Matrix3.clone(values, result);
};
/**
* Creates a Matrix3 instance from a row-major order array.
* The resulting matrix will be in column-major order.
*
* @param {Number[]} values The row-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
Matrix3.fromRowMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values is required.');
}
if (!defined(result)) {
return new Matrix3(values[0], values[1], values[2],
values[3], values[4], values[5],
values[6], values[7], values[8]);
}
result[0] = values[0];
result[1] = values[3];
result[2] = values[6];
result[3] = values[1];
result[4] = values[4];
result[5] = values[7];
result[6] = values[2];
result[7] = values[5];
result[8] = values[8];
return result;
};
/**
* Computes a 3x3 rotation matrix from the provided quaternion.
*
* @param {Quaternion} quaternion the quaternion to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
*/
Matrix3.fromQuaternion = function(quaternion, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
var x2 = quaternion.x * quaternion.x;
var xy = quaternion.x * quaternion.y;
var xz = quaternion.x * quaternion.z;
var xw = quaternion.x * quaternion.w;
var y2 = quaternion.y * quaternion.y;
var yz = quaternion.y * quaternion.z;
var yw = quaternion.y * quaternion.w;
var z2 = quaternion.z * quaternion.z;
var zw = quaternion.z * quaternion.w;
var w2 = quaternion.w * quaternion.w;
var m00 = x2 - y2 - z2 + w2;
var m01 = 2.0 * (xy - zw);
var m02 = 2.0 * (xz + yw);
var m10 = 2.0 * (xy + zw);
var m11 = -x2 + y2 - z2 + w2;
var m12 = 2.0 * (yz - xw);
var m20 = 2.0 * (xz - yw);
var m21 = 2.0 * (yz + xw);
var m22 = -x2 - y2 + z2 + w2;
if (!defined(result)) {
return new Matrix3(m00, m01, m02,
m10, m11, m12,
m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
};
/**
* Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
*
* @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
*/
Matrix3.fromHeadingPitchRoll = function(headingPitchRoll, result) {
if (!defined(headingPitchRoll)) {
throw new DeveloperError('headingPitchRoll is required');
}
var cosTheta = Math.cos(-headingPitchRoll.pitch);
var cosPsi = Math.cos(-headingPitchRoll.heading);
var cosPhi = Math.cos(headingPitchRoll.roll);
var sinTheta = Math.sin(-headingPitchRoll.pitch);
var sinPsi = Math.sin(-headingPitchRoll.heading);
var sinPhi = Math.sin(headingPitchRoll.roll);
var m00 = cosTheta * cosPsi;
var m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
var m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
var m10 = cosTheta * sinPsi;
var m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
var m12 = -sinTheta * cosPhi + cosPhi * sinTheta * sinPsi;
var m20 = -sinTheta;
var m21 = sinPhi * cosTheta;
var m22 = cosPhi * cosTheta;
if (!defined(result)) {
return new Matrix3(m00, m01, m02,
m10, m11, m12,
m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
};
/**
* Computes a Matrix3 instance representing a non-uniform scale.
*
* @param {Cartesian3} scale The x, y, and z scale factors.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [7.0, 0.0, 0.0]
* // [0.0, 8.0, 0.0]
* // [0.0, 0.0, 9.0]
* var m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
*/
Matrix3.fromScale = function(scale, result) {
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix3(
scale.x, 0.0, 0.0,
0.0, scale.y, 0.0,
0.0, 0.0, scale.z);
}
result[0] = scale.x;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = scale.y;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = scale.z;
return result;
};
/**
* Computes a Matrix3 instance representing a uniform scale.
*
* @param {Number} scale The uniform scale factor.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [2.0, 0.0, 0.0]
* // [0.0, 2.0, 0.0]
* // [0.0, 0.0, 2.0]
* var m = Cesium.Matrix3.fromUniformScale(2.0);
*/
Matrix3.fromUniformScale = function(scale, result) {
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix3(
scale, 0.0, 0.0,
0.0, scale, 0.0,
0.0, 0.0, scale);
}
result[0] = scale;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = scale;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = scale;
return result;
};
/**
* Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
*
* @param {Cartesian3} the vector on the left hand side of the cross product operation.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [0.0, -9.0, 8.0]
* // [9.0, 0.0, -7.0]
* // [-8.0, 7.0, 0.0]
* var m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
*/
Matrix3.fromCrossProduct = function(vector, result) {
if (!defined(vector)) {
throw new DeveloperError('vector is required.');
}
if (!defined(result)) {
return new Matrix3(
0.0, -vector.z, vector.y,
vector.z, 0.0, -vector.x,
-vector.y, vector.x, 0.0);
}
result[0] = 0.0;
result[1] = vector.z;
result[2] = -vector.y;
result[3] = -vector.z;
result[4] = 0.0;
result[5] = vector.x;
result[6] = vector.y;
result[7] = -vector.x;
result[8] = 0.0;
return result;
};
/**
* Creates a rotation matrix around the x-axis.
*
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the x-axis.
* var p = new Cesium.Cartesian3(5, 6, 7);
* var m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
* var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
Matrix3.fromRotationX = function(angle, result) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
var cosAngle = Math.cos(angle);
var sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
1.0, 0.0, 0.0,
0.0, cosAngle, -sinAngle,
0.0, sinAngle, cosAngle);
}
result[0] = 1.0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = cosAngle;
result[5] = sinAngle;
result[6] = 0.0;
result[7] = -sinAngle;
result[8] = cosAngle;
return result;
};
/**
* Creates a rotation matrix around the y-axis.
*
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the y-axis.
* var p = new Cesium.Cartesian3(5, 6, 7);
* var m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
* var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
Matrix3.fromRotationY = function(angle, result) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
var cosAngle = Math.cos(angle);
var sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
cosAngle, 0.0, sinAngle,
0.0, 1.0, 0.0,
-sinAngle, 0.0, cosAngle);
}
result[0] = cosAngle;
result[1] = 0.0;
result[2] = -sinAngle;
result[3] = 0.0;
result[4] = 1.0;
result[5] = 0.0;
result[6] = sinAngle;
result[7] = 0.0;
result[8] = cosAngle;
return result;
};
/**
* Creates a rotation matrix around the z-axis.
*
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the z-axis.
* var p = new Cesium.Cartesian3(5, 6, 7);
* var m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
* var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
Matrix3.fromRotationZ = function(angle, result) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
var cosAngle = Math.cos(angle);
var sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
cosAngle, -sinAngle, 0.0,
sinAngle, cosAngle, 0.0,
0.0, 0.0, 1.0);
}
result[0] = cosAngle;
result[1] = sinAngle;
result[2] = 0.0;
result[3] = -sinAngle;
result[4] = cosAngle;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 1.0;
return result;
};
/**
* Creates an Array from the provided Matrix3 instance.
* The array will be in column-major order.
*
* @param {Matrix3} matrix The matrix to use..
* @param {Number[]} [result] The Array onto which to store the result.
* @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
*/
Matrix3.toArray = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
return [matrix[0], matrix[1], matrix[2], matrix[3], matrix[4], matrix[5], matrix[6], matrix[7], matrix[8]];
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
return result;
};
/**
* Computes the array index of the element at the provided row and column.
*
* @param {Number} row The zero-based index of the row.
* @param {Number} column The zero-based index of the column.
* @returns {Number} The index of the element at the provided row and column.
*
* @exception {DeveloperError} row must be 0, 1, or 2.
* @exception {DeveloperError} column must be 0, 1, or 2.
*
* @example
* var myMatrix = new Cesium.Matrix3();
* var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
* var column1Row0 = myMatrix[column1Row0Index]
* myMatrix[column1Row0Index] = 10.0;
*/
Matrix3.getElementIndex = function(column, row) {
if (typeof row !== 'number' || row < 0 || row > 2) {
throw new DeveloperError('row must be 0, 1, or 2.');
}
if (typeof column !== 'number' || column < 0 || column > 2) {
throw new DeveloperError('column must be 0, 1, or 2.');
}
return column * 3 + row;
};
/**
* Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
Matrix3.getColumn = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 2) {
throw new DeveloperError('index must be 0, 1, or 2.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var startIndex = index * 3;
var x = matrix[startIndex];
var y = matrix[startIndex + 1];
var z = matrix[startIndex + 2];
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
Matrix3.setColumn = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 2) {
throw new DeveloperError('index must be 0, 1, or 2.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix3.clone(matrix, result);
var startIndex = index * 3;
result[startIndex] = cartesian.x;
result[startIndex + 1] = cartesian.y;
result[startIndex + 2] = cartesian.z;
return result;
};
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
Matrix3.getRow = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 2) {
throw new DeveloperError('index must be 0, 1, or 2.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = matrix[index];
var y = matrix[index + 3];
var z = matrix[index + 6];
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
Matrix3.setRow = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 2) {
throw new DeveloperError('index must be 0, 1, or 2.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix3.clone(matrix, result);
result[index] = cartesian.x;
result[index + 3] = cartesian.y;
result[index + 6] = cartesian.z;
return result;
};
var scratchColumn = new Cartesian3();
/**
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Matrix3.getScale = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = Cartesian3.magnitude(Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
result.y = Cartesian3.magnitude(Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn));
result.z = Cartesian3.magnitude(Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn));
return result;
};
var scratchScale = new Cartesian3();
/**
* Computes the maximum scale assuming the matrix is an affine transformation.
* The maximum scale is the maximum length of the column vectors.
*
* @param {Matrix3} matrix The matrix.
* @returns {Number} The maximum scale.
*/
Matrix3.getMaximumScale = function(matrix) {
Matrix3.getScale(matrix, scratchScale);
return Cartesian3.maximumComponent(scratchScale);
};
/**
* Computes the product of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.multiply = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
var column0Row1 = left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
var column0Row2 = left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
var column1Row0 = left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
var column1Row1 = left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
var column1Row2 = left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
var column2Row0 = left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
var column2Row1 = left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
var column2Row2 = left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
};
/**
* Computes the sum of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] + right[0];
result[1] = left[1] + right[1];
result[2] = left[2] + right[2];
result[3] = left[3] + right[3];
result[4] = left[4] + right[4];
result[5] = left[5] + right[5];
result[6] = left[6] + right[6];
result[7] = left[7] + right[7];
result[8] = left[8] + right[8];
return result;
};
/**
* Computes the difference of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] - right[0];
result[1] = left[1] - right[1];
result[2] = left[2] - right[2];
result[3] = left[3] - right[3];
result[4] = left[4] - right[4];
result[5] = left[5] - right[5];
result[6] = left[6] - right[6];
result[7] = left[7] - right[7];
result[8] = left[8] - right[8];
return result;
};
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} cartesian The column.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Matrix3.multiplyByVector = function(matrix, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var vX = cartesian.x;
var vY = cartesian.y;
var vZ = cartesian.z;
var x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
var y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
var z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix3} matrix The matrix.
* @param {Number} scalar The number to multiply by.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.multiplyByScalar = function(matrix, scalar, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar must be a number');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
result[4] = matrix[4] * scalar;
result[5] = matrix[5] * scalar;
result[6] = matrix[6] * scalar;
result[7] = matrix[7] * scalar;
result[8] = matrix[8] * scalar;
return result;
};
/**
* Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
*
* @param {Matrix3} matrix The matrix on the left-hand side.
* @param {Cartesian3} scale The non-uniform scale on the right-hand side.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
* Cesium.Matrix3.multiplyByScale(m, scale, m);
*
* @see Matrix3.fromScale
* @see Matrix3.multiplyByUniformScale
*/
Matrix3.multiplyByScale = function(matrix, scale, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0] * scale.x;
result[1] = matrix[1] * scale.x;
result[2] = matrix[2] * scale.x;
result[3] = matrix[3] * scale.y;
result[4] = matrix[4] * scale.y;
result[5] = matrix[5] * scale.y;
result[6] = matrix[6] * scale.z;
result[7] = matrix[7] * scale.z;
result[8] = matrix[8] * scale.z;
return result;
};
/**
* Creates a negated copy of the provided matrix.
*
* @param {Matrix3} matrix The matrix to negate.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.negate = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
result[4] = -matrix[4];
result[5] = -matrix[5];
result[6] = -matrix[6];
result[7] = -matrix[7];
result[8] = -matrix[8];
return result;
};
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix3} matrix The matrix to transpose.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.transpose = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = matrix[0];
var column0Row1 = matrix[3];
var column0Row2 = matrix[6];
var column1Row0 = matrix[1];
var column1Row1 = matrix[4];
var column1Row2 = matrix[7];
var column2Row0 = matrix[2];
var column2Row1 = matrix[5];
var column2Row2 = matrix[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
};
function computeFrobeniusNorm(matrix) {
var norm = 0.0;
for (var i = 0; i < 9; ++i) {
var temp = matrix[i];
norm += temp * temp;
}
return Math.sqrt(norm);
}
var rowVal = [1, 0, 0];
var colVal = [2, 2, 1];
function offDiagonalFrobeniusNorm(matrix) {
// Computes the "off-diagonal" Frobenius norm.
// Assumes matrix is symmetric.
var norm = 0.0;
for (var i = 0; i < 3; ++i) {
var temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
norm += 2.0 * temp * temp;
}
return Math.sqrt(norm);
}
function shurDecomposition(matrix, result) {
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
// section 8.4.2 The 2by2 Symmetric Schur Decomposition.
//
// The routine takes a matrix, which is assumed to be symmetric, and
// finds the largest off-diagonal term, and then creates
// a matrix (result) which can be used to help reduce it
var tolerance = CesiumMath.EPSILON15;
var maxDiagonal = 0.0;
var rotAxis = 1;
// find pivot (rotAxis) based on max diagonal of matrix
for (var i = 0; i < 3; ++i) {
var temp = Math.abs(matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]);
if (temp > maxDiagonal) {
rotAxis = i;
maxDiagonal = temp;
}
}
var c = 1.0;
var s = 0.0;
var p = rowVal[rotAxis];
var q = colVal[rotAxis];
if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
var qq = matrix[Matrix3.getElementIndex(q, q)];
var pp = matrix[Matrix3.getElementIndex(p, p)];
var qp = matrix[Matrix3.getElementIndex(q, p)];
var tau = (qq - pp) / 2.0 / qp;
var t;
if (tau < 0.0) {
t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));
} else {
t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));
}
c = 1.0 / Math.sqrt(1.0 + t * t);
s = t * c;
}
result = Matrix3.clone(Matrix3.IDENTITY, result);
result[Matrix3.getElementIndex(p, p)] = result[Matrix3.getElementIndex(q, q)] = c;
result[Matrix3.getElementIndex(q, p)] = s;
result[Matrix3.getElementIndex(p, q)] = -s;
return result;
}
var jMatrix = new Matrix3();
var jMatrixTranspose = new Matrix3();
/**
* Computes the eigenvectors and eigenvalues of a symmetric matrix.
*
* Returns a diagonal matrix and unitary matrix such that:
* matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)
*
*
* The values along the diagonal of the diagonal matrix are the eigenvalues. The columns
* of the unitary matrix are the corresponding eigenvectors.
*
*
* @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
* @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
* @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
*
* @example
* var a = //... symetric matrix
* var result = {
* unitary : new Cesium.Matrix3(),
* diagonal : new Cesium.Matrix3()
* };
* Cesium.Matrix3.computeEigenDecomposition(a, result);
*
* var unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3());
* var b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3());
* Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a
*
* var lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue
* var v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector
* var c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v)
*/
Matrix3.computeEigenDecomposition = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
// section 8.4.3 The Classical Jacobi Algorithm
var tolerance = CesiumMath.EPSILON20;
var maxSweeps = 10;
var count = 0;
var sweep = 0;
if (!defined(result)) {
result = {};
}
var unitaryMatrix = result.unitary = Matrix3.clone(Matrix3.IDENTITY, result.unitary);
var diagMatrix = result.diagonal = Matrix3.clone(matrix, result.diagonal);
var epsilon = tolerance * computeFrobeniusNorm(diagMatrix);
while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) {
shurDecomposition(diagMatrix, jMatrix);
Matrix3.transpose(jMatrix, jMatrixTranspose);
Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);
Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);
Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);
if (++count > 2) {
++sweep;
count = 0;
}
}
return result;
};
/**
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
*
* @param {Matrix3} matrix The matrix with signed elements.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
Matrix3.abs = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = Math.abs(matrix[0]);
result[1] = Math.abs(matrix[1]);
result[2] = Math.abs(matrix[2]);
result[3] = Math.abs(matrix[3]);
result[4] = Math.abs(matrix[4]);
result[5] = Math.abs(matrix[5]);
result[6] = Math.abs(matrix[6]);
result[7] = Math.abs(matrix[7]);
result[8] = Math.abs(matrix[8]);
return result;
};
/**
* Computes the determinant of the provided matrix.
*
* @param {Matrix3} matrix The matrix to use.
* @returns {Number} The value of the determinant of the matrix.
*/
Matrix3.determinant = function(matrix) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
var m11 = matrix[0];
var m21 = matrix[3];
var m31 = matrix[6];
var m12 = matrix[1];
var m22 = matrix[4];
var m32 = matrix[7];
var m13 = matrix[2];
var m23 = matrix[5];
var m33 = matrix[8];
return m11 * (m22 * m33 - m23 * m32) + m12 * (m23 * m31 - m21 * m33) + m13 * (m21 * m32 - m22 * m31);
};
/**
* Computes the inverse of the provided matrix.
*
* @param {Matrix3} matrix The matrix to invert.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} matrix is not invertible.
*/
Matrix3.inverse = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var m11 = matrix[0];
var m21 = matrix[1];
var m31 = matrix[2];
var m12 = matrix[3];
var m22 = matrix[4];
var m32 = matrix[5];
var m13 = matrix[6];
var m23 = matrix[7];
var m33 = matrix[8];
var determinant = Matrix3.determinant(matrix);
if (Math.abs(determinant) <= CesiumMath.EPSILON15) {
throw new DeveloperError('matrix is not invertible');
}
result[0] = m22 * m33 - m23 * m32;
result[1] = m23 * m31 - m21 * m33;
result[2] = m21 * m32 - m22 * m31;
result[3] = m13 * m32 - m12 * m33;
result[4] = m11 * m33 - m13 * m31;
result[5] = m12 * m31 - m11 * m32;
result[6] = m12 * m23 - m13 * m22;
result[7] = m13 * m21 - m11 * m23;
result[8] = m11 * m22 - m12 * m21;
var scale = 1.0 / determinant;
return Matrix3.multiplyByScalar(result, scale, result);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Matrix3.equals = function(left, right) {
return (left === right) ||
(defined(left) &&
defined(right) &&
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[3] === right[3] &&
left[4] === right[4] &&
left[5] === right[5] &&
left[6] === right[6] &&
left[7] === right[7] &&
left[8] === right[8]);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Matrix3.equalsEpsilon = function(left, right, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon must be a number');
}
return (left === right) ||
(defined(left) &&
defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon &&
Math.abs(left[4] - right[4]) <= epsilon &&
Math.abs(left[5] - right[5]) <= epsilon &&
Math.abs(left[6] - right[6]) <= epsilon &&
Math.abs(left[7] - right[7]) <= epsilon &&
Math.abs(left[8] - right[8]) <= epsilon);
};
/**
* An immutable Matrix3 instance initialized to the identity matrix.
*
* @type {Matrix3}
* @constant
*/
Matrix3.IDENTITY = freezeObject(new Matrix3(1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0));
/**
* An immutable Matrix3 instance initialized to the zero matrix.
*
* @type {Matrix3}
* @constant
*/
Matrix3.ZERO = freezeObject(new Matrix3(0.0, 0.0, 0.0,
0.0, 0.0, 0.0,
0.0, 0.0, 0.0));
/**
* The index into Matrix3 for column 0, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW0 = 0;
/**
* The index into Matrix3 for column 0, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW1 = 1;
/**
* The index into Matrix3 for column 0, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW2 = 2;
/**
* The index into Matrix3 for column 1, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW0 = 3;
/**
* The index into Matrix3 for column 1, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW1 = 4;
/**
* The index into Matrix3 for column 1, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW2 = 5;
/**
* The index into Matrix3 for column 2, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW0 = 6;
/**
* The index into Matrix3 for column 2, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW1 = 7;
/**
* The index into Matrix3 for column 2, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW2 = 8;
defineProperties(Matrix3.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix3.prototype
*
* @type {Number}
*/
length : {
get : function() {
return Matrix3.packedLength;
}
}
});
/**
* Duplicates the provided Matrix3 instance.
*
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
Matrix3.prototype.clone = function(result) {
return Matrix3.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix3.prototype.equals = function(right) {
return Matrix3.equals(this, right);
};
/**
* @private
*/
Matrix3.equalsArray = function(matrix, array, offset) {
return matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3] &&
matrix[4] === array[offset + 4] &&
matrix[5] === array[offset + 5] &&
matrix[6] === array[offset + 6] &&
matrix[7] === array[offset + 7] &&
matrix[8] === array[offset + 8];
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix3.prototype.equalsEpsilon = function(right, epsilon) {
return Matrix3.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1, column2)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
*/
Matrix3.prototype.toString = function() {
return '(' + this[0] + ', ' + this[3] + ', ' + this[6] + ')\n' +
'(' + this[1] + ', ' + this[4] + ', ' + this[7] + ')\n' +
'(' + this[2] + ', ' + this[5] + ', ' + this[8] + ')';
};
return Matrix3;
});
/*global define*/
define('Core/Cartesian4',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./freezeObject',
'./Math'
], function(
defaultValue,
defined,
DeveloperError,
freezeObject,
CesiumMath) {
'use strict';
/**
* A 4D Cartesian point.
* @alias Cartesian4
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
* @param {Number} [w=0.0] The W component.
*
* @see Cartesian2
* @see Cartesian3
* @see Packable
*/
function Cartesian4(x, y, z, w) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = defaultValue(z, 0.0);
/**
* The W component.
* @type {Number}
* @default 0.0
*/
this.w = defaultValue(w, 0.0);
}
/**
* Creates a Cartesian4 instance from x, y, z and w coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Number} z The z coordinate.
* @param {Number} w The w coordinate.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.fromElements = function(x, y, z, w, result) {
if (!defined(result)) {
return new Cartesian4(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Creates a Cartesian4 instance from a {@link Color}. red, green, blue,
* and alpha map to x, y, z, and w, respectively.
*
* @param {Color} color The source color.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.fromColor = function(color, result) {
if (!defined(color)) {
throw new DeveloperError('color is required');
}
if (!defined(result)) {
return new Cartesian4(color.red, color.green, color.blue, color.alpha);
}
result.x = color.red;
result.y = color.green;
result.z = color.blue;
result.w = color.alpha;
return result;
};
/**
* Duplicates a Cartesian4 instance.
*
* @param {Cartesian4} cartesian The Cartesian to duplicate.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian4.clone = function(cartesian, result) {
if (!defined(cartesian)) {
return undefined;
}
if (!defined(result)) {
return new Cartesian4(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
}
result.x = cartesian.x;
result.y = cartesian.y;
result.z = cartesian.z;
result.w = cartesian.w;
return result;
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian4.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian4} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian4.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex++] = value.z;
array[startingIndex] = value.w;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian4} [result] The object into which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Cartesian4();
}
result.x = array[startingIndex++];
result.y = array[startingIndex++];
result.z = array[startingIndex++];
result.w = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian4s into and array of components.
*
* @param {Cartesian4[]} array The array of cartesians to pack.
* @param {Number[]} result The array onto which to store the result.
* @returns {Number[]} The packed array.
*/
Cartesian4.packArray = function(array, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
var length = array.length;
if (!defined(result)) {
result = new Array(length * 4);
} else {
result.length = length * 4;
}
for (var i = 0; i < length; ++i) {
Cartesian4.pack(array[i], result, i * 4);
}
return result;
};
/**
* Unpacks an array of cartesian components into and array of Cartesian4s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian4[]} result The array onto which to store the result.
* @returns {Cartesian4[]} The unpacked array.
*/
Cartesian4.unpackArray = function(array, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
var length = array.length;
if (!defined(result)) {
result = new Array(length / 4);
} else {
result.length = length / 4;
}
for (var i = 0; i < length; i += 4) {
var index = i / 4;
result[index] = Cartesian4.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian4 from four consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose four consecutive elements correspond to the x, y, z, and w components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*
* @example
* // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0)
* var v = [1.0, 2.0, 3.0, 4.0];
* var p = Cesium.Cartesian4.fromArray(v);
*
* // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0) using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 2.0, 3.0, 4.0];
* var p2 = Cesium.Cartesian4.fromArray(v2, 2);
*/
Cartesian4.fromArray = Cartesian4.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian4} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian4.maximumComponent = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return Math.max(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian4} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian4.minimumComponent = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return Math.min(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian4} first A cartesian to compare.
* @param {Cartesian4} second A cartesian to compare.
* @param {Cartesian4} result The object into which to store the result.
* @returns {Cartesian4} A cartesian with the minimum components.
*/
Cartesian4.minimumByComponent = function(first, second, result) {
if (!defined(first)) {
throw new DeveloperError('first is required.');
}
if (!defined(second)) {
throw new DeveloperError('second is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
result.z = Math.min(first.z, second.z);
result.w = Math.min(first.w, second.w);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian4} first A cartesian to compare.
* @param {Cartesian4} second A cartesian to compare.
* @param {Cartesian4} result The object into which to store the result.
* @returns {Cartesian4} A cartesian with the maximum components.
*/
Cartesian4.maximumByComponent = function(first, second, result) {
if (!defined(first)) {
throw new DeveloperError('first is required.');
}
if (!defined(second)) {
throw new DeveloperError('second is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
result.z = Math.max(first.z, second.z);
result.w = Math.max(first.w, second.w);
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian4} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian4.magnitudeSquared = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return cartesian.x * cartesian.x + cartesian.y * cartesian.y + cartesian.z * cartesian.z + cartesian.w * cartesian.w;
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian4} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian4.magnitude = function(cartesian) {
return Math.sqrt(Cartesian4.magnitudeSquared(cartesian));
};
var distanceScratch = new Cartesian4();
/**
* Computes the 4-space distance between two points.
*
* @param {Cartesian4} left The first point to compute the distance from.
* @param {Cartesian4} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* var d = Cesium.Cartesian4.distance(
* new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
* new Cesium.Cartesian4(2.0, 0.0, 0.0, 0.0));
*/
Cartesian4.distance = function(left, right) {
if (!defined(left) || !defined(right)) {
throw new DeveloperError('left and right are required.');
}
Cartesian4.subtract(left, right, distanceScratch);
return Cartesian4.magnitude(distanceScratch);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian4#distance}.
*
* @param {Cartesian4} left The first point to compute the distance from.
* @param {Cartesian4} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* var d = Cesium.Cartesian4.distance(
* new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
* new Cesium.Cartesian4(3.0, 0.0, 0.0, 0.0));
*/
Cartesian4.distanceSquared = function(left, right) {
if (!defined(left) || !defined(right)) {
throw new DeveloperError('left and right are required.');
}
Cartesian4.subtract(left, right, distanceScratch);
return Cartesian4.magnitudeSquared(distanceScratch);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian to be normalized.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.normalize = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var magnitude = Cartesian4.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
result.z = cartesian.z / magnitude;
result.w = cartesian.w / magnitude;
if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z) || isNaN(result.w)) {
throw new DeveloperError('normalized result is not a number');
}
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian4.dot = function(left, right) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
return left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.multiplyComponents = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x * right.x;
result.y = left.y * right.y;
result.z = left.z * right.z;
result.w = left.w * right.w;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.divideComponents = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x / right.x;
result.y = left.y / right.y;
result.z = left.z / right.z;
result.w = left.w / right.w;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
result.w = left.w + right.w;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
result.w = left.w - right.w;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian4} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.multiplyByScalar = function(cartesian, scalar, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
result.z = cartesian.z * scalar;
result.w = cartesian.w * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian4} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.divideByScalar = function(cartesian, scalar, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
result.z = cartesian.z / scalar;
result.w = cartesian.w / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian to be negated.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.negate = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = -cartesian.x;
result.y = -cartesian.y;
result.z = -cartesian.z;
result.w = -cartesian.w;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.abs = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
result.z = Math.abs(cartesian.z);
result.w = Math.abs(cartesian.w);
return result;
};
var lerpScratch = new Cartesian4();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian4} start The value corresponding to t at 0.0.
* @param {Cartesian4}end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.lerp = function(start, end, t, result) {
if (!defined(start)) {
throw new DeveloperError('start is required.');
}
if (!defined(end)) {
throw new DeveloperError('end is required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
Cartesian4.multiplyByScalar(end, t, lerpScratch);
result = Cartesian4.multiplyByScalar(start, 1.0 - t, result);
return Cartesian4.add(lerpScratch, result, result);
};
var mostOrthogonalAxisScratch = new Cartesian4();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The most orthogonal axis.
*/
Cartesian4.mostOrthogonalAxis = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
var f = Cartesian4.normalize(cartesian, mostOrthogonalAxisScratch);
Cartesian4.abs(f, f);
if (f.x <= f.y) {
if (f.x <= f.z) {
if (f.x <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_X, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.z <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.y <= f.z) {
if (f.y <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Y, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.z <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian4} [left] The first Cartesian.
* @param {Cartesian4} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian4.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.x === right.x) &&
(left.y === right.y) &&
(left.z === right.z) &&
(left.w === right.w));
};
/**
* @private
*/
Cartesian4.equalsArray = function(cartesian, array, offset) {
return cartesian.x === array[offset] &&
cartesian.y === array[offset + 1] &&
cartesian.z === array[offset + 2] &&
cartesian.w === array[offset + 3];
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian4} [left] The first Cartesian.
* @param {Cartesian4} [right] The second Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian4.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
return (left === right) ||
(defined(left) &&
defined(right) &&
CesiumMath.equalsEpsilon(left.x, right.x, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.y, right.y, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.z, right.z, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.w, right.w, relativeEpsilon, absoluteEpsilon));
};
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.ZERO = freezeObject(new Cartesian4(0.0, 0.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (1.0, 0.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_X = freezeObject(new Cartesian4(1.0, 0.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 1.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_Y = freezeObject(new Cartesian4(0.0, 1.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 1.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_Z = freezeObject(new Cartesian4(0.0, 0.0, 1.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 1.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_W = freezeObject(new Cartesian4(0.0, 0.0, 0.0, 1.0));
/**
* Duplicates this Cartesian4 instance.
*
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.prototype.clone = function(result) {
return Cartesian4.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian4} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian4.prototype.equals = function(right) {
return Cartesian4.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian4} [right] The right hand side Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian4.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
return Cartesian4.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
};
/**
* Creates a string representing this Cartesian in the format '(x, y)'.
*
* @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
*/
Cartesian4.prototype.toString = function() {
return '(' + this.x + ', ' + this.y + ', ' + this.z + ', ' + this.w + ')';
};
return Cartesian4;
});
/*global define*/
define('Core/RuntimeError',[
'./defined'
], function(
defined) {
'use strict';
/**
* Constructs an exception object that is thrown due to an error that can occur at runtime, e.g.,
* out of memory, could not compile shader, etc. If a function may throw this
* exception, the calling code should be prepared to catch it.
*
* On the other hand, a {@link DeveloperError} indicates an exception due
* to a developer error, e.g., invalid argument, that usually indicates a bug in the
* calling code.
*
* @alias RuntimeError
* @constructor
* @extends Error
*
* @param {String} [message] The error message for this exception.
*
* @see DeveloperError
*/
function RuntimeError(message) {
/**
* 'RuntimeError' indicating that this exception was thrown due to a runtime error.
* @type {String}
* @readonly
*/
this.name = 'RuntimeError';
/**
* The explanation for why this exception was thrown.
* @type {String}
* @readonly
*/
this.message = message;
//Browsers such as IE don't have a stack property until you actually throw the error.
var stack;
try {
throw new Error();
} catch (e) {
stack = e.stack;
}
/**
* The stack trace of this exception, if available.
* @type {String}
* @readonly
*/
this.stack = stack;
}
if (defined(Object.create)) {
RuntimeError.prototype = Object.create(Error.prototype);
RuntimeError.prototype.constructor = RuntimeError;
}
RuntimeError.prototype.toString = function() {
var str = this.name + ': ' + this.message;
if (defined(this.stack)) {
str += '\n' + this.stack.toString();
}
return str;
};
return RuntimeError;
});
/*global define*/
define('Core/Matrix4',[
'./Cartesian3',
'./Cartesian4',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./freezeObject',
'./Math',
'./Matrix3',
'./RuntimeError'
], function(
Cartesian3,
Cartesian4,
defaultValue,
defined,
defineProperties,
DeveloperError,
freezeObject,
CesiumMath,
Matrix3,
RuntimeError) {
'use strict';
/**
* A 4x4 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix4
* @constructor
*
* @param {Number} [column0Row0=0.0] The value for column 0, row 0.
* @param {Number} [column1Row0=0.0] The value for column 1, row 0.
* @param {Number} [column2Row0=0.0] The value for column 2, row 0.
* @param {Number} [column3Row0=0.0] The value for column 3, row 0.
* @param {Number} [column0Row1=0.0] The value for column 0, row 1.
* @param {Number} [column1Row1=0.0] The value for column 1, row 1.
* @param {Number} [column2Row1=0.0] The value for column 2, row 1.
* @param {Number} [column3Row1=0.0] The value for column 3, row 1.
* @param {Number} [column0Row2=0.0] The value for column 0, row 2.
* @param {Number} [column1Row2=0.0] The value for column 1, row 2.
* @param {Number} [column2Row2=0.0] The value for column 2, row 2.
* @param {Number} [column3Row2=0.0] The value for column 3, row 2.
* @param {Number} [column0Row3=0.0] The value for column 0, row 3.
* @param {Number} [column1Row3=0.0] The value for column 1, row 3.
* @param {Number} [column2Row3=0.0] The value for column 2, row 3.
* @param {Number} [column3Row3=0.0] The value for column 3, row 3.
*
* @see Matrix4.fromColumnMajorArray
* @see Matrix4.fromRowMajorArray
* @see Matrix4.fromRotationTranslation
* @see Matrix4.fromTranslationRotationScale
* @see Matrix4.fromTranslationQuaternionRotationScale
* @see Matrix4.fromTranslation
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.fromCamera
* @see Matrix4.computePerspectiveFieldOfView
* @see Matrix4.computeOrthographicOffCenter
* @see Matrix4.computePerspectiveOffCenter
* @see Matrix4.computeInfinitePerspectiveOffCenter
* @see Matrix4.computeViewportTransformation
* @see Matrix4.computeView
* @see Matrix2
* @see Matrix3
* @see Packable
*/
function Matrix4(column0Row0, column1Row0, column2Row0, column3Row0,
column0Row1, column1Row1, column2Row1, column3Row1,
column0Row2, column1Row2, column2Row2, column3Row2,
column0Row3, column1Row3, column2Row3, column3Row3) {
this[0] = defaultValue(column0Row0, 0.0);
this[1] = defaultValue(column0Row1, 0.0);
this[2] = defaultValue(column0Row2, 0.0);
this[3] = defaultValue(column0Row3, 0.0);
this[4] = defaultValue(column1Row0, 0.0);
this[5] = defaultValue(column1Row1, 0.0);
this[6] = defaultValue(column1Row2, 0.0);
this[7] = defaultValue(column1Row3, 0.0);
this[8] = defaultValue(column2Row0, 0.0);
this[9] = defaultValue(column2Row1, 0.0);
this[10] = defaultValue(column2Row2, 0.0);
this[11] = defaultValue(column2Row3, 0.0);
this[12] = defaultValue(column3Row0, 0.0);
this[13] = defaultValue(column3Row1, 0.0);
this[14] = defaultValue(column3Row2, 0.0);
this[15] = defaultValue(column3Row3, 0.0);
}
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Matrix4.packedLength = 16;
/**
* Stores the provided instance into the provided array.
*
* @param {Matrix4} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Matrix4.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value[0];
array[startingIndex++] = value[1];
array[startingIndex++] = value[2];
array[startingIndex++] = value[3];
array[startingIndex++] = value[4];
array[startingIndex++] = value[5];
array[startingIndex++] = value[6];
array[startingIndex++] = value[7];
array[startingIndex++] = value[8];
array[startingIndex++] = value[9];
array[startingIndex++] = value[10];
array[startingIndex++] = value[11];
array[startingIndex++] = value[12];
array[startingIndex++] = value[13];
array[startingIndex++] = value[14];
array[startingIndex] = value[15];
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Matrix4} [result] The object into which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
*/
Matrix4.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Matrix4();
}
result[0] = array[startingIndex++];
result[1] = array[startingIndex++];
result[2] = array[startingIndex++];
result[3] = array[startingIndex++];
result[4] = array[startingIndex++];
result[5] = array[startingIndex++];
result[6] = array[startingIndex++];
result[7] = array[startingIndex++];
result[8] = array[startingIndex++];
result[9] = array[startingIndex++];
result[10] = array[startingIndex++];
result[11] = array[startingIndex++];
result[12] = array[startingIndex++];
result[13] = array[startingIndex++];
result[14] = array[startingIndex++];
result[15] = array[startingIndex];
return result;
};
/**
* Duplicates a Matrix4 instance.
*
* @param {Matrix4} matrix The matrix to duplicate.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided. (Returns undefined if matrix is undefined)
*/
Matrix4.clone = function(matrix, result) {
if (!defined(matrix)) {
return undefined;
}
if (!defined(result)) {
return new Matrix4(matrix[0], matrix[4], matrix[8], matrix[12],
matrix[1], matrix[5], matrix[9], matrix[13],
matrix[2], matrix[6], matrix[10], matrix[14],
matrix[3], matrix[7], matrix[11], matrix[15]);
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
result[9] = matrix[9];
result[10] = matrix[10];
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Creates a Matrix4 from 16 consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose 16 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
*
* @example
* // Create the Matrix4:
* // [1.0, 2.0, 3.0, 4.0]
* // [1.0, 2.0, 3.0, 4.0]
* // [1.0, 2.0, 3.0, 4.0]
* // [1.0, 2.0, 3.0, 4.0]
*
* var v = [1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
* var m = Cesium.Matrix4.fromArray(v);
*
* // Create same Matrix4 with using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
* var m2 = Cesium.Matrix4.fromArray(v2, 2);
*/
Matrix4.fromArray = Matrix4.unpack;
/**
* Computes a Matrix4 instance from a column-major order array.
*
* @param {Number[]} values The column-major order array.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*/
Matrix4.fromColumnMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values is required');
}
return Matrix4.clone(values, result);
};
/**
* Computes a Matrix4 instance from a row-major order array.
* The resulting matrix will be in column-major order.
*
* @param {Number[]} values The row-major order array.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*/
Matrix4.fromRowMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values is required.');
}
if (!defined(result)) {
return new Matrix4(values[0], values[1], values[2], values[3],
values[4], values[5], values[6], values[7],
values[8], values[9], values[10], values[11],
values[12], values[13], values[14], values[15]);
}
result[0] = values[0];
result[1] = values[4];
result[2] = values[8];
result[3] = values[12];
result[4] = values[1];
result[5] = values[5];
result[6] = values[9];
result[7] = values[13];
result[8] = values[2];
result[9] = values[6];
result[10] = values[10];
result[11] = values[14];
result[12] = values[3];
result[13] = values[7];
result[14] = values[11];
result[15] = values[15];
return result;
};
/**
* Computes a Matrix4 instance from a Matrix3 representing the rotation
* and a Cartesian3 representing the translation.
*
* @param {Matrix3} rotation The upper left portion of the matrix representing the rotation.
* @param {Cartesian3} [translation=Cartesian3.ZERO] The upper right portion of the matrix representing the translation.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*/
Matrix4.fromRotationTranslation = function(rotation, translation, result) {
if (!defined(rotation)) {
throw new DeveloperError('rotation is required.');
}
translation = defaultValue(translation, Cartesian3.ZERO);
if (!defined(result)) {
return new Matrix4(rotation[0], rotation[3], rotation[6], translation.x,
rotation[1], rotation[4], rotation[7], translation.y,
rotation[2], rotation[5], rotation[8], translation.z,
0.0, 0.0, 0.0, 1.0);
}
result[0] = rotation[0];
result[1] = rotation[1];
result[2] = rotation[2];
result[3] = 0.0;
result[4] = rotation[3];
result[5] = rotation[4];
result[6] = rotation[5];
result[7] = 0.0;
result[8] = rotation[6];
result[9] = rotation[7];
result[10] = rotation[8];
result[11] = 0.0;
result[12] = translation.x;
result[13] = translation.y;
result[14] = translation.z;
result[15] = 1.0;
return result;
};
/**
* Computes a Matrix4 instance from a translation, rotation, and scale (TRS)
* representation with the rotation represented as a quaternion.
*
* @param {Cartesian3} translation The translation transformation.
* @param {Quaternion} rotation The rotation transformation.
* @param {Cartesian3} scale The non-uniform scale transformation.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*
* @example
* var result = Cesium.Matrix4.fromTranslationQuaternionRotationScale(
* new Cesium.Cartesian3(1.0, 2.0, 3.0), // translation
* Cesium.Quaternion.IDENTITY, // rotation
* new Cesium.Cartesian3(7.0, 8.0, 9.0), // scale
* result);
*/
Matrix4.fromTranslationQuaternionRotationScale = function(translation, rotation, scale, result) {
if (!defined(translation)) {
throw new DeveloperError('translation is required.');
}
if (!defined(rotation)) {
throw new DeveloperError('rotation is required.');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
result = new Matrix4();
}
var scaleX = scale.x;
var scaleY = scale.y;
var scaleZ = scale.z;
var x2 = rotation.x * rotation.x;
var xy = rotation.x * rotation.y;
var xz = rotation.x * rotation.z;
var xw = rotation.x * rotation.w;
var y2 = rotation.y * rotation.y;
var yz = rotation.y * rotation.z;
var yw = rotation.y * rotation.w;
var z2 = rotation.z * rotation.z;
var zw = rotation.z * rotation.w;
var w2 = rotation.w * rotation.w;
var m00 = x2 - y2 - z2 + w2;
var m01 = 2.0 * (xy - zw);
var m02 = 2.0 * (xz + yw);
var m10 = 2.0 * (xy + zw);
var m11 = -x2 + y2 - z2 + w2;
var m12 = 2.0 * (yz - xw);
var m20 = 2.0 * (xz - yw);
var m21 = 2.0 * (yz + xw);
var m22 = -x2 - y2 + z2 + w2;
result[0] = m00 * scaleX;
result[1] = m10 * scaleX;
result[2] = m20 * scaleX;
result[3] = 0.0;
result[4] = m01 * scaleY;
result[5] = m11 * scaleY;
result[6] = m21 * scaleY;
result[7] = 0.0;
result[8] = m02 * scaleZ;
result[9] = m12 * scaleZ;
result[10] = m22 * scaleZ;
result[11] = 0.0;
result[12] = translation.x;
result[13] = translation.y;
result[14] = translation.z;
result[15] = 1.0;
return result;
};
/**
* Creates a Matrix4 instance from a {@link TranslationRotationScale} instance.
*
* @param {TranslationRotationScale} translationRotationScale The instance.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*/
Matrix4.fromTranslationRotationScale = function(translationRotationScale, result) {
if (!defined(translationRotationScale)) {
throw new DeveloperError('translationRotationScale is required.');
}
return Matrix4.fromTranslationQuaternionRotationScale(translationRotationScale.translation, translationRotationScale.rotation, translationRotationScale.scale, result);
};
/**
* Creates a Matrix4 instance from a Cartesian3 representing the translation.
*
* @param {Cartesian3} translation The upper right portion of the matrix representing the translation.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*
* @see Matrix4.multiplyByTranslation
*/
Matrix4.fromTranslation = function(translation, result) {
if (!defined(translation)) {
throw new DeveloperError('translation is required.');
}
return Matrix4.fromRotationTranslation(Matrix3.IDENTITY, translation, result);
};
/**
* Computes a Matrix4 instance representing a non-uniform scale.
*
* @param {Cartesian3} scale The x, y, and z scale factors.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*
* @example
* // Creates
* // [7.0, 0.0, 0.0, 0.0]
* // [0.0, 8.0, 0.0, 0.0]
* // [0.0, 0.0, 9.0, 0.0]
* // [0.0, 0.0, 0.0, 1.0]
* var m = Cesium.Matrix4.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
*/
Matrix4.fromScale = function(scale, result) {
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix4(
scale.x, 0.0, 0.0, 0.0,
0.0, scale.y, 0.0, 0.0,
0.0, 0.0, scale.z, 0.0,
0.0, 0.0, 0.0, 1.0);
}
result[0] = scale.x;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = scale.y;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = scale.z;
result[11] = 0.0;
result[12] = 0.0;
result[13] = 0.0;
result[14] = 0.0;
result[15] = 1.0;
return result;
};
/**
* Computes a Matrix4 instance representing a uniform scale.
*
* @param {Number} scale The uniform scale factor.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*
* @example
* // Creates
* // [2.0, 0.0, 0.0, 0.0]
* // [0.0, 2.0, 0.0, 0.0]
* // [0.0, 0.0, 2.0, 0.0]
* // [0.0, 0.0, 0.0, 1.0]
* var m = Cesium.Matrix4.fromUniformScale(2.0);
*/
Matrix4.fromUniformScale = function(scale, result) {
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix4(scale, 0.0, 0.0, 0.0,
0.0, scale, 0.0, 0.0,
0.0, 0.0, scale, 0.0,
0.0, 0.0, 0.0, 1.0);
}
result[0] = scale;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = scale;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = scale;
result[11] = 0.0;
result[12] = 0.0;
result[13] = 0.0;
result[14] = 0.0;
result[15] = 1.0;
return result;
};
var fromCameraF = new Cartesian3();
var fromCameraR = new Cartesian3();
var fromCameraU = new Cartesian3();
/**
* Computes a Matrix4 instance from a Camera.
*
* @param {Camera} camera The camera to use.
* @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
*/
Matrix4.fromCamera = function(camera, result) {
if (!defined(camera)) {
throw new DeveloperError('camera is required.');
}
var position = camera.position;
var direction = camera.direction;
var up = camera.up;
if (!defined(position)) {
throw new DeveloperError('camera.position is required.');
}
if (!defined(direction)) {
throw new DeveloperError('camera.direction is required.');
}
if (!defined(up)) {
throw new DeveloperError('camera.up is required.');
}
Cartesian3.normalize(direction, fromCameraF);
Cartesian3.normalize(Cartesian3.cross(fromCameraF, up, fromCameraR), fromCameraR);
Cartesian3.normalize(Cartesian3.cross(fromCameraR, fromCameraF, fromCameraU), fromCameraU);
var sX = fromCameraR.x;
var sY = fromCameraR.y;
var sZ = fromCameraR.z;
var fX = fromCameraF.x;
var fY = fromCameraF.y;
var fZ = fromCameraF.z;
var uX = fromCameraU.x;
var uY = fromCameraU.y;
var uZ = fromCameraU.z;
var positionX = position.x;
var positionY = position.y;
var positionZ = position.z;
var t0 = sX * -positionX + sY * -positionY+ sZ * -positionZ;
var t1 = uX * -positionX + uY * -positionY+ uZ * -positionZ;
var t2 = fX * positionX + fY * positionY + fZ * positionZ;
// The code below this comment is an optimized
// version of the commented lines.
// Rather that create two matrices and then multiply,
// we just bake in the multiplcation as part of creation.
// var rotation = new Matrix4(
// sX, sY, sZ, 0.0,
// uX, uY, uZ, 0.0,
// -fX, -fY, -fZ, 0.0,
// 0.0, 0.0, 0.0, 1.0);
// var translation = new Matrix4(
// 1.0, 0.0, 0.0, -position.x,
// 0.0, 1.0, 0.0, -position.y,
// 0.0, 0.0, 1.0, -position.z,
// 0.0, 0.0, 0.0, 1.0);
// return rotation.multiply(translation);
if (!defined(result)) {
return new Matrix4(
sX, sY, sZ, t0,
uX, uY, uZ, t1,
-fX, -fY, -fZ, t2,
0.0, 0.0, 0.0, 1.0);
}
result[0] = sX;
result[1] = uX;
result[2] = -fX;
result[3] = 0.0;
result[4] = sY;
result[5] = uY;
result[6] = -fY;
result[7] = 0.0;
result[8] = sZ;
result[9] = uZ;
result[10] = -fZ;
result[11] = 0.0;
result[12] = t0;
result[13] = t1;
result[14] = t2;
result[15] = 1.0;
return result;
};
/**
* Computes a Matrix4 instance representing a perspective transformation matrix.
*
* @param {Number} fovY The field of view along the Y axis in radians.
* @param {Number} aspectRatio The aspect ratio.
* @param {Number} near The distance to the near plane in meters.
* @param {Number} far The distance to the far plane in meters.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*
* @exception {DeveloperError} fovY must be in (0, PI].
* @exception {DeveloperError} aspectRatio must be greater than zero.
* @exception {DeveloperError} near must be greater than zero.
* @exception {DeveloperError} far must be greater than zero.
*/
Matrix4.computePerspectiveFieldOfView = function(fovY, aspectRatio, near, far, result) {
if (fovY <= 0.0 || fovY > Math.PI) {
throw new DeveloperError('fovY must be in (0, PI].');
}
if (aspectRatio <= 0.0) {
throw new DeveloperError('aspectRatio must be greater than zero.');
}
if (near <= 0.0) {
throw new DeveloperError('near must be greater than zero.');
}
if (far <= 0.0) {
throw new DeveloperError('far must be greater than zero.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var bottom = Math.tan(fovY * 0.5);
var column1Row1 = 1.0 / bottom;
var column0Row0 = column1Row1 / aspectRatio;
var column2Row2 = (far + near) / (near - far);
var column3Row2 = (2.0 * far * near) / (near - far);
result[0] = column0Row0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = column1Row1;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = column2Row2;
result[11] = -1.0;
result[12] = 0.0;
result[13] = 0.0;
result[14] = column3Row2;
result[15] = 0.0;
return result;
};
/**
* Computes a Matrix4 instance representing an orthographic transformation matrix.
*
* @param {Number} left The number of meters to the left of the camera that will be in view.
* @param {Number} right The number of meters to the right of the camera that will be in view.
* @param {Number} bottom The number of meters below of the camera that will be in view.
* @param {Number} top The number of meters above of the camera that will be in view.
* @param {Number} near The distance to the near plane in meters.
* @param {Number} far The distance to the far plane in meters.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.computeOrthographicOffCenter = function(left, right, bottom, top, near, far, result) {
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(far)) {
throw new DeveloperError('far is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var a = 1.0 / (right - left);
var b = 1.0 / (top - bottom);
var c = 1.0 / (far - near);
var tx = -(right + left) * a;
var ty = -(top + bottom) * b;
var tz = -(far + near) * c;
a *= 2.0;
b *= 2.0;
c *= -2.0;
result[0] = a;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = b;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = c;
result[11] = 0.0;
result[12] = tx;
result[13] = ty;
result[14] = tz;
result[15] = 1.0;
return result;
};
/**
* Computes a Matrix4 instance representing an off center perspective transformation.
*
* @param {Number} left The number of meters to the left of the camera that will be in view.
* @param {Number} right The number of meters to the right of the camera that will be in view.
* @param {Number} bottom The number of meters below of the camera that will be in view.
* @param {Number} top The number of meters above of the camera that will be in view.
* @param {Number} near The distance to the near plane in meters.
* @param {Number} far The distance to the far plane in meters.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.computePerspectiveOffCenter = function(left, right, bottom, top, near, far, result) {
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(far)) {
throw new DeveloperError('far is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = 2.0 * near / (right - left);
var column1Row1 = 2.0 * near / (top - bottom);
var column2Row0 = (right + left) / (right - left);
var column2Row1 = (top + bottom) / (top - bottom);
var column2Row2 = -(far + near) / (far - near);
var column2Row3 = -1.0;
var column3Row2 = -2.0 * far * near / (far - near);
result[0] = column0Row0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = column1Row1;
result[6] = 0.0;
result[7] = 0.0;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = column2Row3;
result[12] = 0.0;
result[13] = 0.0;
result[14] = column3Row2;
result[15] = 0.0;
return result;
};
/**
* Computes a Matrix4 instance representing an infinite off center perspective transformation.
*
* @param {Number} left The number of meters to the left of the camera that will be in view.
* @param {Number} right The number of meters to the right of the camera that will be in view.
* @param {Number} bottom The number of meters below of the camera that will be in view.
* @param {Number} top The number of meters above of the camera that will be in view.
* @param {Number} near The distance to the near plane in meters.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.computeInfinitePerspectiveOffCenter = function(left, right, bottom, top, near, result) {
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = 2.0 * near / (right - left);
var column1Row1 = 2.0 * near / (top - bottom);
var column2Row0 = (right + left) / (right - left);
var column2Row1 = (top + bottom) / (top - bottom);
var column2Row2 = -1.0;
var column2Row3 = -1.0;
var column3Row2 = -2.0 * near;
result[0] = column0Row0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = column1Row1;
result[6] = 0.0;
result[7] = 0.0;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = column2Row3;
result[12] = 0.0;
result[13] = 0.0;
result[14] = column3Row2;
result[15] = 0.0;
return result;
};
/**
* Computes a Matrix4 instance that transforms from normalized device coordinates to window coordinates.
*
* @param {Object}[viewport = { x : 0.0, y : 0.0, width : 0.0, height : 0.0 }] The viewport's corners as shown in Example 1.
* @param {Number}[nearDepthRange=0.0] The near plane distance in window coordinates.
* @param {Number}[farDepthRange=1.0] The far plane distance in window coordinates.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Create viewport transformation using an explicit viewport and depth range.
* var m = Cesium.Matrix4.computeViewportTransformation({
* x : 0.0,
* y : 0.0,
* width : 1024.0,
* height : 768.0
* }, 0.0, 1.0, new Cesium.Matrix4());
*/
Matrix4.computeViewportTransformation = function(viewport, nearDepthRange, farDepthRange, result) {
if (!defined(result)) {
throw new DeveloperError('result is required');
}
viewport = defaultValue(viewport, defaultValue.EMPTY_OBJECT);
var x = defaultValue(viewport.x, 0.0);
var y = defaultValue(viewport.y, 0.0);
var width = defaultValue(viewport.width, 0.0);
var height = defaultValue(viewport.height, 0.0);
nearDepthRange = defaultValue(nearDepthRange, 0.0);
farDepthRange = defaultValue(farDepthRange, 1.0);
var halfWidth = width * 0.5;
var halfHeight = height * 0.5;
var halfDepth = (farDepthRange - nearDepthRange) * 0.5;
var column0Row0 = halfWidth;
var column1Row1 = halfHeight;
var column2Row2 = halfDepth;
var column3Row0 = x + halfWidth;
var column3Row1 = y + halfHeight;
var column3Row2 = nearDepthRange + halfDepth;
var column3Row3 = 1.0;
result[0] = column0Row0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = column1Row1;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = column2Row2;
result[11] = 0.0;
result[12] = column3Row0;
result[13] = column3Row1;
result[14] = column3Row2;
result[15] = column3Row3;
return result;
};
/**
* Computes a Matrix4 instance that transforms from world space to view space.
*
* @param {Cartesian3} position The position of the camera.
* @param {Cartesian3} direction The forward direction.
* @param {Cartesian3} up The up direction.
* @param {Cartesian3} right The right direction.
* @param {Matrix4} result The object in which the result will be stored.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.computeView = function(position, direction, up, right, result) {
if (!defined(position)) {
throw new DeveloperError('position is required');
}
if (!defined(direction)) {
throw new DeveloperError('direction is required');
}
if (!defined(up)) {
throw new DeveloperError('up is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = right.x;
result[1] = up.x;
result[2] = -direction.x;
result[3] = 0.0;
result[4] = right.y;
result[5] = up.y;
result[6] = -direction.y;
result[7] = 0.0;
result[8] = right.z;
result[9] = up.z;
result[10] = -direction.z;
result[11] = 0.0;
result[12] = -Cartesian3.dot(right, position);
result[13] = -Cartesian3.dot(up, position);
result[14] = Cartesian3.dot(direction, position);
result[15] = 1.0;
return result;
};
/**
* Computes an Array from the provided Matrix4 instance.
* The array will be in column-major order.
*
* @param {Matrix4} matrix The matrix to use..
* @param {Number[]} [result] The Array onto which to store the result.
* @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
*
* @example
* //create an array from an instance of Matrix4
* // m = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
* var a = Cesium.Matrix4.toArray(m);
*
* // m remains the same
* //creates a = [10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0]
*/
Matrix4.toArray = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
return [matrix[0], matrix[1], matrix[2], matrix[3],
matrix[4], matrix[5], matrix[6], matrix[7],
matrix[8], matrix[9], matrix[10], matrix[11],
matrix[12], matrix[13], matrix[14], matrix[15]];
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
result[9] = matrix[9];
result[10] = matrix[10];
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Computes the array index of the element at the provided row and column.
*
* @param {Number} row The zero-based index of the row.
* @param {Number} column The zero-based index of the column.
* @returns {Number} The index of the element at the provided row and column.
*
* @exception {DeveloperError} row must be 0, 1, 2, or 3.
* @exception {DeveloperError} column must be 0, 1, 2, or 3.
*
* @example
* var myMatrix = new Cesium.Matrix4();
* var column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);
* var column1Row0 = myMatrix[column1Row0Index];
* myMatrix[column1Row0Index] = 10.0;
*/
Matrix4.getElementIndex = function(column, row) {
if (typeof row !== 'number' || row < 0 || row > 3) {
throw new DeveloperError('row must be 0, 1, 2, or 3.');
}
if (typeof column !== 'number' || column < 0 || column > 3) {
throw new DeveloperError('column must be 0, 1, 2, or 3.');
}
return column * 4 + row;
};
/**
* Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to retrieve.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, 2, or 3.
*
* @example
* //returns a Cartesian4 instance with values from the specified column
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* //Example 1: Creates an instance of Cartesian
* var a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());
*
* @example
* //Example 2: Sets values for Cartesian instance
* var a = new Cesium.Cartesian4();
* Cesium.Matrix4.getColumn(m, 2, a);
*
* // a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;
*/
Matrix4.getColumn = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var startIndex = index * 4;
var x = matrix[startIndex];
var y = matrix[startIndex + 1];
var z = matrix[startIndex + 2];
var w = matrix[startIndex + 3];
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to set.
* @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified column.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, 2, or 3.
*
* @example
* //creates a new Matrix4 instance with new column values from the Cartesian4 instance
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* var a = Cesium.Matrix4.setColumn(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
*
* // m remains the same
* // a = [10.0, 11.0, 99.0, 13.0]
* // [14.0, 15.0, 98.0, 17.0]
* // [18.0, 19.0, 97.0, 21.0]
* // [22.0, 23.0, 96.0, 25.0]
*/
Matrix4.setColumn = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix4.clone(matrix, result);
var startIndex = index * 4;
result[startIndex] = cartesian.x;
result[startIndex + 1] = cartesian.y;
result[startIndex + 2] = cartesian.z;
result[startIndex + 3] = cartesian.w;
return result;
};
/**
* Computes a new matrix that replaces the translation in the rightmost column of the provided
* matrix with the provided translation. This assumes the matrix is an affine transformation
*
* @param {Matrix4} matrix The matrix to use.
* @param {Cartesian3} translation The translation that replaces the translation of the provided matrix.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.setTranslation = function(matrix, translation, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(translation)) {
throw new DeveloperError('translation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
result[9] = matrix[9];
result[10] = matrix[10];
result[11] = matrix[11];
result[12] = translation.x;
result[13] = translation.y;
result[14] = translation.z;
result[15] = matrix[15];
return result;
};
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to retrieve.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, 2, or 3.
*
* @example
* //returns a Cartesian4 instance with values from the specified column
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* //Example 1: Returns an instance of Cartesian
* var a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());
*
* @example
* //Example 2: Sets values for a Cartesian instance
* var a = new Cesium.Cartesian4();
* Cesium.Matrix4.getRow(m, 2, a);
*
* // a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;
*/
Matrix4.getRow = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = matrix[index];
var y = matrix[index + 4];
var z = matrix[index + 8];
var w = matrix[index + 12];
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to set.
* @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified row.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, 2, or 3.
*
* @example
* //create a new Matrix4 instance with new row values from the Cartesian4 instance
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* var a = Cesium.Matrix4.setRow(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
*
* // m remains the same
* // a = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [99.0, 98.0, 97.0, 96.0]
* // [22.0, 23.0, 24.0, 25.0]
*/
Matrix4.setRow = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix4.clone(matrix, result);
result[index] = cartesian.x;
result[index + 4] = cartesian.y;
result[index + 8] = cartesian.z;
result[index + 12] = cartesian.w;
return result;
};
var scratchColumn = new Cartesian3();
/**
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter
*/
Matrix4.getScale = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = Cartesian3.magnitude(Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
result.y = Cartesian3.magnitude(Cartesian3.fromElements(matrix[4], matrix[5], matrix[6], scratchColumn));
result.z = Cartesian3.magnitude(Cartesian3.fromElements(matrix[8], matrix[9], matrix[10], scratchColumn));
return result;
};
var scratchScale = new Cartesian3();
/**
* Computes the maximum scale assuming the matrix is an affine transformation.
* The maximum scale is the maximum length of the column vectors in the upper-left
* 3x3 matrix.
*
* @param {Matrix4} matrix The matrix.
* @returns {Number} The maximum scale.
*/
Matrix4.getMaximumScale = function(matrix) {
Matrix4.getScale(matrix, scratchScale);
return Cartesian3.maximumComponent(scratchScale);
};
/**
* Computes the product of two matrices.
*
* @param {Matrix4} left The first matrix.
* @param {Matrix4} right The second matrix.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.multiply = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var left0 = left[0];
var left1 = left[1];
var left2 = left[2];
var left3 = left[3];
var left4 = left[4];
var left5 = left[5];
var left6 = left[6];
var left7 = left[7];
var left8 = left[8];
var left9 = left[9];
var left10 = left[10];
var left11 = left[11];
var left12 = left[12];
var left13 = left[13];
var left14 = left[14];
var left15 = left[15];
var right0 = right[0];
var right1 = right[1];
var right2 = right[2];
var right3 = right[3];
var right4 = right[4];
var right5 = right[5];
var right6 = right[6];
var right7 = right[7];
var right8 = right[8];
var right9 = right[9];
var right10 = right[10];
var right11 = right[11];
var right12 = right[12];
var right13 = right[13];
var right14 = right[14];
var right15 = right[15];
var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2 + left12 * right3;
var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2 + left13 * right3;
var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2 + left14 * right3;
var column0Row3 = left3 * right0 + left7 * right1 + left11 * right2 + left15 * right3;
var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6 + left12 * right7;
var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6 + left13 * right7;
var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6 + left14 * right7;
var column1Row3 = left3 * right4 + left7 * right5 + left11 * right6 + left15 * right7;
var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10 + left12 * right11;
var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10 + left13 * right11;
var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10 + left14 * right11;
var column2Row3 = left3 * right8 + left7 * right9 + left11 * right10 + left15 * right11;
var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12 * right15;
var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13 * right15;
var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14 * right15;
var column3Row3 = left3 * right12 + left7 * right13 + left11 * right14 + left15 * right15;
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column0Row3;
result[4] = column1Row0;
result[5] = column1Row1;
result[6] = column1Row2;
result[7] = column1Row3;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = column2Row3;
result[12] = column3Row0;
result[13] = column3Row1;
result[14] = column3Row2;
result[15] = column3Row3;
return result;
};
/**
* Computes the sum of two matrices.
*
* @param {Matrix4} left The first matrix.
* @param {Matrix4} right The second matrix.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] + right[0];
result[1] = left[1] + right[1];
result[2] = left[2] + right[2];
result[3] = left[3] + right[3];
result[4] = left[4] + right[4];
result[5] = left[5] + right[5];
result[6] = left[6] + right[6];
result[7] = left[7] + right[7];
result[8] = left[8] + right[8];
result[9] = left[9] + right[9];
result[10] = left[10] + right[10];
result[11] = left[11] + right[11];
result[12] = left[12] + right[12];
result[13] = left[13] + right[13];
result[14] = left[14] + right[14];
result[15] = left[15] + right[15];
return result;
};
/**
* Computes the difference of two matrices.
*
* @param {Matrix4} left The first matrix.
* @param {Matrix4} right The second matrix.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] - right[0];
result[1] = left[1] - right[1];
result[2] = left[2] - right[2];
result[3] = left[3] - right[3];
result[4] = left[4] - right[4];
result[5] = left[5] - right[5];
result[6] = left[6] - right[6];
result[7] = left[7] - right[7];
result[8] = left[8] - right[8];
result[9] = left[9] - right[9];
result[10] = left[10] - right[10];
result[11] = left[11] - right[11];
result[12] = left[12] - right[12];
result[13] = left[13] - right[13];
result[14] = left[14] - right[14];
result[15] = left[15] - right[15];
return result;
};
/**
* Computes the product of two matrices assuming the matrices are
* affine transformation matrices, where the upper left 3x3 elements
* are a rotation matrix, and the upper three elements in the fourth
* column are the translation. The bottom row is assumed to be [0, 0, 0, 1].
* The matrix is not verified to be in the proper form.
* This method is faster than computing the product for general 4x4
* matrices using {@link Matrix4.multiply}.
*
* @param {Matrix4} left The first matrix.
* @param {Matrix4} right The second matrix.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* var m1 = new Cesium.Matrix4(1.0, 6.0, 7.0, 0.0, 2.0, 5.0, 8.0, 0.0, 3.0, 4.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0);
* var m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));
* var m3 = Cesium.Matrix4.multiplyTransformation(m1, m2, new Cesium.Matrix4());
*/
Matrix4.multiplyTransformation = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var left0 = left[0];
var left1 = left[1];
var left2 = left[2];
var left4 = left[4];
var left5 = left[5];
var left6 = left[6];
var left8 = left[8];
var left9 = left[9];
var left10 = left[10];
var left12 = left[12];
var left13 = left[13];
var left14 = left[14];
var right0 = right[0];
var right1 = right[1];
var right2 = right[2];
var right4 = right[4];
var right5 = right[5];
var right6 = right[6];
var right8 = right[8];
var right9 = right[9];
var right10 = right[10];
var right12 = right[12];
var right13 = right[13];
var right14 = right[14];
var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12;
var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13;
var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14;
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = 0.0;
result[4] = column1Row0;
result[5] = column1Row1;
result[6] = column1Row2;
result[7] = 0.0;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = 0.0;
result[12] = column3Row0;
result[13] = column3Row1;
result[14] = column3Row2;
result[15] = 1.0;
return result;
};
/**
* Multiplies a transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by a 3x3 rotation matrix. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m); with less allocations and arithmetic operations.
*
* @param {Matrix4} matrix The matrix on the left-hand side.
* @param {Matrix3} rotation The 3x3 rotation matrix on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);
* Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);
*/
Matrix4.multiplyByMatrix3 = function(matrix, rotation, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(rotation)) {
throw new DeveloperError('rotation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var left0 = matrix[0];
var left1 = matrix[1];
var left2 = matrix[2];
var left4 = matrix[4];
var left5 = matrix[5];
var left6 = matrix[6];
var left8 = matrix[8];
var left9 = matrix[9];
var left10 = matrix[10];
var right0 = rotation[0];
var right1 = rotation[1];
var right2 = rotation[2];
var right4 = rotation[3];
var right5 = rotation[4];
var right6 = rotation[5];
var right8 = rotation[6];
var right9 = rotation[7];
var right10 = rotation[8];
var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = 0.0;
result[4] = column1Row0;
result[5] = column1Row1;
result[6] = column1Row2;
result[7] = 0.0;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = 0.0;
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Multiplies a transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by an implicit translation matrix defined by a {@link Cartesian3}. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromTranslation(position), m); with less allocations and arithmetic operations.
*
* @param {Matrix4} matrix The matrix on the left-hand side.
* @param {Cartesian3} translation The translation on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);
* Cesium.Matrix4.multiplyByTranslation(m, position, m);
*/
Matrix4.multiplyByTranslation = function(matrix, translation, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(translation)) {
throw new DeveloperError('translation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = translation.x;
var y = translation.y;
var z = translation.z;
var tx = (x * matrix[0]) + (y * matrix[4]) + (z * matrix[8]) + matrix[12];
var ty = (x * matrix[1]) + (y * matrix[5]) + (z * matrix[9]) + matrix[13];
var tz = (x * matrix[2]) + (y * matrix[6]) + (z * matrix[10]) + matrix[14];
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
result[9] = matrix[9];
result[10] = matrix[10];
result[11] = matrix[11];
result[12] = tx;
result[13] = ty;
result[14] = tz;
result[15] = matrix[15];
return result;
};
var uniformScaleScratch = new Cartesian3();
/**
* Multiplies an affine transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by an implicit uniform scale matrix. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);, where
* m must be an affine matrix.
* This function performs fewer allocations and arithmetic operations.
*
* @param {Matrix4} matrix The affine matrix on the left-hand side.
* @param {Number} scale The uniform scale on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);
* Cesium.Matrix4.multiplyByUniformScale(m, scale, m);
*
* @see Matrix4.fromUniformScale
* @see Matrix4.multiplyByScale
*/
Matrix4.multiplyByUniformScale = function(matrix, scale, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
uniformScaleScratch.x = scale;
uniformScaleScratch.y = scale;
uniformScaleScratch.z = scale;
return Matrix4.multiplyByScale(matrix, uniformScaleScratch, result);
};
/**
* Multiplies an affine transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by an implicit non-uniform scale matrix. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);, where
* m must be an affine matrix.
* This function performs fewer allocations and arithmetic operations.
*
* @param {Matrix4} matrix The affine matrix on the left-hand side.
* @param {Cartesian3} scale The non-uniform scale on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);
* Cesium.Matrix4.multiplyByScale(m, scale, m);
*
* @see Matrix4.fromScale
* @see Matrix4.multiplyByUniformScale
*/
Matrix4.multiplyByScale = function(matrix, scale, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var scaleX = scale.x;
var scaleY = scale.y;
var scaleZ = scale.z;
// Faster than Cartesian3.equals
if ((scaleX === 1.0) && (scaleY === 1.0) && (scaleZ === 1.0)) {
return Matrix4.clone(matrix, result);
}
result[0] = scaleX * matrix[0];
result[1] = scaleX * matrix[1];
result[2] = scaleX * matrix[2];
result[3] = 0.0;
result[4] = scaleY * matrix[4];
result[5] = scaleY * matrix[5];
result[6] = scaleY * matrix[6];
result[7] = 0.0;
result[8] = scaleZ * matrix[8];
result[9] = scaleZ * matrix[9];
result[10] = scaleZ * matrix[10];
result[11] = 0.0;
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = 1.0;
return result;
};
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian4} cartesian The vector.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Matrix4.multiplyByVector = function(matrix, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var vX = cartesian.x;
var vY = cartesian.y;
var vZ = cartesian.z;
var vW = cartesian.w;
var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;
var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;
var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;
var w = matrix[3] * vX + matrix[7] * vY + matrix[11] * vZ + matrix[15] * vW;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
* with a {@link Cartesian4} with a w component of zero.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian3} cartesian The point.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @example
* var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* var result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());
* // A shortcut for
* // Cartesian3 p = ...
* // Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);
*/
Matrix4.multiplyByPointAsVector = function(matrix, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var vX = cartesian.x;
var vY = cartesian.y;
var vZ = cartesian.z;
var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;
var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;
var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
* with a {@link Cartesian4} with a w component of 1, but returns a {@link Cartesian3} instead of a {@link Cartesian4}.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian3} cartesian The point.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @example
* var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* var result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());
*/
Matrix4.multiplyByPoint = function(matrix, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var vX = cartesian.x;
var vY = cartesian.y;
var vZ = cartesian.z;
var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];
var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];
var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14];
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix4} matrix The matrix.
* @param {Number} scalar The number to multiply by.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //create a Matrix4 instance which is a scaled version of the supplied Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* var a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());
*
* // m remains the same
* // a = [-20.0, -22.0, -24.0, -26.0]
* // [-28.0, -30.0, -32.0, -34.0]
* // [-36.0, -38.0, -40.0, -42.0]
* // [-44.0, -46.0, -48.0, -50.0]
*/
Matrix4.multiplyByScalar = function(matrix, scalar, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar must be a number');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
result[4] = matrix[4] * scalar;
result[5] = matrix[5] * scalar;
result[6] = matrix[6] * scalar;
result[7] = matrix[7] * scalar;
result[8] = matrix[8] * scalar;
result[9] = matrix[9] * scalar;
result[10] = matrix[10] * scalar;
result[11] = matrix[11] * scalar;
result[12] = matrix[12] * scalar;
result[13] = matrix[13] * scalar;
result[14] = matrix[14] * scalar;
result[15] = matrix[15] * scalar;
return result;
};
/**
* Computes a negated copy of the provided matrix.
*
* @param {Matrix4} matrix The matrix to negate.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //create a new Matrix4 instance which is a negation of a Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* var a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());
*
* // m remains the same
* // a = [-10.0, -11.0, -12.0, -13.0]
* // [-14.0, -15.0, -16.0, -17.0]
* // [-18.0, -19.0, -20.0, -21.0]
* // [-22.0, -23.0, -24.0, -25.0]
*/
Matrix4.negate = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
result[4] = -matrix[4];
result[5] = -matrix[5];
result[6] = -matrix[6];
result[7] = -matrix[7];
result[8] = -matrix[8];
result[9] = -matrix[9];
result[10] = -matrix[10];
result[11] = -matrix[11];
result[12] = -matrix[12];
result[13] = -matrix[13];
result[14] = -matrix[14];
result[15] = -matrix[15];
return result;
};
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix4} matrix The matrix to transpose.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //returns transpose of a Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* var a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());
*
* // m remains the same
* // a = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*/
Matrix4.transpose = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var matrix1 = matrix[1];
var matrix2 = matrix[2];
var matrix3 = matrix[3];
var matrix6 = matrix[6];
var matrix7 = matrix[7];
var matrix11 = matrix[11];
result[0] = matrix[0];
result[1] = matrix[4];
result[2] = matrix[8];
result[3] = matrix[12];
result[4] = matrix1;
result[5] = matrix[5];
result[6] = matrix[9];
result[7] = matrix[13];
result[8] = matrix2;
result[9] = matrix6;
result[10] = matrix[10];
result[11] = matrix[14];
result[12] = matrix3;
result[13] = matrix7;
result[14] = matrix11;
result[15] = matrix[15];
return result;
};
/**
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
*
* @param {Matrix4} matrix The matrix with signed elements.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.abs = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = Math.abs(matrix[0]);
result[1] = Math.abs(matrix[1]);
result[2] = Math.abs(matrix[2]);
result[3] = Math.abs(matrix[3]);
result[4] = Math.abs(matrix[4]);
result[5] = Math.abs(matrix[5]);
result[6] = Math.abs(matrix[6]);
result[7] = Math.abs(matrix[7]);
result[8] = Math.abs(matrix[8]);
result[9] = Math.abs(matrix[9]);
result[10] = Math.abs(matrix[10]);
result[11] = Math.abs(matrix[11]);
result[12] = Math.abs(matrix[12]);
result[13] = Math.abs(matrix[13]);
result[14] = Math.abs(matrix[14]);
result[15] = Math.abs(matrix[15]);
return result;
};
/**
* Compares the provided matrices componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix4} [left] The first matrix.
* @param {Matrix4} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*
* @example
* //compares two Matrix4 instances
*
* // a = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* // b = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* if(Cesium.Matrix4.equals(a,b)) {
* console.log("Both matrices are equal");
* } else {
* console.log("They are not equal");
* }
*
* //Prints "Both matrices are equal" on the console
*/
Matrix4.equals = function(left, right) {
// Given that most matrices will be transformation matrices, the elements
// are tested in order such that the test is likely to fail as early
// as possible. I _think_ this is just as friendly to the L1 cache
// as testing in index order. It is certainty faster in practice.
return (left === right) ||
(defined(left) &&
defined(right) &&
// Translation
left[12] === right[12] &&
left[13] === right[13] &&
left[14] === right[14] &&
// Rotation/scale
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[4] === right[4] &&
left[5] === right[5] &&
left[6] === right[6] &&
left[8] === right[8] &&
left[9] === right[9] &&
left[10] === right[10] &&
// Bottom row
left[3] === right[3] &&
left[7] === right[7] &&
left[11] === right[11] &&
left[15] === right[15]);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix4} [left] The first matrix.
* @param {Matrix4} [right] The second matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*
* @example
* //compares two Matrix4 instances
*
* // a = [10.5, 14.5, 18.5, 22.5]
* // [11.5, 15.5, 19.5, 23.5]
* // [12.5, 16.5, 20.5, 24.5]
* // [13.5, 17.5, 21.5, 25.5]
*
* // b = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){
* console.log("Difference between both the matrices is less than 0.1");
* } else {
* console.log("Difference between both the matrices is not less than 0.1");
* }
*
* //Prints "Difference between both the matrices is not less than 0.1" on the console
*/
Matrix4.equalsEpsilon = function(left, right, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon must be a number');
}
return (left === right) ||
(defined(left) &&
defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon &&
Math.abs(left[4] - right[4]) <= epsilon &&
Math.abs(left[5] - right[5]) <= epsilon &&
Math.abs(left[6] - right[6]) <= epsilon &&
Math.abs(left[7] - right[7]) <= epsilon &&
Math.abs(left[8] - right[8]) <= epsilon &&
Math.abs(left[9] - right[9]) <= epsilon &&
Math.abs(left[10] - right[10]) <= epsilon &&
Math.abs(left[11] - right[11]) <= epsilon &&
Math.abs(left[12] - right[12]) <= epsilon &&
Math.abs(left[13] - right[13]) <= epsilon &&
Math.abs(left[14] - right[14]) <= epsilon &&
Math.abs(left[15] - right[15]) <= epsilon);
};
/**
* Gets the translation portion of the provided matrix, assuming the matrix is a affine transformation matrix.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Matrix4.getTranslation = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = matrix[12];
result.y = matrix[13];
result.z = matrix[14];
return result;
};
/**
* Gets the upper left 3x3 rotation matrix of the provided matrix, assuming the matrix is a affine transformation matrix.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @example
* // returns a Matrix3 instance from a Matrix4 instance
*
* // m = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* var b = new Cesium.Matrix3();
* Cesium.Matrix4.getRotation(m,b);
*
* // b = [10.0, 14.0, 18.0]
* // [11.0, 15.0, 19.0]
* // [12.0, 16.0, 20.0]
*/
Matrix4.getRotation = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[4];
result[4] = matrix[5];
result[5] = matrix[6];
result[6] = matrix[8];
result[7] = matrix[9];
result[8] = matrix[10];
return result;
};
var scratchInverseRotation = new Matrix3();
var scratchMatrix3Zero = new Matrix3();
var scratchBottomRow = new Cartesian4();
var scratchExpectedBottomRow = new Cartesian4(0.0, 0.0, 0.0, 1.0);
/**
* Computes the inverse of the provided matrix using Cramers Rule.
* If the determinant is zero, the matrix can not be inverted, and an exception is thrown.
* If the matrix is an affine transformation matrix, it is more efficient
* to invert it with {@link Matrix4.inverseTransformation}.
*
* @param {Matrix4} matrix The matrix to invert.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @exception {RuntimeError} matrix is not invertible because its determinate is zero.
*/
Matrix4.inverse = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
// Special case for a zero scale matrix that can occur, for example,
// when a model's node has a [0, 0, 0] scale.
if (Matrix3.equalsEpsilon(Matrix4.getRotation(matrix, scratchInverseRotation), scratchMatrix3Zero, CesiumMath.EPSILON7) &&
Cartesian4.equals(Matrix4.getRow(matrix, 3, scratchBottomRow), scratchExpectedBottomRow)) {
result[0] = 0.0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = 0.0;
result[11] = 0.0;
result[12] = -matrix[12];
result[13] = -matrix[13];
result[14] = -matrix[14];
result[15] = 1.0;
return result;
}
//
// Ported from:
// ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf
//
var src0 = matrix[0];
var src1 = matrix[4];
var src2 = matrix[8];
var src3 = matrix[12];
var src4 = matrix[1];
var src5 = matrix[5];
var src6 = matrix[9];
var src7 = matrix[13];
var src8 = matrix[2];
var src9 = matrix[6];
var src10 = matrix[10];
var src11 = matrix[14];
var src12 = matrix[3];
var src13 = matrix[7];
var src14 = matrix[11];
var src15 = matrix[15];
// calculate pairs for first 8 elements (cofactors)
var tmp0 = src10 * src15;
var tmp1 = src11 * src14;
var tmp2 = src9 * src15;
var tmp3 = src11 * src13;
var tmp4 = src9 * src14;
var tmp5 = src10 * src13;
var tmp6 = src8 * src15;
var tmp7 = src11 * src12;
var tmp8 = src8 * src14;
var tmp9 = src10 * src12;
var tmp10 = src8 * src13;
var tmp11 = src9 * src12;
// calculate first 8 elements (cofactors)
var dst0 = (tmp0 * src5 + tmp3 * src6 + tmp4 * src7) - (tmp1 * src5 + tmp2 * src6 + tmp5 * src7);
var dst1 = (tmp1 * src4 + tmp6 * src6 + tmp9 * src7) - (tmp0 * src4 + tmp7 * src6 + tmp8 * src7);
var dst2 = (tmp2 * src4 + tmp7 * src5 + tmp10 * src7) - (tmp3 * src4 + tmp6 * src5 + tmp11 * src7);
var dst3 = (tmp5 * src4 + tmp8 * src5 + tmp11 * src6) - (tmp4 * src4 + tmp9 * src5 + tmp10 * src6);
var dst4 = (tmp1 * src1 + tmp2 * src2 + tmp5 * src3) - (tmp0 * src1 + tmp3 * src2 + tmp4 * src3);
var dst5 = (tmp0 * src0 + tmp7 * src2 + tmp8 * src3) - (tmp1 * src0 + tmp6 * src2 + tmp9 * src3);
var dst6 = (tmp3 * src0 + tmp6 * src1 + tmp11 * src3) - (tmp2 * src0 + tmp7 * src1 + tmp10 * src3);
var dst7 = (tmp4 * src0 + tmp9 * src1 + tmp10 * src2) - (tmp5 * src0 + tmp8 * src1 + tmp11 * src2);
// calculate pairs for second 8 elements (cofactors)
tmp0 = src2 * src7;
tmp1 = src3 * src6;
tmp2 = src1 * src7;
tmp3 = src3 * src5;
tmp4 = src1 * src6;
tmp5 = src2 * src5;
tmp6 = src0 * src7;
tmp7 = src3 * src4;
tmp8 = src0 * src6;
tmp9 = src2 * src4;
tmp10 = src0 * src5;
tmp11 = src1 * src4;
// calculate second 8 elements (cofactors)
var dst8 = (tmp0 * src13 + tmp3 * src14 + tmp4 * src15) - (tmp1 * src13 + tmp2 * src14 + tmp5 * src15);
var dst9 = (tmp1 * src12 + tmp6 * src14 + tmp9 * src15) - (tmp0 * src12 + tmp7 * src14 + tmp8 * src15);
var dst10 = (tmp2 * src12 + tmp7 * src13 + tmp10 * src15) - (tmp3 * src12 + tmp6 * src13 + tmp11 * src15);
var dst11 = (tmp5 * src12 + tmp8 * src13 + tmp11 * src14) - (tmp4 * src12 + tmp9 * src13 + tmp10 * src14);
var dst12 = (tmp2 * src10 + tmp5 * src11 + tmp1 * src9) - (tmp4 * src11 + tmp0 * src9 + tmp3 * src10);
var dst13 = (tmp8 * src11 + tmp0 * src8 + tmp7 * src10) - (tmp6 * src10 + tmp9 * src11 + tmp1 * src8);
var dst14 = (tmp6 * src9 + tmp11 * src11 + tmp3 * src8) - (tmp10 * src11 + tmp2 * src8 + tmp7 * src9);
var dst15 = (tmp10 * src10 + tmp4 * src8 + tmp9 * src9) - (tmp8 * src9 + tmp11 * src10 + tmp5 * src8);
// calculate determinant
var det = src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
if (Math.abs(det) < CesiumMath.EPSILON20) {
throw new RuntimeError('matrix is not invertible because its determinate is zero.');
}
// calculate matrix inverse
det = 1.0 / det;
result[0] = dst0 * det;
result[1] = dst1 * det;
result[2] = dst2 * det;
result[3] = dst3 * det;
result[4] = dst4 * det;
result[5] = dst5 * det;
result[6] = dst6 * det;
result[7] = dst7 * det;
result[8] = dst8 * det;
result[9] = dst9 * det;
result[10] = dst10 * det;
result[11] = dst11 * det;
result[12] = dst12 * det;
result[13] = dst13 * det;
result[14] = dst14 * det;
result[15] = dst15 * det;
return result;
};
/**
* Computes the inverse of the provided matrix assuming it is
* an affine transformation matrix, where the upper left 3x3 elements
* are a rotation matrix, and the upper three elements in the fourth
* column are the translation. The bottom row is assumed to be [0, 0, 0, 1].
* The matrix is not verified to be in the proper form.
* This method is faster than computing the inverse for a general 4x4
* matrix using {@link Matrix4.inverse}.
*
* @param {Matrix4} matrix The matrix to invert.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.inverseTransformation = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//This function is an optimized version of the below 4 lines.
//var rT = Matrix3.transpose(Matrix4.getRotation(matrix));
//var rTN = Matrix3.negate(rT);
//var rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));
//return Matrix4.fromRotationTranslation(rT, rTT, result);
var matrix0 = matrix[0];
var matrix1 = matrix[1];
var matrix2 = matrix[2];
var matrix4 = matrix[4];
var matrix5 = matrix[5];
var matrix6 = matrix[6];
var matrix8 = matrix[8];
var matrix9 = matrix[9];
var matrix10 = matrix[10];
var vX = matrix[12];
var vY = matrix[13];
var vZ = matrix[14];
var x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;
var y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;
var z = -matrix8 * vX - matrix9 * vY - matrix10 * vZ;
result[0] = matrix0;
result[1] = matrix4;
result[2] = matrix8;
result[3] = 0.0;
result[4] = matrix1;
result[5] = matrix5;
result[6] = matrix9;
result[7] = 0.0;
result[8] = matrix2;
result[9] = matrix6;
result[10] = matrix10;
result[11] = 0.0;
result[12] = x;
result[13] = y;
result[14] = z;
result[15] = 1.0;
return result;
};
/**
* An immutable Matrix4 instance initialized to the identity matrix.
*
* @type {Matrix4}
* @constant
*/
Matrix4.IDENTITY = freezeObject(new Matrix4(1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0));
/**
* An immutable Matrix4 instance initialized to the zero matrix.
*
* @type {Matrix4}
* @constant
*/
Matrix4.ZERO = freezeObject(new Matrix4(0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0));
/**
* The index into Matrix4 for column 0, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW0 = 0;
/**
* The index into Matrix4 for column 0, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW1 = 1;
/**
* The index into Matrix4 for column 0, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW2 = 2;
/**
* The index into Matrix4 for column 0, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW3 = 3;
/**
* The index into Matrix4 for column 1, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW0 = 4;
/**
* The index into Matrix4 for column 1, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW1 = 5;
/**
* The index into Matrix4 for column 1, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW2 = 6;
/**
* The index into Matrix4 for column 1, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW3 = 7;
/**
* The index into Matrix4 for column 2, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW0 = 8;
/**
* The index into Matrix4 for column 2, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW1 = 9;
/**
* The index into Matrix4 for column 2, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW2 = 10;
/**
* The index into Matrix4 for column 2, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW3 = 11;
/**
* The index into Matrix4 for column 3, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW0 = 12;
/**
* The index into Matrix4 for column 3, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW1 = 13;
/**
* The index into Matrix4 for column 3, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW2 = 14;
/**
* The index into Matrix4 for column 3, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW3 = 15;
defineProperties(Matrix4.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix4.prototype
*
* @type {Number}
*/
length : {
get : function() {
return Matrix4.packedLength;
}
}
});
/**
* Duplicates the provided Matrix4 instance.
*
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
*/
Matrix4.prototype.clone = function(result) {
return Matrix4.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix4} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix4.prototype.equals = function(right) {
return Matrix4.equals(this, right);
};
/**
* @private
*/
Matrix4.equalsArray = function(matrix, array, offset) {
return matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3] &&
matrix[4] === array[offset + 4] &&
matrix[5] === array[offset + 5] &&
matrix[6] === array[offset + 6] &&
matrix[7] === array[offset + 7] &&
matrix[8] === array[offset + 8] &&
matrix[9] === array[offset + 9] &&
matrix[10] === array[offset + 10] &&
matrix[11] === array[offset + 11] &&
matrix[12] === array[offset + 12] &&
matrix[13] === array[offset + 13] &&
matrix[14] === array[offset + 14] &&
matrix[15] === array[offset + 15];
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix4} [right] The right hand side matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix4.prototype.equalsEpsilon = function(right, epsilon) {
return Matrix4.equalsEpsilon(this, right, epsilon);
};
/**
* Computes a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1, column2, column3)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.
*/
Matrix4.prototype.toString = function() {
return '(' + this[0] + ', ' + this[4] + ', ' + this[8] + ', ' + this[12] +')\n' +
'(' + this[1] + ', ' + this[5] + ', ' + this[9] + ', ' + this[13] +')\n' +
'(' + this[2] + ', ' + this[6] + ', ' + this[10] + ', ' + this[14] +')\n' +
'(' + this[3] + ', ' + this[7] + ', ' + this[11] + ', ' + this[15] +')';
};
return Matrix4;
});
/*global define*/
define('Core/BoundingSphere',[
'./Cartesian3',
'./Cartographic',
'./defaultValue',
'./defined',
'./DeveloperError',
'./Ellipsoid',
'./GeographicProjection',
'./Intersect',
'./Interval',
'./Matrix3',
'./Matrix4',
'./Rectangle'
], function(
Cartesian3,
Cartographic,
defaultValue,
defined,
DeveloperError,
Ellipsoid,
GeographicProjection,
Intersect,
Interval,
Matrix3,
Matrix4,
Rectangle) {
'use strict';
/**
* A bounding sphere with a center and a radius.
* @alias BoundingSphere
* @constructor
*
* @param {Cartesian3} [center=Cartesian3.ZERO] The center of the bounding sphere.
* @param {Number} [radius=0.0] The radius of the bounding sphere.
*
* @see AxisAlignedBoundingBox
* @see BoundingRectangle
* @see Packable
*/
function BoundingSphere(center, radius) {
/**
* The center point of the sphere.
* @type {Cartesian3}
* @default {@link Cartesian3.ZERO}
*/
this.center = Cartesian3.clone(defaultValue(center, Cartesian3.ZERO));
/**
* The radius of the sphere.
* @type {Number}
* @default 0.0
*/
this.radius = defaultValue(radius, 0.0);
}
var fromPointsXMin = new Cartesian3();
var fromPointsYMin = new Cartesian3();
var fromPointsZMin = new Cartesian3();
var fromPointsXMax = new Cartesian3();
var fromPointsYMax = new Cartesian3();
var fromPointsZMax = new Cartesian3();
var fromPointsCurrentPos = new Cartesian3();
var fromPointsScratch = new Cartesian3();
var fromPointsRitterCenter = new Cartesian3();
var fromPointsMinBoxPt = new Cartesian3();
var fromPointsMaxBoxPt = new Cartesian3();
var fromPointsNaiveCenterScratch = new Cartesian3();
/**
* Computes a tight-fitting bounding sphere enclosing a list of 3D Cartesian points.
* The bounding sphere is computed by running two algorithms, a naive algorithm and
* Ritter's algorithm. The smaller of the two spheres is used to ensure a tight fit.
*
* @param {Cartesian3[]} positions An array of points that the bounding sphere will enclose. Each point must have x, y, and z properties.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
*
* @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
*/
BoundingSphere.fromPoints = function(positions, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
if (!defined(positions) || positions.length === 0) {
result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = 0.0;
return result;
}
var currentPos = Cartesian3.clone(positions[0], fromPointsCurrentPos);
var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
var numPositions = positions.length;
for (var i = 1; i < numPositions; i++) {
Cartesian3.clone(positions[i], currentPos);
var x = currentPos.x;
var y = currentPos.y;
var z = currentPos.z;
// Store points containing the the smallest and largest components
if (x < xMin.x) {
Cartesian3.clone(currentPos, xMin);
}
if (x > xMax.x) {
Cartesian3.clone(currentPos, xMax);
}
if (y < yMin.y) {
Cartesian3.clone(currentPos, yMin);
}
if (y > yMax.y) {
Cartesian3.clone(currentPos, yMax);
}
if (z < zMin.z) {
Cartesian3.clone(currentPos, zMin);
}
if (z > zMax.z) {
Cartesian3.clone(currentPos, zMax);
}
}
// Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
// Set the diameter endpoints to the largest span.
var diameter1 = xMin;
var diameter2 = xMax;
var maxSpan = xSpan;
if (ySpan > maxSpan) {
maxSpan = ySpan;
diameter1 = yMin;
diameter2 = yMax;
}
if (zSpan > maxSpan) {
maxSpan = zSpan;
diameter1 = zMin;
diameter2 = zMax;
}
// Calculate the center of the initial sphere found by Ritter's algorithm
var ritterCenter = fromPointsRitterCenter;
ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
// Calculate the radius of the initial sphere found by Ritter's algorithm
var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
var ritterRadius = Math.sqrt(radiusSquared);
// Find the center of the sphere found using the Naive method.
var minBoxPt = fromPointsMinBoxPt;
minBoxPt.x = xMin.x;
minBoxPt.y = yMin.y;
minBoxPt.z = zMin.z;
var maxBoxPt = fromPointsMaxBoxPt;
maxBoxPt.x = xMax.x;
maxBoxPt.y = yMax.y;
maxBoxPt.z = zMax.z;
var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
// Begin 2nd pass to find naive radius and modify the ritter sphere.
var naiveRadius = 0;
for (i = 0; i < numPositions; i++) {
Cartesian3.clone(positions[i], currentPos);
// Find the furthest point from the naive center to calculate the naive radius.
var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
if (r > naiveRadius) {
naiveRadius = r;
}
// Make adjustments to the Ritter Sphere to include all points.
var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
if (oldCenterToPointSquared > radiusSquared) {
var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
// Calculate new radius to include the point that lies outside
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
radiusSquared = ritterRadius * ritterRadius;
// Calculate center of new Ritter sphere
var oldToNew = oldCenterToPoint - ritterRadius;
ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
}
}
if (ritterRadius < naiveRadius) {
Cartesian3.clone(ritterCenter, result.center);
result.radius = ritterRadius;
} else {
Cartesian3.clone(naiveCenter, result.center);
result.radius = naiveRadius;
}
return result;
};
var defaultProjection = new GeographicProjection();
var fromRectangle2DLowerLeft = new Cartesian3();
var fromRectangle2DUpperRight = new Cartesian3();
var fromRectangle2DSouthwest = new Cartographic();
var fromRectangle2DNortheast = new Cartographic();
/**
* Computes a bounding sphere from an rectangle projected in 2D.
*
* @param {Rectangle} rectangle The rectangle around which to create a bounding sphere.
* @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.fromRectangle2D = function(rectangle, projection, result) {
return BoundingSphere.fromRectangleWithHeights2D(rectangle, projection, 0.0, 0.0, result);
};
/**
* Computes a bounding sphere from an rectangle projected in 2D. The bounding sphere accounts for the
* object's minimum and maximum heights over the rectangle.
*
* @param {Rectangle} rectangle The rectangle around which to create a bounding sphere.
* @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
* @param {Number} [minimumHeight=0.0] The minimum height over the rectangle.
* @param {Number} [maximumHeight=0.0] The maximum height over the rectangle.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.fromRectangleWithHeights2D = function(rectangle, projection, minimumHeight, maximumHeight, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
if (!defined(rectangle)) {
result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = 0.0;
return result;
}
projection = defaultValue(projection, defaultProjection);
Rectangle.southwest(rectangle, fromRectangle2DSouthwest);
fromRectangle2DSouthwest.height = minimumHeight;
Rectangle.northeast(rectangle, fromRectangle2DNortheast);
fromRectangle2DNortheast.height = maximumHeight;
var lowerLeft = projection.project(fromRectangle2DSouthwest, fromRectangle2DLowerLeft);
var upperRight = projection.project(fromRectangle2DNortheast, fromRectangle2DUpperRight);
var width = upperRight.x - lowerLeft.x;
var height = upperRight.y - lowerLeft.y;
var elevation = upperRight.z - lowerLeft.z;
result.radius = Math.sqrt(width * width + height * height + elevation * elevation) * 0.5;
var center = result.center;
center.x = lowerLeft.x + width * 0.5;
center.y = lowerLeft.y + height * 0.5;
center.z = lowerLeft.z + elevation * 0.5;
return result;
};
var fromRectangle3DScratch = [];
/**
* Computes a bounding sphere from an rectangle in 3D. The bounding sphere is created using a subsample of points
* on the ellipsoid and contained in the rectangle. It may not be accurate for all rectangles on all types of ellipsoids.
*
* @param {Rectangle} rectangle The valid rectangle used to create a bounding sphere.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid used to determine positions of the rectangle.
* @param {Number} [surfaceHeight=0.0] The height above the surface of the ellipsoid.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.fromRectangle3D = function(rectangle, ellipsoid, surfaceHeight, result) {
ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
surfaceHeight = defaultValue(surfaceHeight, 0.0);
var positions;
if (defined(rectangle)) {
positions = Rectangle.subsample(rectangle, ellipsoid, surfaceHeight, fromRectangle3DScratch);
}
return BoundingSphere.fromPoints(positions, result);
};
/**
* Computes a tight-fitting bounding sphere enclosing a list of 3D points, where the points are
* stored in a flat array in X, Y, Z, order. The bounding sphere is computed by running two
* algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
* ensure a tight fit.
*
* @param {Number[]} positions An array of points that the bounding sphere will enclose. Each point
* is formed from three elements in the array in the order X, Y, Z.
* @param {Cartesian3} [center=Cartesian3.ZERO] The position to which the positions are relative, which need not be the
* origin of the coordinate system. This is useful when the positions are to be used for
* relative-to-center (RTC) rendering.
* @param {Number} [stride=3] The number of array elements per vertex. It must be at least 3, but it may
* be higher. Regardless of the value of this parameter, the X coordinate of the first position
* is at array index 0, the Y coordinate is at array index 1, and the Z coordinate is at array index
* 2. When stride is 3, the X coordinate of the next position then begins at array index 3. If
* the stride is 5, however, two array elements are skipped and the next position begins at array
* index 5.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
*
* @example
* // Compute the bounding sphere from 3 positions, each specified relative to a center.
* // In addition to the X, Y, and Z coordinates, the points array contains two additional
* // elements per point which are ignored for the purpose of computing the bounding sphere.
* var center = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* var points = [1.0, 2.0, 3.0, 0.1, 0.2,
* 4.0, 5.0, 6.0, 0.1, 0.2,
* 7.0, 8.0, 9.0, 0.1, 0.2];
* var sphere = Cesium.BoundingSphere.fromVertices(points, center, 5);
*
* @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
*/
BoundingSphere.fromVertices = function(positions, center, stride, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
if (!defined(positions) || positions.length === 0) {
result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = 0.0;
return result;
}
center = defaultValue(center, Cartesian3.ZERO);
stride = defaultValue(stride, 3);
if (stride < 3) {
throw new DeveloperError('stride must be 3 or greater.');
}
var currentPos = fromPointsCurrentPos;
currentPos.x = positions[0] + center.x;
currentPos.y = positions[1] + center.y;
currentPos.z = positions[2] + center.z;
var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
var numElements = positions.length;
for (var i = 0; i < numElements; i += stride) {
var x = positions[i] + center.x;
var y = positions[i + 1] + center.y;
var z = positions[i + 2] + center.z;
currentPos.x = x;
currentPos.y = y;
currentPos.z = z;
// Store points containing the the smallest and largest components
if (x < xMin.x) {
Cartesian3.clone(currentPos, xMin);
}
if (x > xMax.x) {
Cartesian3.clone(currentPos, xMax);
}
if (y < yMin.y) {
Cartesian3.clone(currentPos, yMin);
}
if (y > yMax.y) {
Cartesian3.clone(currentPos, yMax);
}
if (z < zMin.z) {
Cartesian3.clone(currentPos, zMin);
}
if (z > zMax.z) {
Cartesian3.clone(currentPos, zMax);
}
}
// Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
// Set the diameter endpoints to the largest span.
var diameter1 = xMin;
var diameter2 = xMax;
var maxSpan = xSpan;
if (ySpan > maxSpan) {
maxSpan = ySpan;
diameter1 = yMin;
diameter2 = yMax;
}
if (zSpan > maxSpan) {
maxSpan = zSpan;
diameter1 = zMin;
diameter2 = zMax;
}
// Calculate the center of the initial sphere found by Ritter's algorithm
var ritterCenter = fromPointsRitterCenter;
ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
// Calculate the radius of the initial sphere found by Ritter's algorithm
var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
var ritterRadius = Math.sqrt(radiusSquared);
// Find the center of the sphere found using the Naive method.
var minBoxPt = fromPointsMinBoxPt;
minBoxPt.x = xMin.x;
minBoxPt.y = yMin.y;
minBoxPt.z = zMin.z;
var maxBoxPt = fromPointsMaxBoxPt;
maxBoxPt.x = xMax.x;
maxBoxPt.y = yMax.y;
maxBoxPt.z = zMax.z;
var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
// Begin 2nd pass to find naive radius and modify the ritter sphere.
var naiveRadius = 0;
for (i = 0; i < numElements; i += stride) {
currentPos.x = positions[i] + center.x;
currentPos.y = positions[i + 1] + center.y;
currentPos.z = positions[i + 2] + center.z;
// Find the furthest point from the naive center to calculate the naive radius.
var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
if (r > naiveRadius) {
naiveRadius = r;
}
// Make adjustments to the Ritter Sphere to include all points.
var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
if (oldCenterToPointSquared > radiusSquared) {
var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
// Calculate new radius to include the point that lies outside
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
radiusSquared = ritterRadius * ritterRadius;
// Calculate center of new Ritter sphere
var oldToNew = oldCenterToPoint - ritterRadius;
ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
}
}
if (ritterRadius < naiveRadius) {
Cartesian3.clone(ritterCenter, result.center);
result.radius = ritterRadius;
} else {
Cartesian3.clone(naiveCenter, result.center);
result.radius = naiveRadius;
}
return result;
};
/**
* Computes a tight-fitting bounding sphere enclosing a list of {@link EncodedCartesian3}s, where the points are
* stored in parallel flat arrays in X, Y, Z, order. The bounding sphere is computed by running two
* algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
* ensure a tight fit.
*
* @param {Number[]} positionsHigh An array of high bits of the encoded cartesians that the bounding sphere will enclose. Each point
* is formed from three elements in the array in the order X, Y, Z.
* @param {Number[]} positionsLow An array of low bits of the encoded cartesians that the bounding sphere will enclose. Each point
* is formed from three elements in the array in the order X, Y, Z.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
*
* @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
*/
BoundingSphere.fromEncodedCartesianVertices = function(positionsHigh, positionsLow, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
if (!defined(positionsHigh) || !defined(positionsLow) || positionsHigh.length !== positionsLow.length || positionsHigh.length === 0) {
result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = 0.0;
return result;
}
var currentPos = fromPointsCurrentPos;
currentPos.x = positionsHigh[0] + positionsLow[0];
currentPos.y = positionsHigh[1] + positionsLow[1];
currentPos.z = positionsHigh[2] + positionsLow[2];
var xMin = Cartesian3.clone(currentPos, fromPointsXMin);
var yMin = Cartesian3.clone(currentPos, fromPointsYMin);
var zMin = Cartesian3.clone(currentPos, fromPointsZMin);
var xMax = Cartesian3.clone(currentPos, fromPointsXMax);
var yMax = Cartesian3.clone(currentPos, fromPointsYMax);
var zMax = Cartesian3.clone(currentPos, fromPointsZMax);
var numElements = positionsHigh.length;
for (var i = 0; i < numElements; i += 3) {
var x = positionsHigh[i] + positionsLow[i];
var y = positionsHigh[i + 1] + positionsLow[i + 1];
var z = positionsHigh[i + 2] + positionsLow[i + 2];
currentPos.x = x;
currentPos.y = y;
currentPos.z = z;
// Store points containing the the smallest and largest components
if (x < xMin.x) {
Cartesian3.clone(currentPos, xMin);
}
if (x > xMax.x) {
Cartesian3.clone(currentPos, xMax);
}
if (y < yMin.y) {
Cartesian3.clone(currentPos, yMin);
}
if (y > yMax.y) {
Cartesian3.clone(currentPos, yMax);
}
if (z < zMin.z) {
Cartesian3.clone(currentPos, zMin);
}
if (z > zMax.z) {
Cartesian3.clone(currentPos, zMax);
}
}
// Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
var xSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(xMax, xMin, fromPointsScratch));
var ySpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(yMax, yMin, fromPointsScratch));
var zSpan = Cartesian3.magnitudeSquared(Cartesian3.subtract(zMax, zMin, fromPointsScratch));
// Set the diameter endpoints to the largest span.
var diameter1 = xMin;
var diameter2 = xMax;
var maxSpan = xSpan;
if (ySpan > maxSpan) {
maxSpan = ySpan;
diameter1 = yMin;
diameter2 = yMax;
}
if (zSpan > maxSpan) {
maxSpan = zSpan;
diameter1 = zMin;
diameter2 = zMax;
}
// Calculate the center of the initial sphere found by Ritter's algorithm
var ritterCenter = fromPointsRitterCenter;
ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
// Calculate the radius of the initial sphere found by Ritter's algorithm
var radiusSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
var ritterRadius = Math.sqrt(radiusSquared);
// Find the center of the sphere found using the Naive method.
var minBoxPt = fromPointsMinBoxPt;
minBoxPt.x = xMin.x;
minBoxPt.y = yMin.y;
minBoxPt.z = zMin.z;
var maxBoxPt = fromPointsMaxBoxPt;
maxBoxPt.x = xMax.x;
maxBoxPt.y = yMax.y;
maxBoxPt.z = zMax.z;
var naiveCenter = Cartesian3.multiplyByScalar(Cartesian3.add(minBoxPt, maxBoxPt, fromPointsScratch), 0.5, fromPointsNaiveCenterScratch);
// Begin 2nd pass to find naive radius and modify the ritter sphere.
var naiveRadius = 0;
for (i = 0; i < numElements; i += 3) {
currentPos.x = positionsHigh[i] + positionsLow[i];
currentPos.y = positionsHigh[i + 1] + positionsLow[i + 1];
currentPos.z = positionsHigh[i + 2] + positionsLow[i + 2];
// Find the furthest point from the naive center to calculate the naive radius.
var r = Cartesian3.magnitude(Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
if (r > naiveRadius) {
naiveRadius = r;
}
// Make adjustments to the Ritter Sphere to include all points.
var oldCenterToPointSquared = Cartesian3.magnitudeSquared(Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
if (oldCenterToPointSquared > radiusSquared) {
var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
// Calculate new radius to include the point that lies outside
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
radiusSquared = ritterRadius * ritterRadius;
// Calculate center of new Ritter sphere
var oldToNew = oldCenterToPoint - ritterRadius;
ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
}
}
if (ritterRadius < naiveRadius) {
Cartesian3.clone(ritterCenter, result.center);
result.radius = ritterRadius;
} else {
Cartesian3.clone(naiveCenter, result.center);
result.radius = naiveRadius;
}
return result;
};
/**
* Computes a bounding sphere from the corner points of an axis-aligned bounding box. The sphere
* tighly and fully encompases the box.
*
* @param {Cartesian3} [corner] The minimum height over the rectangle.
* @param {Cartesian3} [oppositeCorner] The maximum height over the rectangle.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*
* @example
* // Create a bounding sphere around the unit cube
* var sphere = Cesium.BoundingSphere.fromCornerPoints(new Cesium.Cartesian3(-0.5, -0.5, -0.5), new Cesium.Cartesian3(0.5, 0.5, 0.5));
*/
BoundingSphere.fromCornerPoints = function(corner, oppositeCorner, result) {
if (!defined(corner) || !defined(oppositeCorner)) {
throw new DeveloperError('corner and oppositeCorner are required.');
}
if (!defined(result)) {
result = new BoundingSphere();
}
var center = result.center;
Cartesian3.add(corner, oppositeCorner, center);
Cartesian3.multiplyByScalar(center, 0.5, center);
result.radius = Cartesian3.distance(center, oppositeCorner);
return result;
};
/**
* Creates a bounding sphere encompassing an ellipsoid.
*
* @param {Ellipsoid} ellipsoid The ellipsoid around which to create a bounding sphere.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*
* @example
* var boundingSphere = Cesium.BoundingSphere.fromEllipsoid(ellipsoid);
*/
BoundingSphere.fromEllipsoid = function(ellipsoid, result) {
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
if (!defined(result)) {
result = new BoundingSphere();
}
Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = ellipsoid.maximumRadius;
return result;
};
var fromBoundingSpheresScratch = new Cartesian3();
/**
* Computes a tight-fitting bounding sphere enclosing the provided array of bounding spheres.
*
* @param {BoundingSphere[]} boundingSpheres The array of bounding spheres.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.fromBoundingSpheres = function(boundingSpheres, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
if (!defined(boundingSpheres) || boundingSpheres.length === 0) {
result.center = Cartesian3.clone(Cartesian3.ZERO, result.center);
result.radius = 0.0;
return result;
}
var length = boundingSpheres.length;
if (length === 1) {
return BoundingSphere.clone(boundingSpheres[0], result);
}
if (length === 2) {
return BoundingSphere.union(boundingSpheres[0], boundingSpheres[1], result);
}
var positions = [];
for (var i = 0; i < length; i++) {
positions.push(boundingSpheres[i].center);
}
result = BoundingSphere.fromPoints(positions, result);
var center = result.center;
var radius = result.radius;
for (i = 0; i < length; i++) {
var tmp = boundingSpheres[i];
radius = Math.max(radius, Cartesian3.distance(center, tmp.center, fromBoundingSpheresScratch) + tmp.radius);
}
result.radius = radius;
return result;
};
var fromOrientedBoundingBoxScratchU = new Cartesian3();
var fromOrientedBoundingBoxScratchV = new Cartesian3();
var fromOrientedBoundingBoxScratchW = new Cartesian3();
/**
* Computes a tight-fitting bounding sphere enclosing the provided oriented bounding box.
*
* @param {OrientedBoundingBox} orientedBoundingBox The oriented bounding box.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.fromOrientedBoundingBox = function(orientedBoundingBox, result) {
if (!defined(result)) {
result = new BoundingSphere();
}
var halfAxes = orientedBoundingBox.halfAxes;
var u = Matrix3.getColumn(halfAxes, 0, fromOrientedBoundingBoxScratchU);
var v = Matrix3.getColumn(halfAxes, 1, fromOrientedBoundingBoxScratchV);
var w = Matrix3.getColumn(halfAxes, 2, fromOrientedBoundingBoxScratchW);
var uHalf = Cartesian3.magnitude(u);
var vHalf = Cartesian3.magnitude(v);
var wHalf = Cartesian3.magnitude(w);
result.center = Cartesian3.clone(orientedBoundingBox.center, result.center);
result.radius = Math.max(uHalf, vHalf, wHalf);
return result;
};
/**
* Duplicates a BoundingSphere instance.
*
* @param {BoundingSphere} sphere The bounding sphere to duplicate.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided. (Returns undefined if sphere is undefined)
*/
BoundingSphere.clone = function(sphere, result) {
if (!defined(sphere)) {
return undefined;
}
if (!defined(result)) {
return new BoundingSphere(sphere.center, sphere.radius);
}
result.center = Cartesian3.clone(sphere.center, result.center);
result.radius = sphere.radius;
return result;
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
BoundingSphere.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {BoundingSphere} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
BoundingSphere.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
var center = value.center;
array[startingIndex++] = center.x;
array[startingIndex++] = center.y;
array[startingIndex++] = center.z;
array[startingIndex] = value.radius;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {BoundingSphere} [result] The object into which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
*/
BoundingSphere.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new BoundingSphere();
}
var center = result.center;
center.x = array[startingIndex++];
center.y = array[startingIndex++];
center.z = array[startingIndex++];
result.radius = array[startingIndex];
return result;
};
var unionScratch = new Cartesian3();
var unionScratchCenter = new Cartesian3();
/**
* Computes a bounding sphere that contains both the left and right bounding spheres.
*
* @param {BoundingSphere} left A sphere to enclose in a bounding sphere.
* @param {BoundingSphere} right A sphere to enclose in a bounding sphere.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.union = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(result)) {
result = new BoundingSphere();
}
var leftCenter = left.center;
var leftRadius = left.radius;
var rightCenter = right.center;
var rightRadius = right.radius;
var toRightCenter = Cartesian3.subtract(rightCenter, leftCenter, unionScratch);
var centerSeparation = Cartesian3.magnitude(toRightCenter);
if (leftRadius >= (centerSeparation + rightRadius)) {
// Left sphere wins.
left.clone(result);
return result;
}
if (rightRadius >= (centerSeparation + leftRadius)) {
// Right sphere wins.
right.clone(result);
return result;
}
// There are two tangent points, one on far side of each sphere.
var halfDistanceBetweenTangentPoints = (leftRadius + centerSeparation + rightRadius) * 0.5;
// Compute the center point halfway between the two tangent points.
var center = Cartesian3.multiplyByScalar(toRightCenter,
(-leftRadius + halfDistanceBetweenTangentPoints) / centerSeparation, unionScratchCenter);
Cartesian3.add(center, leftCenter, center);
Cartesian3.clone(center, result.center);
result.radius = halfDistanceBetweenTangentPoints;
return result;
};
var expandScratch = new Cartesian3();
/**
* Computes a bounding sphere by enlarging the provided sphere to contain the provided point.
*
* @param {BoundingSphere} sphere A sphere to expand.
* @param {Cartesian3} point A point to enclose in a bounding sphere.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.expand = function(sphere, point, result) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(point)) {
throw new DeveloperError('point is required.');
}
result = BoundingSphere.clone(sphere, result);
var radius = Cartesian3.magnitude(Cartesian3.subtract(point, result.center, expandScratch));
if (radius > result.radius) {
result.radius = radius;
}
return result;
};
/**
* Determines which side of a plane a sphere is located.
*
* @param {BoundingSphere} sphere The bounding sphere to test.
* @param {Plane} plane The plane to test against.
* @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
* the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
* on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
* intersects the plane.
*/
BoundingSphere.intersectPlane = function(sphere, plane) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
var center = sphere.center;
var radius = sphere.radius;
var normal = plane.normal;
var distanceToPlane = Cartesian3.dot(normal, center) + plane.distance;
if (distanceToPlane < -radius) {
// The center point is negative side of the plane normal
return Intersect.OUTSIDE;
} else if (distanceToPlane < radius) {
// The center point is positive side of the plane, but radius extends beyond it; partial overlap
return Intersect.INTERSECTING;
}
return Intersect.INSIDE;
};
/**
* Applies a 4x4 affine transformation matrix to a bounding sphere.
*
* @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
* @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.transform = function(sphere, transform, result) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(transform)) {
throw new DeveloperError('transform is required.');
}
if (!defined(result)) {
result = new BoundingSphere();
}
result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
result.radius = Matrix4.getMaximumScale(transform) * sphere.radius;
return result;
};
var distanceSquaredToScratch = new Cartesian3();
/**
* Computes the estimated distance squared from the closest point on a bounding sphere to a point.
*
* @param {BoundingSphere} sphere The sphere.
* @param {Cartesian3} cartesian The point
* @returns {Number} The estimated distance squared from the bounding sphere to the point.
*
* @example
* // Sort bounding spheres from back to front
* spheres.sort(function(a, b) {
* return Cesium.BoundingSphere.distanceSquaredTo(b, camera.positionWC) - Cesium.BoundingSphere.distanceSquaredTo(a, camera.positionWC);
* });
*/
BoundingSphere.distanceSquaredTo = function(sphere, cartesian) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
var diff = Cartesian3.subtract(sphere.center, cartesian, distanceSquaredToScratch);
return Cartesian3.magnitudeSquared(diff) - sphere.radius * sphere.radius;
};
/**
* Applies a 4x4 affine transformation matrix to a bounding sphere where there is no scale
* The transformation matrix is not verified to have a uniform scale of 1.
* This method is faster than computing the general bounding sphere transform using {@link BoundingSphere.transform}.
*
* @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
* @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*
* @example
* var modelMatrix = Cesium.Transforms.eastNorthUpToFixedFrame(positionOnEllipsoid);
* var boundingSphere = new Cesium.BoundingSphere();
* var newBoundingSphere = Cesium.BoundingSphere.transformWithoutScale(boundingSphere, modelMatrix);
*/
BoundingSphere.transformWithoutScale = function(sphere, transform, result) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(transform)) {
throw new DeveloperError('transform is required.');
}
if (!defined(result)) {
result = new BoundingSphere();
}
result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
result.radius = sphere.radius;
return result;
};
var scratchCartesian3 = new Cartesian3();
/**
* The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
* plus/minus the radius of the bounding sphere.
*
* If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
* closest and farthest planes from position that intersect the bounding sphere.
*
* @param {BoundingSphere} sphere The bounding sphere to calculate the distance to.
* @param {Cartesian3} position The position to calculate the distance from.
* @param {Cartesian3} direction The direction from position.
* @param {Interval} [result] A Interval to store the nearest and farthest distances.
* @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
*/
BoundingSphere.computePlaneDistances = function(sphere, position, direction, result) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(position)) {
throw new DeveloperError('position is required.');
}
if (!defined(direction)) {
throw new DeveloperError('direction is required.');
}
if (!defined(result)) {
result = new Interval();
}
var toCenter = Cartesian3.subtract(sphere.center, position, scratchCartesian3);
var mag = Cartesian3.dot(direction, toCenter);
result.start = mag - sphere.radius;
result.stop = mag + sphere.radius;
return result;
};
var projectTo2DNormalScratch = new Cartesian3();
var projectTo2DEastScratch = new Cartesian3();
var projectTo2DNorthScratch = new Cartesian3();
var projectTo2DWestScratch = new Cartesian3();
var projectTo2DSouthScratch = new Cartesian3();
var projectTo2DCartographicScratch = new Cartographic();
var projectTo2DPositionsScratch = new Array(8);
for (var n = 0; n < 8; ++n) {
projectTo2DPositionsScratch[n] = new Cartesian3();
}
var projectTo2DProjection = new GeographicProjection();
/**
* Creates a bounding sphere in 2D from a bounding sphere in 3D world coordinates.
*
* @param {BoundingSphere} sphere The bounding sphere to transform to 2D.
* @param {Object} [projection=GeographicProjection] The projection to 2D.
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.projectTo2D = function(sphere, projection, result) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
projection = defaultValue(projection, projectTo2DProjection);
var ellipsoid = projection.ellipsoid;
var center = sphere.center;
var radius = sphere.radius;
var normal = ellipsoid.geodeticSurfaceNormal(center, projectTo2DNormalScratch);
var east = Cartesian3.cross(Cartesian3.UNIT_Z, normal, projectTo2DEastScratch);
Cartesian3.normalize(east, east);
var north = Cartesian3.cross(normal, east, projectTo2DNorthScratch);
Cartesian3.normalize(north, north);
Cartesian3.multiplyByScalar(normal, radius, normal);
Cartesian3.multiplyByScalar(north, radius, north);
Cartesian3.multiplyByScalar(east, radius, east);
var south = Cartesian3.negate(north, projectTo2DSouthScratch);
var west = Cartesian3.negate(east, projectTo2DWestScratch);
var positions = projectTo2DPositionsScratch;
// top NE corner
var corner = positions[0];
Cartesian3.add(normal, north, corner);
Cartesian3.add(corner, east, corner);
// top NW corner
corner = positions[1];
Cartesian3.add(normal, north, corner);
Cartesian3.add(corner, west, corner);
// top SW corner
corner = positions[2];
Cartesian3.add(normal, south, corner);
Cartesian3.add(corner, west, corner);
// top SE corner
corner = positions[3];
Cartesian3.add(normal, south, corner);
Cartesian3.add(corner, east, corner);
Cartesian3.negate(normal, normal);
// bottom NE corner
corner = positions[4];
Cartesian3.add(normal, north, corner);
Cartesian3.add(corner, east, corner);
// bottom NW corner
corner = positions[5];
Cartesian3.add(normal, north, corner);
Cartesian3.add(corner, west, corner);
// bottom SW corner
corner = positions[6];
Cartesian3.add(normal, south, corner);
Cartesian3.add(corner, west, corner);
// bottom SE corner
corner = positions[7];
Cartesian3.add(normal, south, corner);
Cartesian3.add(corner, east, corner);
var length = positions.length;
for (var i = 0; i < length; ++i) {
var position = positions[i];
Cartesian3.add(center, position, position);
var cartographic = ellipsoid.cartesianToCartographic(position, projectTo2DCartographicScratch);
projection.project(cartographic, position);
}
result = BoundingSphere.fromPoints(positions, result);
// swizzle center components
center = result.center;
var x = center.x;
var y = center.y;
var z = center.z;
center.x = z;
center.y = x;
center.z = y;
return result;
};
/**
* Determines whether or not a sphere is hidden from view by the occluder.
*
* @param {BoundingSphere} sphere The bounding sphere surrounding the occludee object.
* @param {Occluder} occluder The occluder.
* @returns {Boolean} true if the sphere is not visible; otherwise false.
*/
BoundingSphere.isOccluded = function(sphere, occluder) {
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
if (!defined(occluder)) {
throw new DeveloperError('occluder is required.');
}
return !occluder.isBoundingSphereVisible(sphere);
};
/**
* Compares the provided BoundingSphere componentwise and returns
* true if they are equal, false otherwise.
*
* @param {BoundingSphere} [left] The first BoundingSphere.
* @param {BoundingSphere} [right] The second BoundingSphere.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
BoundingSphere.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
Cartesian3.equals(left.center, right.center) &&
left.radius === right.radius);
};
/**
* Determines which side of a plane the sphere is located.
*
* @param {Plane} plane The plane to test against.
* @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
* the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
* on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
* intersects the plane.
*/
BoundingSphere.prototype.intersectPlane = function(plane) {
return BoundingSphere.intersectPlane(this, plane);
};
/**
* Computes the estimated distance squared from the closest point on a bounding sphere to a point.
*
* @param {Cartesian3} cartesian The point
* @returns {Number} The estimated distance squared from the bounding sphere to the point.
*
* @example
* // Sort bounding spheres from back to front
* spheres.sort(function(a, b) {
* return b.distanceSquaredTo(camera.positionWC) - a.distanceSquaredTo(camera.positionWC);
* });
*/
BoundingSphere.prototype.distanceSquaredTo = function(cartesian) {
return BoundingSphere.distanceSquaredTo(this, cartesian);
};
/**
* The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
* plus/minus the radius of the bounding sphere.
*
* If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
* closest and farthest planes from position that intersect the bounding sphere.
*
* @param {Cartesian3} position The position to calculate the distance from.
* @param {Cartesian3} direction The direction from position.
* @param {Interval} [result] A Interval to store the nearest and farthest distances.
* @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
*/
BoundingSphere.prototype.computePlaneDistances = function(position, direction, result) {
return BoundingSphere.computePlaneDistances(this, position, direction, result);
};
/**
* Determines whether or not a sphere is hidden from view by the occluder.
*
* @param {Occluder} occluder The occluder.
* @returns {Boolean} true if the sphere is not visible; otherwise false.
*/
BoundingSphere.prototype.isOccluded = function(occluder) {
return BoundingSphere.isOccluded(this, occluder);
};
/**
* Compares this BoundingSphere against the provided BoundingSphere componentwise and returns
* true if they are equal, false otherwise.
*
* @param {BoundingSphere} [right] The right hand side BoundingSphere.
* @returns {Boolean} true if they are equal, false otherwise.
*/
BoundingSphere.prototype.equals = function(right) {
return BoundingSphere.equals(this, right);
};
/**
* Duplicates this BoundingSphere instance.
*
* @param {BoundingSphere} [result] The object onto which to store the result.
* @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
*/
BoundingSphere.prototype.clone = function(result) {
return BoundingSphere.clone(this, result);
};
return BoundingSphere;
});
/*global define*/
define('Core/Cartesian2',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./freezeObject',
'./Math'
], function(
defaultValue,
defined,
DeveloperError,
freezeObject,
CesiumMath) {
'use strict';
/**
* A 2D Cartesian point.
* @alias Cartesian2
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
*
* @see Cartesian3
* @see Cartesian4
* @see Packable
*/
function Cartesian2(x, y) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue(y, 0.0);
}
/**
* Creates a Cartesian2 instance from x and y coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromElements = function(x, y, result) {
if (!defined(result)) {
return new Cartesian2(x, y);
}
result.x = x;
result.y = y;
return result;
};
/**
* Duplicates a Cartesian2 instance.
*
* @param {Cartesian2} cartesian The Cartesian to duplicate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian2.clone = function(cartesian, result) {
if (!defined(cartesian)) {
return undefined;
}
if (!defined(result)) {
return new Cartesian2(cartesian.x, cartesian.y);
}
result.x = cartesian.x;
result.y = cartesian.y;
return result;
};
/**
* Creates a Cartesian2 instance from an existing Cartesian3. This simply takes the
* x and y properties of the Cartesian3 and drops z.
* @function
*
* @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian3 = Cartesian2.clone;
/**
* Creates a Cartesian2 instance from an existing Cartesian4. This simply takes the
* x and y properties of the Cartesian4 and drops z and w.
* @function
*
* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian4 = Cartesian2.clone;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian2.packedLength = 2;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian2} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian2.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex] = value.y;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian2} [result] The object into which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Cartesian2();
}
result.x = array[startingIndex++];
result.y = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian2s into and array of components.
*
* @param {Cartesian2[]} array The array of cartesians to pack.
* @param {Number[]} result The array onto which to store the result.
* @returns {Number[]} The packed array.
*/
Cartesian2.packArray = function(array, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
var length = array.length;
if (!defined(result)) {
result = new Array(length * 2);
} else {
result.length = length * 2;
}
for (var i = 0; i < length; ++i) {
Cartesian2.pack(array[i], result, i * 2);
}
return result;
};
/**
* Unpacks an array of cartesian components into and array of Cartesian2s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian2[]} result The array onto which to store the result.
* @returns {Cartesian2[]} The unpacked array.
*/
Cartesian2.unpackArray = function(array, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
var length = array.length;
if (!defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var index = i / 2;
result[index] = Cartesian2.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian2 from two consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*
* @example
* // Create a Cartesian2 with (1.0, 2.0)
* var v = [1.0, 2.0];
* var p = Cesium.Cartesian2.fromArray(v);
*
* // Create a Cartesian2 with (1.0, 2.0) using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 2.0];
* var p2 = Cesium.Cartesian2.fromArray(v2, 2);
*/
Cartesian2.fromArray = Cartesian2.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian2.maximumComponent = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return Math.max(cartesian.x, cartesian.y);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian2.minimumComponent = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return Math.min(cartesian.x, cartesian.y);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the minimum components.
*/
Cartesian2.minimumByComponent = function(first, second, result) {
if (!defined(first)) {
throw new DeveloperError('first is required.');
}
if (!defined(second)) {
throw new DeveloperError('second is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the maximum components.
*/
Cartesian2.maximumByComponent = function(first, second, result) {
if (!defined(first)) {
throw new DeveloperError('first is required.');
}
if (!defined(second)) {
throw new DeveloperError('second is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian2.magnitudeSquared = function(cartesian) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
return cartesian.x * cartesian.x + cartesian.y * cartesian.y;
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian2.magnitude = function(cartesian) {
return Math.sqrt(Cartesian2.magnitudeSquared(cartesian));
};
var distanceScratch = new Cartesian2();
/**
* Computes the distance between two points.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));
*/
Cartesian2.distance = function(left, right) {
if (!defined(left) || !defined(right)) {
throw new DeveloperError('left and right are required.');
}
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitude(distanceScratch);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian2#distance}.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));
*/
Cartesian2.distanceSquared = function(left, right) {
if (!defined(left) || !defined(right)) {
throw new DeveloperError('left and right are required.');
}
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitudeSquared(distanceScratch);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be normalized.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.normalize = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var magnitude = Cartesian2.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
if (isNaN(result.x) || isNaN(result.y)) {
throw new DeveloperError('normalized result is not a number');
}
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian2.dot = function(left, right) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
return left.x * right.x + left.y * right.y;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyComponents = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x * right.x;
result.y = left.y * right.y;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideComponents = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x / right.x;
result.y = left.y / right.y;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x + right.x;
result.y = left.y + right.y;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x - right.x;
result.y = left.y - right.y;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyByScalar = function(cartesian, scalar, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideByScalar = function(cartesian, scalar, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be negated.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.negate = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = -cartesian.x;
result.y = -cartesian.y;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.abs = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
return result;
};
var lerpScratch = new Cartesian2();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian2} start The value corresponding to t at 0.0.
* @param {Cartesian2} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.lerp = function(start, end, t, result) {
if (!defined(start)) {
throw new DeveloperError('start is required.');
}
if (!defined(end)) {
throw new DeveloperError('end is required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
Cartesian2.multiplyByScalar(end, t, lerpScratch);
result = Cartesian2.multiplyByScalar(start, 1.0 - t, result);
return Cartesian2.add(lerpScratch, result, result);
};
var angleBetweenScratch = new Cartesian2();
var angleBetweenScratch2 = new Cartesian2();
/**
* Returns the angle, in radians, between the provided Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The angle between the Cartesians.
*/
Cartesian2.angleBetween = function(left, right) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
Cartesian2.normalize(left, angleBetweenScratch);
Cartesian2.normalize(right, angleBetweenScratch2);
return CesiumMath.acosClamped(Cartesian2.dot(angleBetweenScratch, angleBetweenScratch2));
};
var mostOrthogonalAxisScratch = new Cartesian2();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The most orthogonal axis.
*/
Cartesian2.mostOrthogonalAxis = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
var f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch);
Cartesian2.abs(f, f);
if (f.x <= f.y) {
result = Cartesian2.clone(Cartesian2.UNIT_X, result);
} else {
result = Cartesian2.clone(Cartesian2.UNIT_Y, result);
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian2.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.x === right.x) &&
(left.y === right.y));
};
/**
* @private
*/
Cartesian2.equalsArray = function(cartesian, array, offset) {
return cartesian.x === array[offset] &&
cartesian.y === array[offset + 1];
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian2.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
return (left === right) ||
(defined(left) &&
defined(right) &&
CesiumMath.equalsEpsilon(left.x, right.x, relativeEpsilon, absoluteEpsilon) &&
CesiumMath.equalsEpsilon(left.y, right.y, relativeEpsilon, absoluteEpsilon));
};
/**
* An immutable Cartesian2 instance initialized to (0.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.ZERO = freezeObject(new Cartesian2(0.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (1.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_X = freezeObject(new Cartesian2(1.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (0.0, 1.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_Y = freezeObject(new Cartesian2(0.0, 1.0));
/**
* Duplicates this Cartesian2 instance.
*
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.prototype.clone = function(result) {
return Cartesian2.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian2.prototype.equals = function(right) {
return Cartesian2.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @param {Number} relativeEpsilon The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian2.prototype.equalsEpsilon = function(right, relativeEpsilon, absoluteEpsilon) {
return Cartesian2.equalsEpsilon(this, right, relativeEpsilon, absoluteEpsilon);
};
/**
* Creates a string representing this Cartesian in the format '(x, y)'.
*
* @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
*/
Cartesian2.prototype.toString = function() {
return '(' + this.x + ', ' + this.y + ')';
};
return Cartesian2;
});
/*global define*/
define('Core/Fullscreen',[
'./defined',
'./defineProperties'
], function(
defined,
defineProperties) {
'use strict';
var _supportsFullscreen;
var _names = {
requestFullscreen : undefined,
exitFullscreen : undefined,
fullscreenEnabled : undefined,
fullscreenElement : undefined,
fullscreenchange : undefined,
fullscreenerror : undefined
};
/**
* Browser-independent functions for working with the standard fullscreen API.
*
* @exports Fullscreen
*
* @see {@link http://dvcs.w3.org/hg/fullscreen/raw-file/tip/Overview.html|W3C Fullscreen Living Specification}
*/
var Fullscreen = {};
defineProperties(Fullscreen, {
/**
* The element that is currently fullscreen, if any. To simply check if the
* browser is in fullscreen mode or not, use {@link Fullscreen#fullscreen}.
* @memberof Fullscreen
* @type {Object}
* @readonly
*/
element : {
get : function() {
if (!Fullscreen.supportsFullscreen()) {
return undefined;
}
return document[_names.fullscreenElement];
}
},
/**
* The name of the event on the document that is fired when fullscreen is
* entered or exited. This event name is intended for use with addEventListener.
* In your event handler, to determine if the browser is in fullscreen mode or not,
* use {@link Fullscreen#fullscreen}.
* @memberof Fullscreen
* @type {String}
* @readonly
*/
changeEventName : {
get : function() {
if (!Fullscreen.supportsFullscreen()) {
return undefined;
}
return _names.fullscreenchange;
}
},
/**
* The name of the event that is fired when a fullscreen error
* occurs. This event name is intended for use with addEventListener.
* @memberof Fullscreen
* @type {String}
* @readonly
*/
errorEventName : {
get : function() {
if (!Fullscreen.supportsFullscreen()) {
return undefined;
}
return _names.fullscreenerror;
}
},
/**
* Determine whether the browser will allow an element to be made fullscreen, or not.
* For example, by default, iframes cannot go fullscreen unless the containing page
* adds an "allowfullscreen" attribute (or prefixed equivalent).
* @memberof Fullscreen
* @type {Boolean}
* @readonly
*/
enabled : {
get : function() {
if (!Fullscreen.supportsFullscreen()) {
return undefined;
}
return document[_names.fullscreenEnabled];
}
},
/**
* Determines if the browser is currently in fullscreen mode.
* @memberof Fullscreen
* @type {Boolean}
* @readonly
*/
fullscreen : {
get : function() {
if (!Fullscreen.supportsFullscreen()) {
return undefined;
}
return Fullscreen.element !== null;
}
}
});
/**
* Detects whether the browser supports the standard fullscreen API.
*
* @returns {Boolean} true if the browser supports the standard fullscreen API,
* false otherwise.
*/
Fullscreen.supportsFullscreen = function() {
if (defined(_supportsFullscreen)) {
return _supportsFullscreen;
}
_supportsFullscreen = false;
var body = document.body;
if (typeof body.requestFullscreen === 'function') {
// go with the unprefixed, standard set of names
_names.requestFullscreen = 'requestFullscreen';
_names.exitFullscreen = 'exitFullscreen';
_names.fullscreenEnabled = 'fullscreenEnabled';
_names.fullscreenElement = 'fullscreenElement';
_names.fullscreenchange = 'fullscreenchange';
_names.fullscreenerror = 'fullscreenerror';
_supportsFullscreen = true;
return _supportsFullscreen;
}
//check for the correct combination of prefix plus the various names that browsers use
var prefixes = ['webkit', 'moz', 'o', 'ms', 'khtml'];
var name;
for (var i = 0, len = prefixes.length; i < len; ++i) {
var prefix = prefixes[i];
// casing of Fullscreen differs across browsers
name = prefix + 'RequestFullscreen';
if (typeof body[name] === 'function') {
_names.requestFullscreen = name;
_supportsFullscreen = true;
} else {
name = prefix + 'RequestFullScreen';
if (typeof body[name] === 'function') {
_names.requestFullscreen = name;
_supportsFullscreen = true;
}
}
// disagreement about whether it's "exit" as per spec, or "cancel"
name = prefix + 'ExitFullscreen';
if (typeof document[name] === 'function') {
_names.exitFullscreen = name;
} else {
name = prefix + 'CancelFullScreen';
if (typeof document[name] === 'function') {
_names.exitFullscreen = name;
}
}
// casing of Fullscreen differs across browsers
name = prefix + 'FullscreenEnabled';
if (document[name] !== undefined) {
_names.fullscreenEnabled = name;
} else {
name = prefix + 'FullScreenEnabled';
if (document[name] !== undefined) {
_names.fullscreenEnabled = name;
}
}
// casing of Fullscreen differs across browsers
name = prefix + 'FullscreenElement';
if (document[name] !== undefined) {
_names.fullscreenElement = name;
} else {
name = prefix + 'FullScreenElement';
if (document[name] !== undefined) {
_names.fullscreenElement = name;
}
}
// thankfully, event names are all lowercase per spec
name = prefix + 'fullscreenchange';
// event names do not have 'on' in the front, but the property on the document does
if (document['on' + name] !== undefined) {
//except on IE
if (prefix === 'ms') {
name = 'MSFullscreenChange';
}
_names.fullscreenchange = name;
}
name = prefix + 'fullscreenerror';
if (document['on' + name] !== undefined) {
//except on IE
if (prefix === 'ms') {
name = 'MSFullscreenError';
}
_names.fullscreenerror = name;
}
}
return _supportsFullscreen;
};
/**
* Asynchronously requests the browser to enter fullscreen mode on the given element.
* If fullscreen mode is not supported by the browser, does nothing.
*
* @param {Object} element The HTML element which will be placed into fullscreen mode.
* @param {HMDVRDevice} [vrDevice] The VR device.
*
* @example
* // Put the entire page into fullscreen.
* Cesium.Fullscreen.requestFullscreen(document.body)
*
* // Place only the Cesium canvas into fullscreen.
* Cesium.Fullscreen.requestFullscreen(scene.canvas)
*/
Fullscreen.requestFullscreen = function(element, vrDevice) {
if (!Fullscreen.supportsFullscreen()) {
return;
}
element[_names.requestFullscreen]({ vrDisplay: vrDevice });
};
/**
* Asynchronously exits fullscreen mode. If the browser is not currently
* in fullscreen, or if fullscreen mode is not supported by the browser, does nothing.
*/
Fullscreen.exitFullscreen = function() {
if (!Fullscreen.supportsFullscreen()) {
return;
}
document[_names.exitFullscreen]();
};
return Fullscreen;
});
/*global define*/
define('Core/FeatureDetection',[
'./defaultValue',
'./defined',
'./Fullscreen'
], function(
defaultValue,
defined,
Fullscreen) {
'use strict';
var theNavigator;
if (typeof navigator !== 'undefined') {
theNavigator = navigator;
} else {
theNavigator = {};
}
function extractVersion(versionString) {
var parts = versionString.split('.');
for (var i = 0, len = parts.length; i < len; ++i) {
parts[i] = parseInt(parts[i], 10);
}
return parts;
}
var isChromeResult;
var chromeVersionResult;
function isChrome() {
if (!defined(isChromeResult)) {
isChromeResult = false;
// Edge contains Chrome in the user agent too
if (!isEdge()) {
var fields = (/ Chrome\/([\.0-9]+)/).exec(theNavigator.userAgent);
if (fields !== null) {
isChromeResult = true;
chromeVersionResult = extractVersion(fields[1]);
}
}
}
return isChromeResult;
}
function chromeVersion() {
return isChrome() && chromeVersionResult;
}
var isSafariResult;
var safariVersionResult;
function isSafari() {
if (!defined(isSafariResult)) {
isSafariResult = false;
// Chrome and Edge contain Safari in the user agent too
if (!isChrome() && !isEdge() && (/ Safari\/[\.0-9]+/).test(theNavigator.userAgent)) {
var fields = (/ Version\/([\.0-9]+)/).exec(theNavigator.userAgent);
if (fields !== null) {
isSafariResult = true;
safariVersionResult = extractVersion(fields[1]);
}
}
}
return isSafariResult;
}
function safariVersion() {
return isSafari() && safariVersionResult;
}
var isWebkitResult;
var webkitVersionResult;
function isWebkit() {
if (!defined(isWebkitResult)) {
isWebkitResult = false;
var fields = (/ AppleWebKit\/([\.0-9]+)(\+?)/).exec(theNavigator.userAgent);
if (fields !== null) {
isWebkitResult = true;
webkitVersionResult = extractVersion(fields[1]);
webkitVersionResult.isNightly = !!fields[2];
}
}
return isWebkitResult;
}
function webkitVersion() {
return isWebkit() && webkitVersionResult;
}
var isInternetExplorerResult;
var internetExplorerVersionResult;
function isInternetExplorer() {
if (!defined(isInternetExplorerResult)) {
isInternetExplorerResult = false;
var fields;
if (theNavigator.appName === 'Microsoft Internet Explorer') {
fields = /MSIE ([0-9]{1,}[\.0-9]{0,})/.exec(theNavigator.userAgent);
if (fields !== null) {
isInternetExplorerResult = true;
internetExplorerVersionResult = extractVersion(fields[1]);
}
} else if (theNavigator.appName === 'Netscape') {
fields = /Trident\/.*rv:([0-9]{1,}[\.0-9]{0,})/.exec(theNavigator.userAgent);
if (fields !== null) {
isInternetExplorerResult = true;
internetExplorerVersionResult = extractVersion(fields[1]);
}
}
}
return isInternetExplorerResult;
}
function internetExplorerVersion() {
return isInternetExplorer() && internetExplorerVersionResult;
}
var isEdgeResult;
var edgeVersionResult;
function isEdge() {
if (!defined(isEdgeResult)) {
isEdgeResult = false;
var fields = (/ Edge\/([\.0-9]+)/).exec(theNavigator.userAgent);
if (fields !== null) {
isEdgeResult = true;
edgeVersionResult = extractVersion(fields[1]);
}
}
return isEdgeResult;
}
function edgeVersion() {
return isEdge() && edgeVersionResult;
}
var isFirefoxResult;
var firefoxVersionResult;
function isFirefox() {
if (!defined(isFirefoxResult)) {
isFirefoxResult = false;
var fields = /Firefox\/([\.0-9]+)/.exec(theNavigator.userAgent);
if (fields !== null) {
isFirefoxResult = true;
firefoxVersionResult = extractVersion(fields[1]);
}
}
return isFirefoxResult;
}
var isWindowsResult;
function isWindows() {
if (!defined(isWindowsResult)) {
isWindowsResult = /Windows/i.test(theNavigator.appVersion);
}
return isWindowsResult;
}
function firefoxVersion() {
return isFirefox() && firefoxVersionResult;
}
var hasPointerEvents;
function supportsPointerEvents() {
if (!defined(hasPointerEvents)) {
//While navigator.pointerEnabled is deprecated in the W3C specification
//we still need to use it if it exists in order to support browsers
//that rely on it, such as the Windows WebBrowser control which defines
//PointerEvent but sets navigator.pointerEnabled to false.
hasPointerEvents = typeof PointerEvent !== 'undefined' && (!defined(theNavigator.pointerEnabled) || theNavigator.pointerEnabled);
}
return hasPointerEvents;
}
var imageRenderingValueResult;
var supportsImageRenderingPixelatedResult;
function supportsImageRenderingPixelated() {
if (!defined(supportsImageRenderingPixelatedResult)) {
var canvas = document.createElement('canvas');
canvas.setAttribute('style',
'image-rendering: -moz-crisp-edges;' +
'image-rendering: pixelated;');
//canvas.style.imageRendering will be undefined, null or an empty string on unsupported browsers.
var tmp = canvas.style.imageRendering;
supportsImageRenderingPixelatedResult = defined(tmp) && tmp !== '';
if (supportsImageRenderingPixelatedResult) {
imageRenderingValueResult = tmp;
}
}
return supportsImageRenderingPixelatedResult;
}
function imageRenderingValue() {
return supportsImageRenderingPixelated() ? imageRenderingValueResult : undefined;
}
/**
* A set of functions to detect whether the current browser supports
* various features.
*
* @exports FeatureDetection
*/
var FeatureDetection = {
isChrome : isChrome,
chromeVersion : chromeVersion,
isSafari : isSafari,
safariVersion : safariVersion,
isWebkit : isWebkit,
webkitVersion : webkitVersion,
isInternetExplorer : isInternetExplorer,
internetExplorerVersion : internetExplorerVersion,
isEdge : isEdge,
edgeVersion : edgeVersion,
isFirefox : isFirefox,
firefoxVersion : firefoxVersion,
isWindows : isWindows,
hardwareConcurrency : defaultValue(theNavigator.hardwareConcurrency, 3),
supportsPointerEvents : supportsPointerEvents,
supportsImageRenderingPixelated: supportsImageRenderingPixelated,
imageRenderingValue: imageRenderingValue
};
/**
* Detects whether the current browser supports the full screen standard.
*
* @returns {Boolean} true if the browser supports the full screen standard, false if not.
*
* @see Fullscreen
* @see {@link http://dvcs.w3.org/hg/fullscreen/raw-file/tip/Overview.html|W3C Fullscreen Living Specification}
*/
FeatureDetection.supportsFullscreen = function() {
return Fullscreen.supportsFullscreen();
};
/**
* Detects whether the current browser supports typed arrays.
*
* @returns {Boolean} true if the browser supports typed arrays, false if not.
*
* @see {@link http://www.khronos.org/registry/typedarray/specs/latest/|Typed Array Specification}
*/
FeatureDetection.supportsTypedArrays = function() {
return typeof ArrayBuffer !== 'undefined';
};
/**
* Detects whether the current browser supports Web Workers.
*
* @returns {Boolean} true if the browsers supports Web Workers, false if not.
*
* @see {@link http://www.w3.org/TR/workers/}
*/
FeatureDetection.supportsWebWorkers = function() {
return typeof Worker !== 'undefined';
};
return FeatureDetection;
});
/*global define*/
define('Core/WebGLConstants',[
'./freezeObject'
], function(
freezeObject) {
'use strict';
/**
* Enum containing WebGL Constant values by name.
* for use without an active WebGL context, or in cases where certain constants are unavailable using the WebGL context
* (For example, in [Safari 9]{@link https://github.com/AnalyticalGraphicsInc/cesium/issues/2989}).
*
* These match the constants from the [WebGL 1.0]{@link https://www.khronos.org/registry/webgl/specs/latest/1.0/}
* and [WebGL 2.0]{@link https://www.khronos.org/registry/webgl/specs/latest/2.0/}
* specifications.
*
* @exports WebGLConstants
*/
var WebGLConstants = {
DEPTH_BUFFER_BIT : 0x00000100,
STENCIL_BUFFER_BIT : 0x00000400,
COLOR_BUFFER_BIT : 0x00004000,
POINTS : 0x0000,
LINES : 0x0001,
LINE_LOOP : 0x0002,
LINE_STRIP : 0x0003,
TRIANGLES : 0x0004,
TRIANGLE_STRIP : 0x0005,
TRIANGLE_FAN : 0x0006,
ZERO : 0,
ONE : 1,
SRC_COLOR : 0x0300,
ONE_MINUS_SRC_COLOR : 0x0301,
SRC_ALPHA : 0x0302,
ONE_MINUS_SRC_ALPHA : 0x0303,
DST_ALPHA : 0x0304,
ONE_MINUS_DST_ALPHA : 0x0305,
DST_COLOR : 0x0306,
ONE_MINUS_DST_COLOR : 0x0307,
SRC_ALPHA_SATURATE : 0x0308,
FUNC_ADD : 0x8006,
BLEND_EQUATION : 0x8009,
BLEND_EQUATION_RGB : 0x8009, // same as BLEND_EQUATION
BLEND_EQUATION_ALPHA : 0x883D,
FUNC_SUBTRACT : 0x800A,
FUNC_REVERSE_SUBTRACT : 0x800B,
BLEND_DST_RGB : 0x80C8,
BLEND_SRC_RGB : 0x80C9,
BLEND_DST_ALPHA : 0x80CA,
BLEND_SRC_ALPHA : 0x80CB,
CONSTANT_COLOR : 0x8001,
ONE_MINUS_CONSTANT_COLOR : 0x8002,
CONSTANT_ALPHA : 0x8003,
ONE_MINUS_CONSTANT_ALPHA : 0x8004,
BLEND_COLOR : 0x8005,
ARRAY_BUFFER : 0x8892,
ELEMENT_ARRAY_BUFFER : 0x8893,
ARRAY_BUFFER_BINDING : 0x8894,
ELEMENT_ARRAY_BUFFER_BINDING : 0x8895,
STREAM_DRAW : 0x88E0,
STATIC_DRAW : 0x88E4,
DYNAMIC_DRAW : 0x88E8,
BUFFER_SIZE : 0x8764,
BUFFER_USAGE : 0x8765,
CURRENT_VERTEX_ATTRIB : 0x8626,
FRONT : 0x0404,
BACK : 0x0405,
FRONT_AND_BACK : 0x0408,
CULL_FACE : 0x0B44,
BLEND : 0x0BE2,
DITHER : 0x0BD0,
STENCIL_TEST : 0x0B90,
DEPTH_TEST : 0x0B71,
SCISSOR_TEST : 0x0C11,
POLYGON_OFFSET_FILL : 0x8037,
SAMPLE_ALPHA_TO_COVERAGE : 0x809E,
SAMPLE_COVERAGE : 0x80A0,
NO_ERROR : 0,
INVALID_ENUM : 0x0500,
INVALID_VALUE : 0x0501,
INVALID_OPERATION : 0x0502,
OUT_OF_MEMORY : 0x0505,
CW : 0x0900,
CCW : 0x0901,
LINE_WIDTH : 0x0B21,
ALIASED_POINT_SIZE_RANGE : 0x846D,
ALIASED_LINE_WIDTH_RANGE : 0x846E,
CULL_FACE_MODE : 0x0B45,
FRONT_FACE : 0x0B46,
DEPTH_RANGE : 0x0B70,
DEPTH_WRITEMASK : 0x0B72,
DEPTH_CLEAR_VALUE : 0x0B73,
DEPTH_FUNC : 0x0B74,
STENCIL_CLEAR_VALUE : 0x0B91,
STENCIL_FUNC : 0x0B92,
STENCIL_FAIL : 0x0B94,
STENCIL_PASS_DEPTH_FAIL : 0x0B95,
STENCIL_PASS_DEPTH_PASS : 0x0B96,
STENCIL_REF : 0x0B97,
STENCIL_VALUE_MASK : 0x0B93,
STENCIL_WRITEMASK : 0x0B98,
STENCIL_BACK_FUNC : 0x8800,
STENCIL_BACK_FAIL : 0x8801,
STENCIL_BACK_PASS_DEPTH_FAIL : 0x8802,
STENCIL_BACK_PASS_DEPTH_PASS : 0x8803,
STENCIL_BACK_REF : 0x8CA3,
STENCIL_BACK_VALUE_MASK : 0x8CA4,
STENCIL_BACK_WRITEMASK : 0x8CA5,
VIEWPORT : 0x0BA2,
SCISSOR_BOX : 0x0C10,
COLOR_CLEAR_VALUE : 0x0C22,
COLOR_WRITEMASK : 0x0C23,
UNPACK_ALIGNMENT : 0x0CF5,
PACK_ALIGNMENT : 0x0D05,
MAX_TEXTURE_SIZE : 0x0D33,
MAX_VIEWPORT_DIMS : 0x0D3A,
SUBPIXEL_BITS : 0x0D50,
RED_BITS : 0x0D52,
GREEN_BITS : 0x0D53,
BLUE_BITS : 0x0D54,
ALPHA_BITS : 0x0D55,
DEPTH_BITS : 0x0D56,
STENCIL_BITS : 0x0D57,
POLYGON_OFFSET_UNITS : 0x2A00,
POLYGON_OFFSET_FACTOR : 0x8038,
TEXTURE_BINDING_2D : 0x8069,
SAMPLE_BUFFERS : 0x80A8,
SAMPLES : 0x80A9,
SAMPLE_COVERAGE_VALUE : 0x80AA,
SAMPLE_COVERAGE_INVERT : 0x80AB,
COMPRESSED_TEXTURE_FORMATS : 0x86A3,
DONT_CARE : 0x1100,
FASTEST : 0x1101,
NICEST : 0x1102,
GENERATE_MIPMAP_HINT : 0x8192,
BYTE : 0x1400,
UNSIGNED_BYTE : 0x1401,
SHORT : 0x1402,
UNSIGNED_SHORT : 0x1403,
INT : 0x1404,
UNSIGNED_INT : 0x1405,
FLOAT : 0x1406,
DEPTH_COMPONENT : 0x1902,
ALPHA : 0x1906,
RGB : 0x1907,
RGBA : 0x1908,
LUMINANCE : 0x1909,
LUMINANCE_ALPHA : 0x190A,
UNSIGNED_SHORT_4_4_4_4 : 0x8033,
UNSIGNED_SHORT_5_5_5_1 : 0x8034,
UNSIGNED_SHORT_5_6_5 : 0x8363,
FRAGMENT_SHADER : 0x8B30,
VERTEX_SHADER : 0x8B31,
MAX_VERTEX_ATTRIBS : 0x8869,
MAX_VERTEX_UNIFORM_VECTORS : 0x8DFB,
MAX_VARYING_VECTORS : 0x8DFC,
MAX_COMBINED_TEXTURE_IMAGE_UNITS : 0x8B4D,
MAX_VERTEX_TEXTURE_IMAGE_UNITS : 0x8B4C,
MAX_TEXTURE_IMAGE_UNITS : 0x8872,
MAX_FRAGMENT_UNIFORM_VECTORS : 0x8DFD,
SHADER_TYPE : 0x8B4F,
DELETE_STATUS : 0x8B80,
LINK_STATUS : 0x8B82,
VALIDATE_STATUS : 0x8B83,
ATTACHED_SHADERS : 0x8B85,
ACTIVE_UNIFORMS : 0x8B86,
ACTIVE_ATTRIBUTES : 0x8B89,
SHADING_LANGUAGE_VERSION : 0x8B8C,
CURRENT_PROGRAM : 0x8B8D,
NEVER : 0x0200,
LESS : 0x0201,
EQUAL : 0x0202,
LEQUAL : 0x0203,
GREATER : 0x0204,
NOTEQUAL : 0x0205,
GEQUAL : 0x0206,
ALWAYS : 0x0207,
KEEP : 0x1E00,
REPLACE : 0x1E01,
INCR : 0x1E02,
DECR : 0x1E03,
INVERT : 0x150A,
INCR_WRAP : 0x8507,
DECR_WRAP : 0x8508,
VENDOR : 0x1F00,
RENDERER : 0x1F01,
VERSION : 0x1F02,
NEAREST : 0x2600,
LINEAR : 0x2601,
NEAREST_MIPMAP_NEAREST : 0x2700,
LINEAR_MIPMAP_NEAREST : 0x2701,
NEAREST_MIPMAP_LINEAR : 0x2702,
LINEAR_MIPMAP_LINEAR : 0x2703,
TEXTURE_MAG_FILTER : 0x2800,
TEXTURE_MIN_FILTER : 0x2801,
TEXTURE_WRAP_S : 0x2802,
TEXTURE_WRAP_T : 0x2803,
TEXTURE_2D : 0x0DE1,
TEXTURE : 0x1702,
TEXTURE_CUBE_MAP : 0x8513,
TEXTURE_BINDING_CUBE_MAP : 0x8514,
TEXTURE_CUBE_MAP_POSITIVE_X : 0x8515,
TEXTURE_CUBE_MAP_NEGATIVE_X : 0x8516,
TEXTURE_CUBE_MAP_POSITIVE_Y : 0x8517,
TEXTURE_CUBE_MAP_NEGATIVE_Y : 0x8518,
TEXTURE_CUBE_MAP_POSITIVE_Z : 0x8519,
TEXTURE_CUBE_MAP_NEGATIVE_Z : 0x851A,
MAX_CUBE_MAP_TEXTURE_SIZE : 0x851C,
TEXTURE0 : 0x84C0,
TEXTURE1 : 0x84C1,
TEXTURE2 : 0x84C2,
TEXTURE3 : 0x84C3,
TEXTURE4 : 0x84C4,
TEXTURE5 : 0x84C5,
TEXTURE6 : 0x84C6,
TEXTURE7 : 0x84C7,
TEXTURE8 : 0x84C8,
TEXTURE9 : 0x84C9,
TEXTURE10 : 0x84CA,
TEXTURE11 : 0x84CB,
TEXTURE12 : 0x84CC,
TEXTURE13 : 0x84CD,
TEXTURE14 : 0x84CE,
TEXTURE15 : 0x84CF,
TEXTURE16 : 0x84D0,
TEXTURE17 : 0x84D1,
TEXTURE18 : 0x84D2,
TEXTURE19 : 0x84D3,
TEXTURE20 : 0x84D4,
TEXTURE21 : 0x84D5,
TEXTURE22 : 0x84D6,
TEXTURE23 : 0x84D7,
TEXTURE24 : 0x84D8,
TEXTURE25 : 0x84D9,
TEXTURE26 : 0x84DA,
TEXTURE27 : 0x84DB,
TEXTURE28 : 0x84DC,
TEXTURE29 : 0x84DD,
TEXTURE30 : 0x84DE,
TEXTURE31 : 0x84DF,
ACTIVE_TEXTURE : 0x84E0,
REPEAT : 0x2901,
CLAMP_TO_EDGE : 0x812F,
MIRRORED_REPEAT : 0x8370,
FLOAT_VEC2 : 0x8B50,
FLOAT_VEC3 : 0x8B51,
FLOAT_VEC4 : 0x8B52,
INT_VEC2 : 0x8B53,
INT_VEC3 : 0x8B54,
INT_VEC4 : 0x8B55,
BOOL : 0x8B56,
BOOL_VEC2 : 0x8B57,
BOOL_VEC3 : 0x8B58,
BOOL_VEC4 : 0x8B59,
FLOAT_MAT2 : 0x8B5A,
FLOAT_MAT3 : 0x8B5B,
FLOAT_MAT4 : 0x8B5C,
SAMPLER_2D : 0x8B5E,
SAMPLER_CUBE : 0x8B60,
VERTEX_ATTRIB_ARRAY_ENABLED : 0x8622,
VERTEX_ATTRIB_ARRAY_SIZE : 0x8623,
VERTEX_ATTRIB_ARRAY_STRIDE : 0x8624,
VERTEX_ATTRIB_ARRAY_TYPE : 0x8625,
VERTEX_ATTRIB_ARRAY_NORMALIZED : 0x886A,
VERTEX_ATTRIB_ARRAY_POINTER : 0x8645,
VERTEX_ATTRIB_ARRAY_BUFFER_BINDING : 0x889F,
IMPLEMENTATION_COLOR_READ_TYPE : 0x8B9A,
IMPLEMENTATION_COLOR_READ_FORMAT : 0x8B9B,
COMPILE_STATUS : 0x8B81,
LOW_FLOAT : 0x8DF0,
MEDIUM_FLOAT : 0x8DF1,
HIGH_FLOAT : 0x8DF2,
LOW_INT : 0x8DF3,
MEDIUM_INT : 0x8DF4,
HIGH_INT : 0x8DF5,
FRAMEBUFFER : 0x8D40,
RENDERBUFFER : 0x8D41,
RGBA4 : 0x8056,
RGB5_A1 : 0x8057,
RGB565 : 0x8D62,
DEPTH_COMPONENT16 : 0x81A5,
STENCIL_INDEX : 0x1901,
STENCIL_INDEX8 : 0x8D48,
DEPTH_STENCIL : 0x84F9,
RENDERBUFFER_WIDTH : 0x8D42,
RENDERBUFFER_HEIGHT : 0x8D43,
RENDERBUFFER_INTERNAL_FORMAT : 0x8D44,
RENDERBUFFER_RED_SIZE : 0x8D50,
RENDERBUFFER_GREEN_SIZE : 0x8D51,
RENDERBUFFER_BLUE_SIZE : 0x8D52,
RENDERBUFFER_ALPHA_SIZE : 0x8D53,
RENDERBUFFER_DEPTH_SIZE : 0x8D54,
RENDERBUFFER_STENCIL_SIZE : 0x8D55,
FRAMEBUFFER_ATTACHMENT_OBJECT_TYPE : 0x8CD0,
FRAMEBUFFER_ATTACHMENT_OBJECT_NAME : 0x8CD1,
FRAMEBUFFER_ATTACHMENT_TEXTURE_LEVEL : 0x8CD2,
FRAMEBUFFER_ATTACHMENT_TEXTURE_CUBE_MAP_FACE : 0x8CD3,
COLOR_ATTACHMENT0 : 0x8CE0,
DEPTH_ATTACHMENT : 0x8D00,
STENCIL_ATTACHMENT : 0x8D20,
DEPTH_STENCIL_ATTACHMENT : 0x821A,
NONE : 0,
FRAMEBUFFER_COMPLETE : 0x8CD5,
FRAMEBUFFER_INCOMPLETE_ATTACHMENT : 0x8CD6,
FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT : 0x8CD7,
FRAMEBUFFER_INCOMPLETE_DIMENSIONS : 0x8CD9,
FRAMEBUFFER_UNSUPPORTED : 0x8CDD,
FRAMEBUFFER_BINDING : 0x8CA6,
RENDERBUFFER_BINDING : 0x8CA7,
MAX_RENDERBUFFER_SIZE : 0x84E8,
INVALID_FRAMEBUFFER_OPERATION : 0x0506,
UNPACK_FLIP_Y_WEBGL : 0x9240,
UNPACK_PREMULTIPLY_ALPHA_WEBGL : 0x9241,
CONTEXT_LOST_WEBGL : 0x9242,
UNPACK_COLORSPACE_CONVERSION_WEBGL : 0x9243,
BROWSER_DEFAULT_WEBGL : 0x9244,
// Desktop OpenGL
DOUBLE : 0x140A,
// WebGL 2
READ_BUFFER : 0x0C02,
UNPACK_ROW_LENGTH : 0x0CF2,
UNPACK_SKIP_ROWS : 0x0CF3,
UNPACK_SKIP_PIXELS : 0x0CF4,
PACK_ROW_LENGTH : 0x0D02,
PACK_SKIP_ROWS : 0x0D03,
PACK_SKIP_PIXELS : 0x0D04,
COLOR : 0x1800,
DEPTH : 0x1801,
STENCIL : 0x1802,
RED : 0x1903,
RGB8 : 0x8051,
RGBA8 : 0x8058,
RGB10_A2 : 0x8059,
TEXTURE_BINDING_3D : 0x806A,
UNPACK_SKIP_IMAGES : 0x806D,
UNPACK_IMAGE_HEIGHT : 0x806E,
TEXTURE_3D : 0x806F,
TEXTURE_WRAP_R : 0x8072,
MAX_3D_TEXTURE_SIZE : 0x8073,
UNSIGNED_INT_2_10_10_10_REV : 0x8368,
MAX_ELEMENTS_VERTICES : 0x80E8,
MAX_ELEMENTS_INDICES : 0x80E9,
TEXTURE_MIN_LOD : 0x813A,
TEXTURE_MAX_LOD : 0x813B,
TEXTURE_BASE_LEVEL : 0x813C,
TEXTURE_MAX_LEVEL : 0x813D,
MIN : 0x8007,
MAX : 0x8008,
DEPTH_COMPONENT24 : 0x81A6,
MAX_TEXTURE_LOD_BIAS : 0x84FD,
TEXTURE_COMPARE_MODE : 0x884C,
TEXTURE_COMPARE_FUNC : 0x884D,
CURRENT_QUERY : 0x8865,
QUERY_RESULT : 0x8866,
QUERY_RESULT_AVAILABLE : 0x8867,
STREAM_READ : 0x88E1,
STREAM_COPY : 0x88E2,
STATIC_READ : 0x88E5,
STATIC_COPY : 0x88E6,
DYNAMIC_READ : 0x88E9,
DYNAMIC_COPY : 0x88EA,
MAX_DRAW_BUFFERS : 0x8824,
DRAW_BUFFER0 : 0x8825,
DRAW_BUFFER1 : 0x8826,
DRAW_BUFFER2 : 0x8827,
DRAW_BUFFER3 : 0x8828,
DRAW_BUFFER4 : 0x8829,
DRAW_BUFFER5 : 0x882A,
DRAW_BUFFER6 : 0x882B,
DRAW_BUFFER7 : 0x882C,
DRAW_BUFFER8 : 0x882D,
DRAW_BUFFER9 : 0x882E,
DRAW_BUFFER10 : 0x882F,
DRAW_BUFFER11 : 0x8830,
DRAW_BUFFER12 : 0x8831,
DRAW_BUFFER13 : 0x8832,
DRAW_BUFFER14 : 0x8833,
DRAW_BUFFER15 : 0x8834,
MAX_FRAGMENT_UNIFORM_COMPONENTS : 0x8B49,
MAX_VERTEX_UNIFORM_COMPONENTS : 0x8B4A,
SAMPLER_3D : 0x8B5F,
SAMPLER_2D_SHADOW : 0x8B62,
FRAGMENT_SHADER_DERIVATIVE_HINT : 0x8B8B,
PIXEL_PACK_BUFFER : 0x88EB,
PIXEL_UNPACK_BUFFER : 0x88EC,
PIXEL_PACK_BUFFER_BINDING : 0x88ED,
PIXEL_UNPACK_BUFFER_BINDING : 0x88EF,
FLOAT_MAT2x3 : 0x8B65,
FLOAT_MAT2x4 : 0x8B66,
FLOAT_MAT3x2 : 0x8B67,
FLOAT_MAT3x4 : 0x8B68,
FLOAT_MAT4x2 : 0x8B69,
FLOAT_MAT4x3 : 0x8B6A,
SRGB : 0x8C40,
SRGB8 : 0x8C41,
SRGB8_ALPHA8 : 0x8C43,
COMPARE_REF_TO_TEXTURE : 0x884E,
RGBA32F : 0x8814,
RGB32F : 0x8815,
RGBA16F : 0x881A,
RGB16F : 0x881B,
VERTEX_ATTRIB_ARRAY_INTEGER : 0x88FD,
MAX_ARRAY_TEXTURE_LAYERS : 0x88FF,
MIN_PROGRAM_TEXEL_OFFSET : 0x8904,
MAX_PROGRAM_TEXEL_OFFSET : 0x8905,
MAX_VARYING_COMPONENTS : 0x8B4B,
TEXTURE_2D_ARRAY : 0x8C1A,
TEXTURE_BINDING_2D_ARRAY : 0x8C1D,
R11F_G11F_B10F : 0x8C3A,
UNSIGNED_INT_10F_11F_11F_REV : 0x8C3B,
RGB9_E5 : 0x8C3D,
UNSIGNED_INT_5_9_9_9_REV : 0x8C3E,
TRANSFORM_FEEDBACK_BUFFER_MODE : 0x8C7F,
MAX_TRANSFORM_FEEDBACK_SEPARATE_COMPONENTS : 0x8C80,
TRANSFORM_FEEDBACK_VARYINGS : 0x8C83,
TRANSFORM_FEEDBACK_BUFFER_START : 0x8C84,
TRANSFORM_FEEDBACK_BUFFER_SIZE : 0x8C85,
TRANSFORM_FEEDBACK_PRIMITIVES_WRITTEN : 0x8C88,
RASTERIZER_DISCARD : 0x8C89,
MAX_TRANSFORM_FEEDBACK_INTERLEAVED_COMPONENTS : 0x8C8A,
MAX_TRANSFORM_FEEDBACK_SEPARATE_ATTRIBS : 0x8C8B,
INTERLEAVED_ATTRIBS : 0x8C8C,
SEPARATE_ATTRIBS : 0x8C8D,
TRANSFORM_FEEDBACK_BUFFER : 0x8C8E,
TRANSFORM_FEEDBACK_BUFFER_BINDING : 0x8C8F,
RGBA32UI : 0x8D70,
RGB32UI : 0x8D71,
RGBA16UI : 0x8D76,
RGB16UI : 0x8D77,
RGBA8UI : 0x8D7C,
RGB8UI : 0x8D7D,
RGBA32I : 0x8D82,
RGB32I : 0x8D83,
RGBA16I : 0x8D88,
RGB16I : 0x8D89,
RGBA8I : 0x8D8E,
RGB8I : 0x8D8F,
RED_INTEGER : 0x8D94,
RGB_INTEGER : 0x8D98,
RGBA_INTEGER : 0x8D99,
SAMPLER_2D_ARRAY : 0x8DC1,
SAMPLER_2D_ARRAY_SHADOW : 0x8DC4,
SAMPLER_CUBE_SHADOW : 0x8DC5,
UNSIGNED_INT_VEC2 : 0x8DC6,
UNSIGNED_INT_VEC3 : 0x8DC7,
UNSIGNED_INT_VEC4 : 0x8DC8,
INT_SAMPLER_2D : 0x8DCA,
INT_SAMPLER_3D : 0x8DCB,
INT_SAMPLER_CUBE : 0x8DCC,
INT_SAMPLER_2D_ARRAY : 0x8DCF,
UNSIGNED_INT_SAMPLER_2D : 0x8DD2,
UNSIGNED_INT_SAMPLER_3D : 0x8DD3,
UNSIGNED_INT_SAMPLER_CUBE : 0x8DD4,
UNSIGNED_INT_SAMPLER_2D_ARRAY : 0x8DD7,
DEPTH_COMPONENT32F : 0x8CAC,
DEPTH32F_STENCIL8 : 0x8CAD,
FLOAT_32_UNSIGNED_INT_24_8_REV : 0x8DAD,
FRAMEBUFFER_ATTACHMENT_COLOR_ENCODING : 0x8210,
FRAMEBUFFER_ATTACHMENT_COMPONENT_TYPE : 0x8211,
FRAMEBUFFER_ATTACHMENT_RED_SIZE : 0x8212,
FRAMEBUFFER_ATTACHMENT_GREEN_SIZE : 0x8213,
FRAMEBUFFER_ATTACHMENT_BLUE_SIZE : 0x8214,
FRAMEBUFFER_ATTACHMENT_ALPHA_SIZE : 0x8215,
FRAMEBUFFER_ATTACHMENT_DEPTH_SIZE : 0x8216,
FRAMEBUFFER_ATTACHMENT_STENCIL_SIZE : 0x8217,
FRAMEBUFFER_DEFAULT : 0x8218,
UNSIGNED_INT_24_8 : 0x84FA,
DEPTH24_STENCIL8 : 0x88F0,
UNSIGNED_NORMALIZED : 0x8C17,
DRAW_FRAMEBUFFER_BINDING : 0x8CA6, // Same as FRAMEBUFFER_BINDING
READ_FRAMEBUFFER : 0x8CA8,
DRAW_FRAMEBUFFER : 0x8CA9,
READ_FRAMEBUFFER_BINDING : 0x8CAA,
RENDERBUFFER_SAMPLES : 0x8CAB,
FRAMEBUFFER_ATTACHMENT_TEXTURE_LAYER : 0x8CD4,
MAX_COLOR_ATTACHMENTS : 0x8CDF,
COLOR_ATTACHMENT1 : 0x8CE1,
COLOR_ATTACHMENT2 : 0x8CE2,
COLOR_ATTACHMENT3 : 0x8CE3,
COLOR_ATTACHMENT4 : 0x8CE4,
COLOR_ATTACHMENT5 : 0x8CE5,
COLOR_ATTACHMENT6 : 0x8CE6,
COLOR_ATTACHMENT7 : 0x8CE7,
COLOR_ATTACHMENT8 : 0x8CE8,
COLOR_ATTACHMENT9 : 0x8CE9,
COLOR_ATTACHMENT10 : 0x8CEA,
COLOR_ATTACHMENT11 : 0x8CEB,
COLOR_ATTACHMENT12 : 0x8CEC,
COLOR_ATTACHMENT13 : 0x8CED,
COLOR_ATTACHMENT14 : 0x8CEE,
COLOR_ATTACHMENT15 : 0x8CEF,
FRAMEBUFFER_INCOMPLETE_MULTISAMPLE : 0x8D56,
MAX_SAMPLES : 0x8D57,
HALF_FLOAT : 0x140B,
RG : 0x8227,
RG_INTEGER : 0x8228,
R8 : 0x8229,
RG8 : 0x822B,
R16F : 0x822D,
R32F : 0x822E,
RG16F : 0x822F,
RG32F : 0x8230,
R8I : 0x8231,
R8UI : 0x8232,
R16I : 0x8233,
R16UI : 0x8234,
R32I : 0x8235,
R32UI : 0x8236,
RG8I : 0x8237,
RG8UI : 0x8238,
RG16I : 0x8239,
RG16UI : 0x823A,
RG32I : 0x823B,
RG32UI : 0x823C,
VERTEX_ARRAY_BINDING : 0x85B5,
R8_SNORM : 0x8F94,
RG8_SNORM : 0x8F95,
RGB8_SNORM : 0x8F96,
RGBA8_SNORM : 0x8F97,
SIGNED_NORMALIZED : 0x8F9C,
COPY_READ_BUFFER : 0x8F36,
COPY_WRITE_BUFFER : 0x8F37,
COPY_READ_BUFFER_BINDING : 0x8F36, // Same as COPY_READ_BUFFER
COPY_WRITE_BUFFER_BINDING : 0x8F37, // Same as COPY_WRITE_BUFFER
UNIFORM_BUFFER : 0x8A11,
UNIFORM_BUFFER_BINDING : 0x8A28,
UNIFORM_BUFFER_START : 0x8A29,
UNIFORM_BUFFER_SIZE : 0x8A2A,
MAX_VERTEX_UNIFORM_BLOCKS : 0x8A2B,
MAX_FRAGMENT_UNIFORM_BLOCKS : 0x8A2D,
MAX_COMBINED_UNIFORM_BLOCKS : 0x8A2E,
MAX_UNIFORM_BUFFER_BINDINGS : 0x8A2F,
MAX_UNIFORM_BLOCK_SIZE : 0x8A30,
MAX_COMBINED_VERTEX_UNIFORM_COMPONENTS : 0x8A31,
MAX_COMBINED_FRAGMENT_UNIFORM_COMPONENTS : 0x8A33,
UNIFORM_BUFFER_OFFSET_ALIGNMENT : 0x8A34,
ACTIVE_UNIFORM_BLOCKS : 0x8A36,
UNIFORM_TYPE : 0x8A37,
UNIFORM_SIZE : 0x8A38,
UNIFORM_BLOCK_INDEX : 0x8A3A,
UNIFORM_OFFSET : 0x8A3B,
UNIFORM_ARRAY_STRIDE : 0x8A3C,
UNIFORM_MATRIX_STRIDE : 0x8A3D,
UNIFORM_IS_ROW_MAJOR : 0x8A3E,
UNIFORM_BLOCK_BINDING : 0x8A3F,
UNIFORM_BLOCK_DATA_SIZE : 0x8A40,
UNIFORM_BLOCK_ACTIVE_UNIFORMS : 0x8A42,
UNIFORM_BLOCK_ACTIVE_UNIFORM_INDICES : 0x8A43,
UNIFORM_BLOCK_REFERENCED_BY_VERTEX_SHADER : 0x8A44,
UNIFORM_BLOCK_REFERENCED_BY_FRAGMENT_SHADER : 0x8A46,
INVALID_INDEX : 0xFFFFFFFF,
MAX_VERTEX_OUTPUT_COMPONENTS : 0x9122,
MAX_FRAGMENT_INPUT_COMPONENTS : 0x9125,
MAX_SERVER_WAIT_TIMEOUT : 0x9111,
OBJECT_TYPE : 0x9112,
SYNC_CONDITION : 0x9113,
SYNC_STATUS : 0x9114,
SYNC_FLAGS : 0x9115,
SYNC_FENCE : 0x9116,
SYNC_GPU_COMMANDS_COMPLETE : 0x9117,
UNSIGNALED : 0x9118,
SIGNALED : 0x9119,
ALREADY_SIGNALED : 0x911A,
TIMEOUT_EXPIRED : 0x911B,
CONDITION_SATISFIED : 0x911C,
WAIT_FAILED : 0x911D,
SYNC_FLUSH_COMMANDS_BIT : 0x00000001,
VERTEX_ATTRIB_ARRAY_DIVISOR : 0x88FE,
ANY_SAMPLES_PASSED : 0x8C2F,
ANY_SAMPLES_PASSED_CONSERVATIVE : 0x8D6A,
SAMPLER_BINDING : 0x8919,
RGB10_A2UI : 0x906F,
INT_2_10_10_10_REV : 0x8D9F,
TRANSFORM_FEEDBACK : 0x8E22,
TRANSFORM_FEEDBACK_PAUSED : 0x8E23,
TRANSFORM_FEEDBACK_ACTIVE : 0x8E24,
TRANSFORM_FEEDBACK_BINDING : 0x8E25,
COMPRESSED_R11_EAC : 0x9270,
COMPRESSED_SIGNED_R11_EAC : 0x9271,
COMPRESSED_RG11_EAC : 0x9272,
COMPRESSED_SIGNED_RG11_EAC : 0x9273,
COMPRESSED_RGB8_ETC2 : 0x9274,
COMPRESSED_SRGB8_ETC2 : 0x9275,
COMPRESSED_RGB8_PUNCHTHROUGH_ALPHA1_ETC2 : 0x9276,
COMPRESSED_SRGB8_PUNCHTHROUGH_ALPHA1_ETC2 : 0x9277,
COMPRESSED_RGBA8_ETC2_EAC : 0x9278,
COMPRESSED_SRGB8_ALPHA8_ETC2_EAC : 0x9279,
TEXTURE_IMMUTABLE_FORMAT : 0x912F,
MAX_ELEMENT_INDEX : 0x8D6B,
TEXTURE_IMMUTABLE_LEVELS : 0x82DF
};
return freezeObject(WebGLConstants);
});
/*global define*/
define('Core/ComponentDatatype',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./FeatureDetection',
'./freezeObject',
'./WebGLConstants'
], function(
defaultValue,
defined,
DeveloperError,
FeatureDetection,
freezeObject,
WebGLConstants) {
'use strict';
// Bail out if the browser doesn't support typed arrays, to prevent the setup function
// from failing, since we won't be able to create a WebGL context anyway.
if (!FeatureDetection.supportsTypedArrays()) {
return {};
}
/**
* WebGL component datatypes. Components are intrinsics,
* which form attributes, which form vertices.
*
* @exports ComponentDatatype
*/
var ComponentDatatype = {
/**
* 8-bit signed byte corresponding to gl.BYTE and the type
* of an element in Int8Array.
*
* @type {Number}
* @constant
*/
BYTE : WebGLConstants.BYTE,
/**
* 8-bit unsigned byte corresponding to UNSIGNED_BYTE and the type
* of an element in Uint8Array.
*
* @type {Number}
* @constant
*/
UNSIGNED_BYTE : WebGLConstants.UNSIGNED_BYTE,
/**
* 16-bit signed short corresponding to SHORT and the type
* of an element in Int16Array.
*
* @type {Number}
* @constant
*/
SHORT : WebGLConstants.SHORT,
/**
* 16-bit unsigned short corresponding to UNSIGNED_SHORT and the type
* of an element in Uint16Array.
*
* @type {Number}
* @constant
*/
UNSIGNED_SHORT : WebGLConstants.UNSIGNED_SHORT,
/**
* 32-bit signed int corresponding to INT and the type
* of an element in Int32Array.
*
* @memberOf ComponentDatatype
*
* @type {Number}
* @constant
*/
INT : WebGLConstants.INT,
/**
* 32-bit unsigned int corresponding to UNSIGNED_INT and the type
* of an element in Uint32Array.
*
* @memberOf ComponentDatatype
*
* @type {Number}
* @constant
*/
UNSIGNED_INT : WebGLConstants.UNSIGNED_INT,
/**
* 32-bit floating-point corresponding to FLOAT and the type
* of an element in Float32Array.
*
* @type {Number}
* @constant
*/
FLOAT : WebGLConstants.FLOAT,
/**
* 64-bit floating-point corresponding to gl.DOUBLE (in Desktop OpenGL;
* this is not supported in WebGL, and is emulated in Cesium via {@link GeometryPipeline.encodeAttribute})
* and the type of an element in Float64Array.
*
* @memberOf ComponentDatatype
*
* @type {Number}
* @constant
* @default 0x140A
*/
DOUBLE : WebGLConstants.DOUBLE
};
/**
* Returns the size, in bytes, of the corresponding datatype.
*
* @param {ComponentDatatype} componentDatatype The component datatype to get the size of.
* @returns {Number} The size in bytes.
*
* @exception {DeveloperError} componentDatatype is not a valid value.
*
* @example
* // Returns Int8Array.BYTES_PER_ELEMENT
* var size = Cesium.ComponentDatatype.getSizeInBytes(Cesium.ComponentDatatype.BYTE);
*/
ComponentDatatype.getSizeInBytes = function(componentDatatype){
if (!defined(componentDatatype)) {
throw new DeveloperError('value is required.');
}
switch (componentDatatype) {
case ComponentDatatype.BYTE:
return Int8Array.BYTES_PER_ELEMENT;
case ComponentDatatype.UNSIGNED_BYTE:
return Uint8Array.BYTES_PER_ELEMENT;
case ComponentDatatype.SHORT:
return Int16Array.BYTES_PER_ELEMENT;
case ComponentDatatype.UNSIGNED_SHORT:
return Uint16Array.BYTES_PER_ELEMENT;
case ComponentDatatype.INT:
return Int32Array.BYTES_PER_ELEMENT;
case ComponentDatatype.UNSIGNED_INT:
return Uint32Array.BYTES_PER_ELEMENT;
case ComponentDatatype.FLOAT:
return Float32Array.BYTES_PER_ELEMENT;
case ComponentDatatype.DOUBLE:
return Float64Array.BYTES_PER_ELEMENT;
default:
throw new DeveloperError('componentDatatype is not a valid value.');
}
};
/**
* Gets the {@link ComponentDatatype} for the provided TypedArray instance.
*
* @param {TypedArray} array The typed array.
* @returns {ComponentDatatype} The ComponentDatatype for the provided array, or undefined if the array is not a TypedArray.
*/
ComponentDatatype.fromTypedArray = function(array) {
if (array instanceof Int8Array) {
return ComponentDatatype.BYTE;
}
if (array instanceof Uint8Array) {
return ComponentDatatype.UNSIGNED_BYTE;
}
if (array instanceof Int16Array) {
return ComponentDatatype.SHORT;
}
if (array instanceof Uint16Array) {
return ComponentDatatype.UNSIGNED_SHORT;
}
if (array instanceof Int32Array) {
return ComponentDatatype.INT;
}
if (array instanceof Uint32Array) {
return ComponentDatatype.UNSIGNED_INT;
}
if (array instanceof Float32Array) {
return ComponentDatatype.FLOAT;
}
if (array instanceof Float64Array) {
return ComponentDatatype.DOUBLE;
}
};
/**
* Validates that the provided component datatype is a valid {@link ComponentDatatype}
*
* @param {ComponentDatatype} componentDatatype The component datatype to validate.
* @returns {Boolean} true if the provided component datatype is a valid value; otherwise, false.
*
* @example
* if (!Cesium.ComponentDatatype.validate(componentDatatype)) {
* throw new Cesium.DeveloperError('componentDatatype must be a valid value.');
* }
*/
ComponentDatatype.validate = function(componentDatatype) {
return defined(componentDatatype) &&
(componentDatatype === ComponentDatatype.BYTE ||
componentDatatype === ComponentDatatype.UNSIGNED_BYTE ||
componentDatatype === ComponentDatatype.SHORT ||
componentDatatype === ComponentDatatype.UNSIGNED_SHORT ||
componentDatatype === ComponentDatatype.INT ||
componentDatatype === ComponentDatatype.UNSIGNED_INT ||
componentDatatype === ComponentDatatype.FLOAT ||
componentDatatype === ComponentDatatype.DOUBLE);
};
/**
* Creates a typed array corresponding to component data type.
*
* @param {ComponentDatatype} componentDatatype The component data type.
* @param {Number|Array} valuesOrLength The length of the array to create or an array.
* @returns {Int8Array|Uint8Array|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} A typed array.
*
* @exception {DeveloperError} componentDatatype is not a valid value.
*
* @example
* // creates a Float32Array with length of 100
* var typedArray = Cesium.ComponentDatatype.createTypedArray(Cesium.ComponentDatatype.FLOAT, 100);
*/
ComponentDatatype.createTypedArray = function(componentDatatype, valuesOrLength) {
if (!defined(componentDatatype)) {
throw new DeveloperError('componentDatatype is required.');
}
if (!defined(valuesOrLength)) {
throw new DeveloperError('valuesOrLength is required.');
}
switch (componentDatatype) {
case ComponentDatatype.BYTE:
return new Int8Array(valuesOrLength);
case ComponentDatatype.UNSIGNED_BYTE:
return new Uint8Array(valuesOrLength);
case ComponentDatatype.SHORT:
return new Int16Array(valuesOrLength);
case ComponentDatatype.UNSIGNED_SHORT:
return new Uint16Array(valuesOrLength);
case ComponentDatatype.INT:
return new Int32Array(valuesOrLength);
case ComponentDatatype.UNSIGNED_INT:
return new Uint32Array(valuesOrLength);
case ComponentDatatype.FLOAT:
return new Float32Array(valuesOrLength);
case ComponentDatatype.DOUBLE:
return new Float64Array(valuesOrLength);
default:
throw new DeveloperError('componentDatatype is not a valid value.');
}
};
/**
* Creates a typed view of an array of bytes.
*
* @param {ComponentDatatype} componentDatatype The type of the view to create.
* @param {ArrayBuffer} buffer The buffer storage to use for the view.
* @param {Number} [byteOffset] The offset, in bytes, to the first element in the view.
* @param {Number} [length] The number of elements in the view.
* @returns {Int8Array|Uint8Array|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} A typed array view of the buffer.
*
* @exception {DeveloperError} componentDatatype is not a valid value.
*/
ComponentDatatype.createArrayBufferView = function(componentDatatype, buffer, byteOffset, length) {
if (!defined(componentDatatype)) {
throw new DeveloperError('componentDatatype is required.');
}
if (!defined(buffer)) {
throw new DeveloperError('buffer is required.');
}
byteOffset = defaultValue(byteOffset, 0);
length = defaultValue(length, (buffer.byteLength - byteOffset) / ComponentDatatype.getSizeInBytes(componentDatatype));
switch (componentDatatype) {
case ComponentDatatype.BYTE:
return new Int8Array(buffer, byteOffset, length);
case ComponentDatatype.UNSIGNED_BYTE:
return new Uint8Array(buffer, byteOffset, length);
case ComponentDatatype.SHORT:
return new Int16Array(buffer, byteOffset, length);
case ComponentDatatype.UNSIGNED_SHORT:
return new Uint16Array(buffer, byteOffset, length);
case ComponentDatatype.INT:
return new Int32Array(buffer, byteOffset, length);
case ComponentDatatype.UNSIGNED_INT:
return new Uint32Array(buffer, byteOffset, length);
case ComponentDatatype.FLOAT:
return new Float32Array(buffer, byteOffset, length);
case ComponentDatatype.DOUBLE:
return new Float64Array(buffer, byteOffset, length);
default:
throw new DeveloperError('componentDatatype is not a valid value.');
}
};
/**
* Get the ComponentDatatype from its name.
*
* @param {String} name The name of the ComponentDatatype.
* @returns {ComponentDatatype} The ComponentDatatype.
*
* @exception {DeveloperError} name is not a valid value.
*/
ComponentDatatype.fromName = function(name) {
switch (name) {
case 'BYTE':
return ComponentDatatype.BYTE;
case 'UNSIGNED_BYTE':
return ComponentDatatype.UNSIGNED_BYTE;
case 'SHORT':
return ComponentDatatype.SHORT;
case 'UNSIGNED_SHORT':
return ComponentDatatype.UNSIGNED_SHORT;
case 'INT':
return ComponentDatatype.INT;
case 'UNSIGNED_INT':
return ComponentDatatype.UNSIGNED_INT;
case 'FLOAT':
return ComponentDatatype.FLOAT;
case 'DOUBLE':
return ComponentDatatype.DOUBLE;
default:
throw new DeveloperError('name is not a valid value.');
}
};
return freezeObject(ComponentDatatype);
});
/*global define*/
define('Core/GeometryType',[
'./freezeObject'
], function(
freezeObject) {
'use strict';
/**
* @private
*/
var GeometryType = {
NONE : 0,
TRIANGLES : 1,
LINES : 2,
POLYLINES : 3
};
return freezeObject(GeometryType);
});
/*global define*/
define('Core/PrimitiveType',[
'./freezeObject',
'./WebGLConstants'
], function(
freezeObject,
WebGLConstants) {
'use strict';
/**
* The type of a geometric primitive, i.e., points, lines, and triangles.
*
* @exports PrimitiveType
*/
var PrimitiveType = {
/**
* Points primitive where each vertex (or index) is a separate point.
*
* @type {Number}
* @constant
*/
POINTS : WebGLConstants.POINTS,
/**
* Lines primitive where each two vertices (or indices) is a line segment. Line segments are not necessarily connected.
*
* @type {Number}
* @constant
*/
LINES : WebGLConstants.LINES,
/**
* Line loop primitive where each vertex (or index) after the first connects a line to
* the previous vertex, and the last vertex implicitly connects to the first.
*
* @type {Number}
* @constant
*/
LINE_LOOP : WebGLConstants.LINE_LOOP,
/**
* Line strip primitive where each vertex (or index) after the first connects a line to the previous vertex.
*
* @type {Number}
* @constant
*/
LINE_STRIP : WebGLConstants.LINE_STRIP,
/**
* Triangles primitive where each three vertices (or indices) is a triangle. Triangles do not necessarily share edges.
*
* @type {Number}
* @constant
*/
TRIANGLES : WebGLConstants.TRIANGLES,
/**
* Triangle strip primitive where each vertex (or index) after the first two connect to
* the previous two vertices forming a triangle. For example, this can be used to model a wall.
*
* @type {Number}
* @constant
*/
TRIANGLE_STRIP : WebGLConstants.TRIANGLE_STRIP,
/**
* Triangle fan primitive where each vertex (or index) after the first two connect to
* the previous vertex and the first vertex forming a triangle. For example, this can be used
* to model a cone or circle.
*
* @type {Number}
* @constant
*/
TRIANGLE_FAN : WebGLConstants.TRIANGLE_FAN,
/**
* @private
*/
validate : function(primitiveType) {
return primitiveType === PrimitiveType.POINTS ||
primitiveType === PrimitiveType.LINES ||
primitiveType === PrimitiveType.LINE_LOOP ||
primitiveType === PrimitiveType.LINE_STRIP ||
primitiveType === PrimitiveType.TRIANGLES ||
primitiveType === PrimitiveType.TRIANGLE_STRIP ||
primitiveType === PrimitiveType.TRIANGLE_FAN;
}
};
return freezeObject(PrimitiveType);
});
/*global define*/
define('Core/Geometry',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./GeometryType',
'./PrimitiveType'
], function(
defaultValue,
defined,
DeveloperError,
GeometryType,
PrimitiveType) {
'use strict';
/**
* A geometry representation with attributes forming vertices and optional index data
* defining primitives. Geometries and an {@link Appearance}, which describes the shading,
* can be assigned to a {@link Primitive} for visualization. A Primitive can
* be created from many heterogeneous - in many cases - geometries for performance.
*
* Geometries can be transformed and optimized using functions in {@link GeometryPipeline}.
*
*
* @alias Geometry
* @constructor
*
* @param {Object} options Object with the following properties:
* @param {GeometryAttributes} options.attributes Attributes, which make up the geometry's vertices.
* @param {PrimitiveType} [options.primitiveType=PrimitiveType.TRIANGLES] The type of primitives in the geometry.
* @param {Uint16Array|Uint32Array} [options.indices] Optional index data that determines the primitives in the geometry.
* @param {BoundingSphere} [options.boundingSphere] An optional bounding sphere that fully enclosed the geometry.
*
* @see PolygonGeometry
* @see RectangleGeometry
* @see EllipseGeometry
* @see CircleGeometry
* @see WallGeometry
* @see SimplePolylineGeometry
* @see BoxGeometry
* @see EllipsoidGeometry
*
* @demo {@link http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Geometry%20and%20Appearances.html|Geometry and Appearances Demo}
*
* @example
* // Create geometry with a position attribute and indexed lines.
* var positions = new Float64Array([
* 0.0, 0.0, 0.0,
* 7500000.0, 0.0, 0.0,
* 0.0, 7500000.0, 0.0
* ]);
*
* var geometry = new Cesium.Geometry({
* attributes : {
* position : new Cesium.GeometryAttribute({
* componentDatatype : Cesium.ComponentDatatype.DOUBLE,
* componentsPerAttribute : 3,
* values : positions
* })
* },
* indices : new Uint16Array([0, 1, 1, 2, 2, 0]),
* primitiveType : Cesium.PrimitiveType.LINES,
* boundingSphere : Cesium.BoundingSphere.fromVertices(positions)
* });
*/
function Geometry(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
if (!defined(options.attributes)) {
throw new DeveloperError('options.attributes is required.');
}
/**
* Attributes, which make up the geometry's vertices. Each property in this object corresponds to a
* {@link GeometryAttribute} containing the attribute's data.
*
* Attributes are always stored non-interleaved in a Geometry.
*
*
* There are reserved attribute names with well-known semantics. The following attributes
* are created by a Geometry (depending on the provided {@link VertexFormat}.
*
* position - 3D vertex position. 64-bit floating-point (for precision). 3 components per attribute. See {@link VertexFormat#position}.normal - Normal (normalized), commonly used for lighting. 32-bit floating-point. 3 components per attribute. See {@link VertexFormat#normal}.st - 2D texture coordinate. 32-bit floating-point. 2 components per attribute. See {@link VertexFormat#st}.binormal - Binormal (normalized), used for tangent-space effects like bump mapping. 32-bit floating-point. 3 components per attribute. See {@link VertexFormat#binormal}.tangent - Tangent (normalized), used for tangent-space effects like bump mapping. 32-bit floating-point. 3 components per attribute. See {@link VertexFormat#tangent}.
*
*
* The following attribute names are generally not created by a Geometry, but are added
* to a Geometry by a {@link Primitive} or {@link GeometryPipeline} functions to prepare
* the geometry for rendering.
*
* position3DHigh - High 32 bits for encoded 64-bit position computed with {@link GeometryPipeline.encodeAttribute}. 32-bit floating-point. 4 components per attribute.position3DLow - Low 32 bits for encoded 64-bit position computed with {@link GeometryPipeline.encodeAttribute}. 32-bit floating-point. 4 components per attribute.position3DHigh - High 32 bits for encoded 64-bit 2D (Columbus view) position computed with {@link GeometryPipeline.encodeAttribute}. 32-bit floating-point. 4 components per attribute.position2DLow - Low 32 bits for encoded 64-bit 2D (Columbus view) position computed with {@link GeometryPipeline.encodeAttribute}. 32-bit floating-point. 4 components per attribute.color - RGBA color (normalized) usually from {@link GeometryInstance#color}. 32-bit floating-point. 4 components per attribute.pickColor - RGBA color used for picking. 32-bit floating-point. 4 components per attribute.
*
*
* @type GeometryAttributes
*
* @default undefined
*
*
* @example
* geometry.attributes.position = new Cesium.GeometryAttribute({
* componentDatatype : Cesium.ComponentDatatype.FLOAT,
* componentsPerAttribute : 3,
* values : new Float32Array(0)
* });
*
* @see GeometryAttribute
* @see VertexFormat
*/
this.attributes = options.attributes;
/**
* Optional index data that - along with {@link Geometry#primitiveType} -
* determines the primitives in the geometry.
*
* @type Array
*
* @default undefined
*/
this.indices = options.indices;
/**
* The type of primitives in the geometry. This is most often {@link PrimitiveType.TRIANGLES},
* but can varying based on the specific geometry.
*
* @type PrimitiveType
*
* @default undefined
*/
this.primitiveType = defaultValue(options.primitiveType, PrimitiveType.TRIANGLES);
/**
* An optional bounding sphere that fully encloses the geometry. This is
* commonly used for culling.
*
* @type BoundingSphere
*
* @default undefined
*/
this.boundingSphere = options.boundingSphere;
/**
* @private
*/
this.geometryType = defaultValue(options.geometryType, GeometryType.NONE);
/**
* @private
*/
this.boundingSphereCV = options.boundingSphereCV;
}
/**
* Computes the number of vertices in a geometry. The runtime is linear with
* respect to the number of attributes in a vertex, not the number of vertices.
*
* @param {Geometry} geometry The geometry.
* @returns {Number} The number of vertices in the geometry.
*
* @example
* var numVertices = Cesium.Geometry.computeNumberOfVertices(geometry);
*/
Geometry.computeNumberOfVertices = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var numberOfVertices = -1;
for ( var property in geometry.attributes) {
if (geometry.attributes.hasOwnProperty(property) &&
defined(geometry.attributes[property]) &&
defined(geometry.attributes[property].values)) {
var attribute = geometry.attributes[property];
var num = attribute.values.length / attribute.componentsPerAttribute;
if ((numberOfVertices !== num) && (numberOfVertices !== -1)) {
throw new DeveloperError('All attribute lists must have the same number of attributes.');
}
numberOfVertices = num;
}
}
return numberOfVertices;
};
return Geometry;
});
/*global define*/
define('Core/GeometryAttribute',[
'./defaultValue',
'./defined',
'./DeveloperError'
], function(
defaultValue,
defined,
DeveloperError) {
'use strict';
/**
* Values and type information for geometry attributes. A {@link Geometry}
* generally contains one or more attributes. All attributes together form
* the geometry's vertices.
*
* @alias GeometryAttribute
* @constructor
*
* @param {Object} [options] Object with the following properties:
* @param {ComponentDatatype} [options.componentDatatype] The datatype of each component in the attribute, e.g., individual elements in values.
* @param {Number} [options.componentsPerAttribute] A number between 1 and 4 that defines the number of components in an attributes.
* @param {Boolean} [options.normalize=false] When true and componentDatatype is an integer format, indicate that the components should be mapped to the range [0, 1] (unsigned) or [-1, 1] (signed) when they are accessed as floating-point for rendering.
* @param {TypedArray} [options.values] The values for the attributes stored in a typed array.
*
* @exception {DeveloperError} options.componentsPerAttribute must be between 1 and 4.
*
*
* @example
* var geometry = new Cesium.Geometry({
* attributes : {
* position : new Cesium.GeometryAttribute({
* componentDatatype : Cesium.ComponentDatatype.FLOAT,
* componentsPerAttribute : 3,
* values : new Float32Array([
* 0.0, 0.0, 0.0,
* 7500000.0, 0.0, 0.0,
* 0.0, 7500000.0, 0.0
* ])
* })
* },
* primitiveType : Cesium.PrimitiveType.LINE_LOOP
* });
*
* @see Geometry
*/
function GeometryAttribute(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
if (!defined(options.componentDatatype)) {
throw new DeveloperError('options.componentDatatype is required.');
}
if (!defined(options.componentsPerAttribute)) {
throw new DeveloperError('options.componentsPerAttribute is required.');
}
if (options.componentsPerAttribute < 1 || options.componentsPerAttribute > 4) {
throw new DeveloperError('options.componentsPerAttribute must be between 1 and 4.');
}
if (!defined(options.values)) {
throw new DeveloperError('options.values is required.');
}
/**
* The datatype of each component in the attribute, e.g., individual elements in
* {@link GeometryAttribute#values}.
*
* @type ComponentDatatype
*
* @default undefined
*/
this.componentDatatype = options.componentDatatype;
/**
* A number between 1 and 4 that defines the number of components in an attributes.
* For example, a position attribute with x, y, and z components would have 3 as
* shown in the code example.
*
* @type Number
*
* @default undefined
*
* @example
* attribute.componentDatatype = Cesium.ComponentDatatype.FLOAT;
* attribute.componentsPerAttribute = 3;
* attribute.values = new Float32Array([
* 0.0, 0.0, 0.0,
* 7500000.0, 0.0, 0.0,
* 0.0, 7500000.0, 0.0
* ]);
*/
this.componentsPerAttribute = options.componentsPerAttribute;
/**
* When true and componentDatatype is an integer format,
* indicate that the components should be mapped to the range [0, 1] (unsigned)
* or [-1, 1] (signed) when they are accessed as floating-point for rendering.
*
* This is commonly used when storing colors using {@link ComponentDatatype.UNSIGNED_BYTE}.
*
*
* @type Boolean
*
* @default false
*
* @example
* attribute.componentDatatype = Cesium.ComponentDatatype.UNSIGNED_BYTE;
* attribute.componentsPerAttribute = 4;
* attribute.normalize = true;
* attribute.values = new Uint8Array([
* Cesium.Color.floatToByte(color.red),
* Cesium.Color.floatToByte(color.green),
* Cesium.Color.floatToByte(color.blue),
* Cesium.Color.floatToByte(color.alpha)
* ]);
*/
this.normalize = defaultValue(options.normalize, false);
/**
* The values for the attributes stored in a typed array. In the code example,
* every three elements in values defines one attributes since
* componentsPerAttribute is 3.
*
* @type TypedArray
*
* @default undefined
*
* @example
* attribute.componentDatatype = Cesium.ComponentDatatype.FLOAT;
* attribute.componentsPerAttribute = 3;
* attribute.values = new Float32Array([
* 0.0, 0.0, 0.0,
* 7500000.0, 0.0, 0.0,
* 0.0, 7500000.0, 0.0
* ]);
*/
this.values = options.values;
}
return GeometryAttribute;
});
/*global define*/
define('Core/GeometryAttributes',[
'./defaultValue'
], function(
defaultValue) {
'use strict';
/**
* Attributes, which make up a geometry's vertices. Each property in this object corresponds to a
* {@link GeometryAttribute} containing the attribute's data.
*
* Attributes are always stored non-interleaved in a Geometry.
*
*
* @alias GeometryAttributes
* @constructor
*/
function GeometryAttributes(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
/**
* The 3D position attribute.
*
* 64-bit floating-point (for precision). 3 components per attribute.
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.position = options.position;
/**
* The normal attribute (normalized), which is commonly used for lighting.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.normal = options.normal;
/**
* The 2D texture coordinate attribute.
*
* 32-bit floating-point. 2 components per attribute
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.st = options.st;
/**
* The binormal attribute (normalized), which is used for tangent-space effects like bump mapping.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.binormal = options.binormal;
/**
* The tangent attribute (normalized), which is used for tangent-space effects like bump mapping.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.tangent = options.tangent;
/**
* The color attribute.
*
* 8-bit unsigned integer. 4 components per attribute.
*
*
* @type GeometryAttribute
*
* @default undefined
*/
this.color = options.color;
}
return GeometryAttributes;
});
/*global define*/
define('Core/GeometryInstance',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./Matrix4'
], function(
defaultValue,
defined,
DeveloperError,
Matrix4) {
'use strict';
/**
* Geometry instancing allows one {@link Geometry} object to be positions in several
* different locations and colored uniquely. For example, one {@link BoxGeometry} can
* be instanced several times, each with a different modelMatrix to change
* its position, rotation, and scale.
*
* @alias GeometryInstance
* @constructor
*
* @param {Object} options Object with the following properties:
* @param {Geometry} options.geometry The geometry to instance.
* @param {Matrix4} [options.modelMatrix=Matrix4.IDENTITY] The model matrix that transforms to transform the geometry from model to world coordinates.
* @param {Object} [options.id] A user-defined object to return when the instance is picked with {@link Scene#pick} or get/set per-instance attributes with {@link Primitive#getGeometryInstanceAttributes}.
* @param {Object} [options.attributes] Per-instance attributes like a show or color attribute shown in the example below.
*
*
* @example
* // Create geometry for a box, and two instances that refer to it.
* // One instance positions the box on the bottom and colored aqua.
* // The other instance positions the box on the top and color white.
* var geometry = Cesium.BoxGeometry.fromDimensions({
* vertexFormat : Cesium.VertexFormat.POSITION_AND_NORMAL,
* dimensions : new Cesium.Cartesian3(1000000.0, 1000000.0, 500000.0)
* });
* var instanceBottom = new Cesium.GeometryInstance({
* geometry : geometry,
* modelMatrix : Cesium.Matrix4.multiplyByTranslation(Cesium.Transforms.eastNorthUpToFixedFrame(
* Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883)), new Cesium.Cartesian3(0.0, 0.0, 1000000.0), new Cesium.Matrix4()),
* attributes : {
* color : Cesium.ColorGeometryInstanceAttribute.fromColor(Cesium.Color.AQUA)
* },
* id : 'bottom'
* });
* var instanceTop = new Cesium.GeometryInstance({
* geometry : geometry,
* modelMatrix : Cesium.Matrix4.multiplyByTranslation(Cesium.Transforms.eastNorthUpToFixedFrame(
* Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883)), new Cesium.Cartesian3(0.0, 0.0, 3000000.0), new Cesium.Matrix4()),
* attributes : {
* color : Cesium.ColorGeometryInstanceAttribute.fromColor(Cesium.Color.AQUA)
* },
* id : 'top'
* });
*
* @see Geometry
*/
function GeometryInstance(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
if (!defined(options.geometry)) {
throw new DeveloperError('options.geometry is required.');
}
/**
* The geometry being instanced.
*
* @type Geometry
*
* @default undefined
*/
this.geometry = options.geometry;
/**
* The 4x4 transformation matrix that transforms the geometry from model to world coordinates.
* When this is the identity matrix, the geometry is drawn in world coordinates, i.e., Earth's WGS84 coordinates.
* Local reference frames can be used by providing a different transformation matrix, like that returned
* by {@link Transforms.eastNorthUpToFixedFrame}.
*
* @type Matrix4
*
* @default Matrix4.IDENTITY
*/
this.modelMatrix = Matrix4.clone(defaultValue(options.modelMatrix, Matrix4.IDENTITY));
/**
* User-defined object returned when the instance is picked or used to get/set per-instance attributes.
*
* @type Object
*
* @default undefined
*
* @see Scene#pick
* @see Primitive#getGeometryInstanceAttributes
*/
this.id = options.id;
/**
* Used for picking primitives that wrap geometry instances.
*
* @private
*/
this.pickPrimitive = options.pickPrimitive;
/**
* Per-instance attributes like {@link ColorGeometryInstanceAttribute} or {@link ShowGeometryInstanceAttribute}.
* {@link Geometry} attributes varying per vertex; these attributes are constant for the entire instance.
*
* @type Object
*
* @default undefined
*/
this.attributes = defaultValue(options.attributes, {});
/**
* @private
*/
this.westHemisphereGeometry = undefined;
/**
* @private
*/
this.eastHemisphereGeometry = undefined;
}
return GeometryInstance;
});
/*global define*/
define('Core/AttributeCompression',[
'./Cartesian2',
'./Cartesian3',
'./defined',
'./DeveloperError',
'./Math'
], function(
Cartesian2,
Cartesian3,
defined,
DeveloperError,
CesiumMath) {
'use strict';
/**
* Attribute compression and decompression functions.
*
* @exports AttributeCompression
*
* @private
*/
var AttributeCompression = {};
/**
* Encodes a normalized vector into 2 SNORM values in the range of [0-rangeMax] following the 'oct' encoding.
*
* Oct encoding is a compact representation of unit length vectors.
* The 'oct' encoding is described in "A Survey of Efficient Representations of Independent Unit Vectors",
* Cigolle et al 2014: {@link http://jcgt.org/published/0003/02/01/}
*
* @param {Cartesian3} vector The normalized vector to be compressed into 2 component 'oct' encoding.
* @param {Cartesian2} result The 2 component oct-encoded unit length vector.
* @param {Number} rangeMax The maximum value of the SNORM range. The encoded vector is stored in log2(rangeMax+1) bits.
* @returns {Cartesian2} The 2 component oct-encoded unit length vector.
*
* @exception {DeveloperError} vector must be normalized.
*
* @see AttributeCompression.octDecodeInRange
*/
AttributeCompression.octEncodeInRange = function(vector, rangeMax, result) {
if (!defined(vector)) {
throw new DeveloperError('vector is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
var magSquared = Cartesian3.magnitudeSquared(vector);
if (Math.abs(magSquared - 1.0) > CesiumMath.EPSILON6) {
throw new DeveloperError('vector must be normalized.');
}
result.x = vector.x / (Math.abs(vector.x) + Math.abs(vector.y) + Math.abs(vector.z));
result.y = vector.y / (Math.abs(vector.x) + Math.abs(vector.y) + Math.abs(vector.z));
if (vector.z < 0) {
var x = result.x;
var y = result.y;
result.x = (1.0 - Math.abs(y)) * CesiumMath.signNotZero(x);
result.y = (1.0 - Math.abs(x)) * CesiumMath.signNotZero(y);
}
result.x = CesiumMath.toSNorm(result.x, rangeMax);
result.y = CesiumMath.toSNorm(result.y, rangeMax);
return result;
};
/**
* Encodes a normalized vector into 2 SNORM values in the range of [0-255] following the 'oct' encoding.
*
* @param {Cartesian3} vector The normalized vector to be compressed into 2 byte 'oct' encoding.
* @param {Cartesian2} result The 2 byte oct-encoded unit length vector.
* @returns {Cartesian2} The 2 byte oct-encoded unit length vector.
*
* @exception {DeveloperError} vector must be normalized.
*
* @see AttributeCompression.octEncodeInRange
* @see AttributeCompression.octDecode
*/
AttributeCompression.octEncode = function(vector, result) {
return AttributeCompression.octEncodeInRange(vector, 255, result);
};
/**
* Decodes a unit-length vector in 'oct' encoding to a normalized 3-component vector.
*
* @param {Number} x The x component of the oct-encoded unit length vector.
* @param {Number} y The y component of the oct-encoded unit length vector.
* @param {Number} rangeMax The maximum value of the SNORM range. The encoded vector is stored in log2(rangeMax+1) bits.
* @param {Cartesian3} result The decoded and normalized vector
* @returns {Cartesian3} The decoded and normalized vector.
*
* @exception {DeveloperError} x and y must be an unsigned normalized integer between 0 and rangeMax.
*
* @see AttributeCompression.octEncodeInRange
*/
AttributeCompression.octDecodeInRange = function(x, y, rangeMax, result) {
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
if (x < 0 || x > rangeMax || y < 0 || y > rangeMax) {
throw new DeveloperError('x and y must be a signed normalized integer between 0 and ' + rangeMax);
}
result.x = CesiumMath.fromSNorm(x, rangeMax);
result.y = CesiumMath.fromSNorm(y, rangeMax);
result.z = 1.0 - (Math.abs(result.x) + Math.abs(result.y));
if (result.z < 0.0)
{
var oldVX = result.x;
result.x = (1.0 - Math.abs(result.y)) * CesiumMath.signNotZero(oldVX);
result.y = (1.0 - Math.abs(oldVX)) * CesiumMath.signNotZero(result.y);
}
return Cartesian3.normalize(result, result);
};
/**
* Decodes a unit-length vector in 2 byte 'oct' encoding to a normalized 3-component vector.
*
* @param {Number} x The x component of the oct-encoded unit length vector.
* @param {Number} y The y component of the oct-encoded unit length vector.
* @param {Cartesian3} result The decoded and normalized vector.
* @returns {Cartesian3} The decoded and normalized vector.
*
* @exception {DeveloperError} x and y must be an unsigned normalized integer between 0 and 255.
*
* @see AttributeCompression.octDecodeInRange
*/
AttributeCompression.octDecode = function(x, y, result) {
return AttributeCompression.octDecodeInRange(x, y, 255, result);
};
/**
* Packs an oct encoded vector into a single floating-point number.
*
* @param {Cartesian2} encoded The oct encoded vector.
* @returns {Number} The oct encoded vector packed into a single float.
*
*/
AttributeCompression.octPackFloat = function(encoded) {
if (!defined(encoded)) {
throw new DeveloperError('encoded is required.');
}
return 256.0 * encoded.x + encoded.y;
};
var scratchEncodeCart2 = new Cartesian2();
/**
* Encodes a normalized vector into 2 SNORM values in the range of [0-255] following the 'oct' encoding and
* stores those values in a single float-point number.
*
* @param {Cartesian3} vector The normalized vector to be compressed into 2 byte 'oct' encoding.
* @returns {Number} The 2 byte oct-encoded unit length vector.
*
* @exception {DeveloperError} vector must be normalized.
*/
AttributeCompression.octEncodeFloat = function(vector) {
AttributeCompression.octEncode(vector, scratchEncodeCart2);
return AttributeCompression.octPackFloat(scratchEncodeCart2);
};
/**
* Decodes a unit-length vector in 'oct' encoding packed in a floating-point number to a normalized 3-component vector.
*
* @param {Number} value The oct-encoded unit length vector stored as a single floating-point number.
* @param {Cartesian3} result The decoded and normalized vector
* @returns {Cartesian3} The decoded and normalized vector.
*
*/
AttributeCompression.octDecodeFloat = function(value, result) {
if (!defined(value)) {
throw new DeveloperError('value is required.');
}
var temp = value / 256.0;
var x = Math.floor(temp);
var y = (temp - x) * 256.0;
return AttributeCompression.octDecode(x, y, result);
};
/**
* Encodes three normalized vectors into 6 SNORM values in the range of [0-255] following the 'oct' encoding and
* packs those into two floating-point numbers.
*
* @param {Cartesian3} v1 A normalized vector to be compressed.
* @param {Cartesian3} v2 A normalized vector to be compressed.
* @param {Cartesian3} v3 A normalized vector to be compressed.
* @param {Cartesian2} result The 'oct' encoded vectors packed into two floating-point numbers.
* @returns {Cartesian2} The 'oct' encoded vectors packed into two floating-point numbers.
*
*/
AttributeCompression.octPack = function(v1, v2, v3, result) {
if (!defined(v1)) {
throw new DeveloperError('v1 is required.');
}
if (!defined(v2)) {
throw new DeveloperError('v2 is required.');
}
if (!defined(v3)) {
throw new DeveloperError('v3 is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
var encoded1 = AttributeCompression.octEncodeFloat(v1);
var encoded2 = AttributeCompression.octEncodeFloat(v2);
var encoded3 = AttributeCompression.octEncode(v3, scratchEncodeCart2);
result.x = 65536.0 * encoded3.x + encoded1;
result.y = 65536.0 * encoded3.y + encoded2;
return result;
};
/**
* Decodes three unit-length vectors in 'oct' encoding packed into a floating-point number to a normalized 3-component vector.
*
* @param {Cartesian2} packed The three oct-encoded unit length vectors stored as two floating-point number.
* @param {Cartesian3} v1 One decoded and normalized vector.
* @param {Cartesian3} v2 One decoded and normalized vector.
* @param {Cartesian3} v3 One decoded and normalized vector.
*/
AttributeCompression.octUnpack = function(packed, v1, v2, v3) {
if (!defined(packed)) {
throw new DeveloperError('packed is required.');
}
if (!defined(v1)) {
throw new DeveloperError('v1 is required.');
}
if (!defined(v2)) {
throw new DeveloperError('v2 is required.');
}
if (!defined(v3)) {
throw new DeveloperError('v3 is required.');
}
var temp = packed.x / 65536.0;
var x = Math.floor(temp);
var encodedFloat1 = (temp - x) * 65536.0;
temp = packed.y / 65536.0;
var y = Math.floor(temp);
var encodedFloat2 = (temp - y) * 65536.0;
AttributeCompression.octDecodeFloat(encodedFloat1, v1);
AttributeCompression.octDecodeFloat(encodedFloat2, v2);
AttributeCompression.octDecode(x, y, v3);
};
/**
* Pack texture coordinates into a single float. The texture coordinates will only preserve 12 bits of precision.
*
* @param {Cartesian2} textureCoordinates The texture coordinates to compress. Both coordinates must be in the range 0.0-1.0.
* @returns {Number} The packed texture coordinates.
*
*/
AttributeCompression.compressTextureCoordinates = function(textureCoordinates) {
if (!defined(textureCoordinates)) {
throw new DeveloperError('textureCoordinates is required.');
}
// Move x and y to the range 0-4095;
var x = (textureCoordinates.x * 4095.0) | 0;
var y = (textureCoordinates.y * 4095.0) | 0;
return 4096.0 * x + y;
};
/**
* Decompresses texture coordinates that were packed into a single float.
*
* @param {Number} compressed The compressed texture coordinates.
* @param {Cartesian2} result The decompressed texture coordinates.
* @returns {Cartesian2} The modified result parameter.
*
*/
AttributeCompression.decompressTextureCoordinates = function(compressed, result) {
if (!defined(compressed)) {
throw new DeveloperError('compressed is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required.');
}
var temp = compressed / 4096.0;
var xZeroTo4095 = Math.floor(temp);
result.x = xZeroTo4095 / 4095.0;
result.y = (compressed - xZeroTo4095 * 4096) / 4095;
return result;
};
return AttributeCompression;
});
/*global define*/
define('Core/barycentricCoordinates',[
'./Cartesian2',
'./Cartesian3',
'./defined',
'./DeveloperError'
], function(
Cartesian2,
Cartesian3,
defined,
DeveloperError) {
'use strict';
var scratchCartesian1 = new Cartesian3();
var scratchCartesian2 = new Cartesian3();
var scratchCartesian3 = new Cartesian3();
/**
* Computes the barycentric coordinates for a point with respect to a triangle.
*
* @exports barycentricCoordinates
*
* @param {Cartesian2|Cartesian3} point The point to test.
* @param {Cartesian2|Cartesian3} p0 The first point of the triangle, corresponding to the barycentric x-axis.
* @param {Cartesian2|Cartesian3} p1 The second point of the triangle, corresponding to the barycentric y-axis.
* @param {Cartesian2|Cartesian3} p2 The third point of the triangle, corresponding to the barycentric z-axis.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*
* @example
* // Returns Cartesian3.UNIT_X
* var p = new Cesium.Cartesian3(-1.0, 0.0, 0.0);
* var b = Cesium.barycentricCoordinates(p,
* new Cesium.Cartesian3(-1.0, 0.0, 0.0),
* new Cesium.Cartesian3( 1.0, 0.0, 0.0),
* new Cesium.Cartesian3( 0.0, 1.0, 1.0));
*/
function barycentricCoordinates(point, p0, p1, p2, result) {
if (!defined(point) || !defined(p0) || !defined(p1) || !defined(p2)) {
throw new DeveloperError('point, p0, p1, and p2 are required.');
}
if (!defined(result)) {
result = new Cartesian3();
}
// Implementation based on http://www.blackpawn.com/texts/pointinpoly/default.html.
var v0, v1, v2;
var dot00, dot01, dot02, dot11, dot12;
if(!defined(p0.z)) {
v0 = Cartesian2.subtract(p1, p0, scratchCartesian1);
v1 = Cartesian2.subtract(p2, p0, scratchCartesian2);
v2 = Cartesian2.subtract(point, p0, scratchCartesian3);
dot00 = Cartesian2.dot(v0, v0);
dot01 = Cartesian2.dot(v0, v1);
dot02 = Cartesian2.dot(v0, v2);
dot11 = Cartesian2.dot(v1, v1);
dot12 = Cartesian2.dot(v1, v2);
} else {
v0 = Cartesian3.subtract(p1, p0, scratchCartesian1);
v1 = Cartesian3.subtract(p2, p0, scratchCartesian2);
v2 = Cartesian3.subtract(point, p0, scratchCartesian3);
dot00 = Cartesian3.dot(v0, v0);
dot01 = Cartesian3.dot(v0, v1);
dot02 = Cartesian3.dot(v0, v2);
dot11 = Cartesian3.dot(v1, v1);
dot12 = Cartesian3.dot(v1, v2);
}
var q = 1.0 / (dot00 * dot11 - dot01 * dot01);
result.y = (dot11 * dot02 - dot01 * dot12) * q;
result.z = (dot00 * dot12 - dot01 * dot02) * q;
result.x = 1.0 - result.y - result.z;
return result;
}
return barycentricCoordinates;
});
/*global define*/
define('Core/EncodedCartesian3',[
'./Cartesian3',
'./defined',
'./DeveloperError'
], function(
Cartesian3,
defined,
DeveloperError) {
'use strict';
/**
* A fixed-point encoding of a {@link Cartesian3} with 64-bit floating-point components, as two {@link Cartesian3}
* values that, when converted to 32-bit floating-point and added, approximate the original input.
*
* This is used to encode positions in vertex buffers for rendering without jittering artifacts
* as described in {@link http://blogs.agi.com/insight3d/index.php/2008/09/03/precisions-precisions/|Precisions, Precisions}.
*
*
* @alias EncodedCartesian3
* @constructor
*
* @private
*/
function EncodedCartesian3() {
/**
* The high bits for each component. Bits 0 to 22 store the whole value. Bits 23 to 31 are not used.
*
* @type {Cartesian3}
* @default {@link Cartesian3.ZERO}
*/
this.high = Cartesian3.clone(Cartesian3.ZERO);
/**
* The low bits for each component. Bits 7 to 22 store the whole value, and bits 0 to 6 store the fraction. Bits 23 to 31 are not used.
*
* @type {Cartesian3}
* @default {@link Cartesian3.ZERO}
*/
this.low = Cartesian3.clone(Cartesian3.ZERO);
}
/**
* Encodes a 64-bit floating-point value as two floating-point values that, when converted to
* 32-bit floating-point and added, approximate the original input. The returned object
* has high and low properties for the high and low bits, respectively.
*
* The fixed-point encoding follows {@link http://blogs.agi.com/insight3d/index.php/2008/09/03/precisions-precisions/|Precisions, Precisions}.
*
*
* @param {Number} value The floating-point value to encode.
* @param {Object} [result] The object onto which to store the result.
* @returns {Object} The modified result parameter or a new instance if one was not provided.
*
* @example
* var value = 1234567.1234567;
* var splitValue = Cesium.EncodedCartesian3.encode(value);
*/
EncodedCartesian3.encode = function(value, result) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(result)) {
result = {
high : 0.0,
low : 0.0
};
}
var doubleHigh;
if (value >= 0.0) {
doubleHigh = Math.floor(value / 65536.0) * 65536.0;
result.high = doubleHigh;
result.low = value - doubleHigh;
} else {
doubleHigh = Math.floor(-value / 65536.0) * 65536.0;
result.high = -doubleHigh;
result.low = value + doubleHigh;
}
return result;
};
var scratchEncode = {
high : 0.0,
low : 0.0
};
/**
* Encodes a {@link Cartesian3} with 64-bit floating-point components as two {@link Cartesian3}
* values that, when converted to 32-bit floating-point and added, approximate the original input.
*
* The fixed-point encoding follows {@link http://blogs.agi.com/insight3d/index.php/2008/09/03/precisions-precisions/|Precisions, Precisions}.
*
*
* @param {Cartesian3} cartesian The cartesian to encode.
* @param {EncodedCartesian3} [result] The object onto which to store the result.
* @returns {EncodedCartesian3} The modified result parameter or a new EncodedCartesian3 instance if one was not provided.
*
* @example
* var cart = new Cesium.Cartesian3(-10000000.0, 0.0, 10000000.0);
* var encoded = Cesium.EncodedCartesian3.fromCartesian(cart);
*/
EncodedCartesian3.fromCartesian = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
result = new EncodedCartesian3();
}
var high = result.high;
var low = result.low;
EncodedCartesian3.encode(cartesian.x, scratchEncode);
high.x = scratchEncode.high;
low.x = scratchEncode.low;
EncodedCartesian3.encode(cartesian.y, scratchEncode);
high.y = scratchEncode.high;
low.y = scratchEncode.low;
EncodedCartesian3.encode(cartesian.z, scratchEncode);
high.z = scratchEncode.high;
low.z = scratchEncode.low;
return result;
};
var encodedP = new EncodedCartesian3();
/**
* Encodes the provided cartesian, and writes it to an array with high
* components followed by low components, i.e. [high.x, high.y, high.z, low.x, low.y, low.z].
*
* This is used to create interleaved high-precision position vertex attributes.
*
*
* @param {Cartesian3} cartesian The cartesian to encode.
* @param {Number[]} cartesianArray The array to write to.
* @param {Number} index The index into the array to start writing. Six elements will be written.
*
* @exception {DeveloperError} index must be a number greater than or equal to 0.
*
* @example
* var positions = [
* new Cesium.Cartesian3(),
* // ...
* ];
* var encodedPositions = new Float32Array(2 * 3 * positions.length);
* var j = 0;
* for (var i = 0; i < positions.length; ++i) {
* Cesium.EncodedCartesian3.writeElement(positions[i], encodedPositions, j);
* j += 6;
* }
*/
EncodedCartesian3.writeElements = function(cartesian, cartesianArray, index) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(cartesianArray)) {
throw new DeveloperError('cartesianArray is required');
}
if (typeof index !== 'number' || index < 0) {
throw new DeveloperError('index must be a number greater than or equal to 0.');
}
EncodedCartesian3.fromCartesian(cartesian, encodedP);
var high = encodedP.high;
var low = encodedP.low;
cartesianArray[index] = high.x;
cartesianArray[index + 1] = high.y;
cartesianArray[index + 2] = high.z;
cartesianArray[index + 3] = low.x;
cartesianArray[index + 4] = low.y;
cartesianArray[index + 5] = low.z;
};
return EncodedCartesian3;
});
/*global define*/
define('Core/IndexDatatype',[
'./defined',
'./DeveloperError',
'./freezeObject',
'./Math',
'./WebGLConstants'
], function(
defined,
DeveloperError,
freezeObject,
CesiumMath,
WebGLConstants) {
'use strict';
/**
* Constants for WebGL index datatypes. These corresponds to the
* type parameter of {@link http://www.khronos.org/opengles/sdk/docs/man/xhtml/glDrawElements.xml|drawElements}.
*
* @exports IndexDatatype
*/
var IndexDatatype = {
/**
* 8-bit unsigned byte corresponding to UNSIGNED_BYTE and the type
* of an element in Uint8Array.
*
* @type {Number}
* @constant
*/
UNSIGNED_BYTE : WebGLConstants.UNSIGNED_BYTE,
/**
* 16-bit unsigned short corresponding to UNSIGNED_SHORT and the type
* of an element in Uint16Array.
*
* @type {Number}
* @constant
*/
UNSIGNED_SHORT : WebGLConstants.UNSIGNED_SHORT,
/**
* 32-bit unsigned int corresponding to UNSIGNED_INT and the type
* of an element in Uint32Array.
*
* @type {Number}
* @constant
*/
UNSIGNED_INT : WebGLConstants.UNSIGNED_INT
};
/**
* Returns the size, in bytes, of the corresponding datatype.
*
* @param {IndexDatatype} indexDatatype The index datatype to get the size of.
* @returns {Number} The size in bytes.
*
* @example
* // Returns 2
* var size = Cesium.IndexDatatype.getSizeInBytes(Cesium.IndexDatatype.UNSIGNED_SHORT);
*/
IndexDatatype.getSizeInBytes = function(indexDatatype) {
switch(indexDatatype) {
case IndexDatatype.UNSIGNED_BYTE:
return Uint8Array.BYTES_PER_ELEMENT;
case IndexDatatype.UNSIGNED_SHORT:
return Uint16Array.BYTES_PER_ELEMENT;
case IndexDatatype.UNSIGNED_INT:
return Uint32Array.BYTES_PER_ELEMENT;
}
throw new DeveloperError('indexDatatype is required and must be a valid IndexDatatype constant.');
};
/**
* Validates that the provided index datatype is a valid {@link IndexDatatype}.
*
* @param {IndexDatatype} indexDatatype The index datatype to validate.
* @returns {Boolean} true if the provided index datatype is a valid value; otherwise, false.
*
* @example
* if (!Cesium.IndexDatatype.validate(indexDatatype)) {
* throw new Cesium.DeveloperError('indexDatatype must be a valid value.');
* }
*/
IndexDatatype.validate = function(indexDatatype) {
return defined(indexDatatype) &&
(indexDatatype === IndexDatatype.UNSIGNED_BYTE ||
indexDatatype === IndexDatatype.UNSIGNED_SHORT ||
indexDatatype === IndexDatatype.UNSIGNED_INT);
};
/**
* Creates a typed array that will store indices, using either
* or Uint32Array depending on the number of vertices.
*
* @param {Number} numberOfVertices Number of vertices that the indices will reference.
* @param {Any} indicesLengthOrArray Passed through to the typed array constructor.
* @returns {Uint16Array|Uint32Array} A Uint16Array or Uint32Array constructed with indicesLengthOrArray.
*
* @example
* this.indices = Cesium.IndexDatatype.createTypedArray(positions.length / 3, numberOfIndices);
*/
IndexDatatype.createTypedArray = function(numberOfVertices, indicesLengthOrArray) {
if (!defined(numberOfVertices)) {
throw new DeveloperError('numberOfVertices is required.');
}
if (numberOfVertices >= CesiumMath.SIXTY_FOUR_KILOBYTES) {
return new Uint32Array(indicesLengthOrArray);
}
return new Uint16Array(indicesLengthOrArray);
};
/**
* Creates a typed array from a source array buffer. The resulting typed array will store indices, using either
* or Uint32Array depending on the number of vertices.
*
* @param {Number} numberOfVertices Number of vertices that the indices will reference.
* @param {ArrayBuffer} sourceArray Passed through to the typed array constructor.
* @param {Number} byteOffset Passed through to the typed array constructor.
* @param {Number} length Passed through to the typed array constructor.
* @returns {Uint16Array|Uint32Array} A Uint16Array or Uint32Array constructed with sourceArray, byteOffset, and length.
*
*/
IndexDatatype.createTypedArrayFromArrayBuffer = function(numberOfVertices, sourceArray, byteOffset, length) {
if (!defined(numberOfVertices)) {
throw new DeveloperError('numberOfVertices is required.');
}
if (!defined(sourceArray)) {
throw new DeveloperError('sourceArray is required.');
}
if (!defined(byteOffset)) {
throw new DeveloperError('byteOffset is required.');
}
if (numberOfVertices >= CesiumMath.SIXTY_FOUR_KILOBYTES) {
return new Uint32Array(sourceArray, byteOffset, length);
}
return new Uint16Array(sourceArray, byteOffset, length);
};
return freezeObject(IndexDatatype);
});
/*global define*/
define('Core/QuadraticRealPolynomial',[
'./DeveloperError',
'./Math'
], function(
DeveloperError,
CesiumMath) {
'use strict';
/**
* Defines functions for 2nd order polynomial functions of one variable with only real coefficients.
*
* @exports QuadraticRealPolynomial
*/
var QuadraticRealPolynomial = {};
/**
* Provides the discriminant of the quadratic equation from the supplied coefficients.
*
* @param {Number} a The coefficient of the 2nd order monomial.
* @param {Number} b The coefficient of the 1st order monomial.
* @param {Number} c The coefficient of the 0th order monomial.
* @returns {Number} The value of the discriminant.
*/
QuadraticRealPolynomial.computeDiscriminant = function(a, b, c) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
var discriminant = b * b - 4.0 * a * c;
return discriminant;
};
function addWithCancellationCheck(left, right, tolerance) {
var difference = left + right;
if ((CesiumMath.sign(left) !== CesiumMath.sign(right)) &&
Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance) {
return 0.0;
}
return difference;
}
/**
* Provides the real valued roots of the quadratic polynomial with the provided coefficients.
*
* @param {Number} a The coefficient of the 2nd order monomial.
* @param {Number} b The coefficient of the 1st order monomial.
* @param {Number} c The coefficient of the 0th order monomial.
* @returns {Number[]} The real valued roots.
*/
QuadraticRealPolynomial.computeRealRoots = function(a, b, c) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
var ratio;
if (a === 0.0) {
if (b === 0.0) {
// Constant function: c = 0.
return [];
}
// Linear function: b * x + c = 0.
return [-c / b];
} else if (b === 0.0) {
if (c === 0.0) {
// 2nd order monomial: a * x^2 = 0.
return [0.0, 0.0];
}
var cMagnitude = Math.abs(c);
var aMagnitude = Math.abs(a);
if ((cMagnitude < aMagnitude) && (cMagnitude / aMagnitude < CesiumMath.EPSILON14)) { // c ~= 0.0.
// 2nd order monomial: a * x^2 = 0.
return [0.0, 0.0];
} else if ((cMagnitude > aMagnitude) && (aMagnitude / cMagnitude < CesiumMath.EPSILON14)) { // a ~= 0.0.
// Constant function: c = 0.
return [];
}
// a * x^2 + c = 0
ratio = -c / a;
if (ratio < 0.0) {
// Both roots are complex.
return [];
}
// Both roots are real.
var root = Math.sqrt(ratio);
return [-root, root];
} else if (c === 0.0) {
// a * x^2 + b * x = 0
ratio = -b / a;
if (ratio < 0.0) {
return [ratio, 0.0];
}
return [0.0, ratio];
}
// a * x^2 + b * x + c = 0
var b2 = b * b;
var four_ac = 4.0 * a * c;
var radicand = addWithCancellationCheck(b2, -four_ac, CesiumMath.EPSILON14);
if (radicand < 0.0) {
// Both roots are complex.
return [];
}
var q = -0.5 * addWithCancellationCheck(b, CesiumMath.sign(b) * Math.sqrt(radicand), CesiumMath.EPSILON14);
if (b > 0.0) {
return [q / a, c / q];
}
return [c / q, q / a];
};
return QuadraticRealPolynomial;
});
/*global define*/
define('Core/CubicRealPolynomial',[
'./DeveloperError',
'./QuadraticRealPolynomial'
], function(
DeveloperError,
QuadraticRealPolynomial) {
'use strict';
/**
* Defines functions for 3rd order polynomial functions of one variable with only real coefficients.
*
* @exports CubicRealPolynomial
*/
var CubicRealPolynomial = {};
/**
* Provides the discriminant of the cubic equation from the supplied coefficients.
*
* @param {Number} a The coefficient of the 3rd order monomial.
* @param {Number} b The coefficient of the 2nd order monomial.
* @param {Number} c The coefficient of the 1st order monomial.
* @param {Number} d The coefficient of the 0th order monomial.
* @returns {Number} The value of the discriminant.
*/
CubicRealPolynomial.computeDiscriminant = function(a, b, c, d) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
if (typeof d !== 'number') {
throw new DeveloperError('d is a required number.');
}
var a2 = a * a;
var b2 = b * b;
var c2 = c * c;
var d2 = d * d;
var discriminant = 18.0 * a * b * c * d + b2 * c2 - 27.0 * a2 * d2 - 4.0 * (a * c2 * c + b2 * b * d);
return discriminant;
};
function computeRealRoots(a, b, c, d) {
var A = a;
var B = b / 3.0;
var C = c / 3.0;
var D = d;
var AC = A * C;
var BD = B * D;
var B2 = B * B;
var C2 = C * C;
var delta1 = A * C - B2;
var delta2 = A * D - B * C;
var delta3 = B * D - C2;
var discriminant = 4.0 * delta1 * delta3 - delta2 * delta2;
var temp;
var temp1;
if (discriminant < 0.0) {
var ABar;
var CBar;
var DBar;
if (B2 * BD >= AC * C2) {
ABar = A;
CBar = delta1;
DBar = -2.0 * B * delta1 + A * delta2;
} else {
ABar = D;
CBar = delta3;
DBar = -D * delta2 + 2.0 * C * delta3;
}
var s = (DBar < 0.0) ? -1.0 : 1.0; // This is not Math.Sign()!
var temp0 = -s * Math.abs(ABar) * Math.sqrt(-discriminant);
temp1 = -DBar + temp0;
var x = temp1 / 2.0;
var p = x < 0.0 ? -Math.pow(-x, 1.0 / 3.0) : Math.pow(x, 1.0 / 3.0);
var q = (temp1 === temp0) ? -p : -CBar / p;
temp = (CBar <= 0.0) ? p + q : -DBar / (p * p + q * q + CBar);
if (B2 * BD >= AC * C2) {
return [(temp - B) / A];
}
return [-D / (temp + C)];
}
var CBarA = delta1;
var DBarA = -2.0 * B * delta1 + A * delta2;
var CBarD = delta3;
var DBarD = -D * delta2 + 2.0 * C * delta3;
var squareRootOfDiscriminant = Math.sqrt(discriminant);
var halfSquareRootOf3 = Math.sqrt(3.0) / 2.0;
var theta = Math.abs(Math.atan2(A * squareRootOfDiscriminant, -DBarA) / 3.0);
temp = 2.0 * Math.sqrt(-CBarA);
var cosine = Math.cos(theta);
temp1 = temp * cosine;
var temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));
var numeratorLarge = (temp1 + temp3 > 2.0 * B) ? temp1 - B : temp3 - B;
var denominatorLarge = A;
var root1 = numeratorLarge / denominatorLarge;
theta = Math.abs(Math.atan2(D * squareRootOfDiscriminant, -DBarD) / 3.0);
temp = 2.0 * Math.sqrt(-CBarD);
cosine = Math.cos(theta);
temp1 = temp * cosine;
temp3 = temp * (-cosine / 2.0 - halfSquareRootOf3 * Math.sin(theta));
var numeratorSmall = -D;
var denominatorSmall = (temp1 + temp3 < 2.0 * C) ? temp1 + C : temp3 + C;
var root3 = numeratorSmall / denominatorSmall;
var E = denominatorLarge * denominatorSmall;
var F = -numeratorLarge * denominatorSmall - denominatorLarge * numeratorSmall;
var G = numeratorLarge * numeratorSmall;
var root2 = (C * F - B * G) / (-B * F + C * E);
if (root1 <= root2) {
if (root1 <= root3) {
if (root2 <= root3) {
return [root1, root2, root3];
}
return [root1, root3, root2];
}
return [root3, root1, root2];
}
if (root1 <= root3) {
return [root2, root1, root3];
}
if (root2 <= root3) {
return [root2, root3, root1];
}
return [root3, root2, root1];
}
/**
* Provides the real valued roots of the cubic polynomial with the provided coefficients.
*
* @param {Number} a The coefficient of the 3rd order monomial.
* @param {Number} b The coefficient of the 2nd order monomial.
* @param {Number} c The coefficient of the 1st order monomial.
* @param {Number} d The coefficient of the 0th order monomial.
* @returns {Number[]} The real valued roots.
*/
CubicRealPolynomial.computeRealRoots = function(a, b, c, d) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
if (typeof d !== 'number') {
throw new DeveloperError('d is a required number.');
}
var roots;
var ratio;
if (a === 0.0) {
// Quadratic function: b * x^2 + c * x + d = 0.
return QuadraticRealPolynomial.computeRealRoots(b, c, d);
} else if (b === 0.0) {
if (c === 0.0) {
if (d === 0.0) {
// 3rd order monomial: a * x^3 = 0.
return [0.0, 0.0, 0.0];
}
// a * x^3 + d = 0
ratio = -d / a;
var root = (ratio < 0.0) ? -Math.pow(-ratio, 1.0 / 3.0) : Math.pow(ratio, 1.0 / 3.0);
return [root, root, root];
} else if (d === 0.0) {
// x * (a * x^2 + c) = 0.
roots = QuadraticRealPolynomial.computeRealRoots(a, 0, c);
// Return the roots in ascending order.
if (roots.Length === 0) {
return [0.0];
}
return [roots[0], 0.0, roots[1]];
}
// Deflated cubic polynomial: a * x^3 + c * x + d= 0.
return computeRealRoots(a, 0, c, d);
} else if (c === 0.0) {
if (d === 0.0) {
// x^2 * (a * x + b) = 0.
ratio = -b / a;
if (ratio < 0.0) {
return [ratio, 0.0, 0.0];
}
return [0.0, 0.0, ratio];
}
// a * x^3 + b * x^2 + d = 0.
return computeRealRoots(a, b, 0, d);
} else if (d === 0.0) {
// x * (a * x^2 + b * x + c) = 0
roots = QuadraticRealPolynomial.computeRealRoots(a, b, c);
// Return the roots in ascending order.
if (roots.length === 0) {
return [0.0];
} else if (roots[1] <= 0.0) {
return [roots[0], roots[1], 0.0];
} else if (roots[0] >= 0.0) {
return [0.0, roots[0], roots[1]];
}
return [roots[0], 0.0, roots[1]];
}
return computeRealRoots(a, b, c, d);
};
return CubicRealPolynomial;
});
/*global define*/
define('Core/QuarticRealPolynomial',[
'./CubicRealPolynomial',
'./DeveloperError',
'./Math',
'./QuadraticRealPolynomial'
], function(
CubicRealPolynomial,
DeveloperError,
CesiumMath,
QuadraticRealPolynomial) {
'use strict';
/**
* Defines functions for 4th order polynomial functions of one variable with only real coefficients.
*
* @exports QuarticRealPolynomial
*/
var QuarticRealPolynomial = {};
/**
* Provides the discriminant of the quartic equation from the supplied coefficients.
*
* @param {Number} a The coefficient of the 4th order monomial.
* @param {Number} b The coefficient of the 3rd order monomial.
* @param {Number} c The coefficient of the 2nd order monomial.
* @param {Number} d The coefficient of the 1st order monomial.
* @param {Number} e The coefficient of the 0th order monomial.
* @returns {Number} The value of the discriminant.
*/
QuarticRealPolynomial.computeDiscriminant = function(a, b, c, d, e) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
if (typeof d !== 'number') {
throw new DeveloperError('d is a required number.');
}
if (typeof e !== 'number') {
throw new DeveloperError('e is a required number.');
}
var a2 = a * a;
var a3 = a2 * a;
var b2 = b * b;
var b3 = b2 * b;
var c2 = c * c;
var c3 = c2 * c;
var d2 = d * d;
var d3 = d2 * d;
var e2 = e * e;
var e3 = e2 * e;
var discriminant = (b2 * c2 * d2 - 4.0 * b3 * d3 - 4.0 * a * c3 * d2 + 18 * a * b * c * d3 - 27.0 * a2 * d2 * d2 + 256.0 * a3 * e3) +
e * (18.0 * b3 * c * d - 4.0 * b2 * c3 + 16.0 * a * c2 * c2 - 80.0 * a * b * c2 * d - 6.0 * a * b2 * d2 + 144.0 * a2 * c * d2) +
e2 * (144.0 * a * b2 * c - 27.0 * b2 * b2 - 128.0 * a2 * c2 - 192.0 * a2 * b * d);
return discriminant;
};
function original(a3, a2, a1, a0) {
var a3Squared = a3 * a3;
var p = a2 - 3.0 * a3Squared / 8.0;
var q = a1 - a2 * a3 / 2.0 + a3Squared * a3 / 8.0;
var r = a0 - a1 * a3 / 4.0 + a2 * a3Squared / 16.0 - 3.0 * a3Squared * a3Squared / 256.0;
// Find the roots of the cubic equations: h^6 + 2 p h^4 + (p^2 - 4 r) h^2 - q^2 = 0.
var cubicRoots = CubicRealPolynomial.computeRealRoots(1.0, 2.0 * p, p * p - 4.0 * r, -q * q);
if (cubicRoots.length > 0) {
var temp = -a3 / 4.0;
// Use the largest positive root.
var hSquared = cubicRoots[cubicRoots.length - 1];
if (Math.abs(hSquared) < CesiumMath.EPSILON14) {
// y^4 + p y^2 + r = 0.
var roots = QuadraticRealPolynomial.computeRealRoots(1.0, p, r);
if (roots.length === 2) {
var root0 = roots[0];
var root1 = roots[1];
var y;
if (root0 >= 0.0 && root1 >= 0.0) {
var y0 = Math.sqrt(root0);
var y1 = Math.sqrt(root1);
return [temp - y1, temp - y0, temp + y0, temp + y1];
} else if (root0 >= 0.0 && root1 < 0.0) {
y = Math.sqrt(root0);
return [temp - y, temp + y];
} else if (root0 < 0.0 && root1 >= 0.0) {
y = Math.sqrt(root1);
return [temp - y, temp + y];
}
}
return [];
} else if (hSquared > 0.0) {
var h = Math.sqrt(hSquared);
var m = (p + hSquared - q / h) / 2.0;
var n = (p + hSquared + q / h) / 2.0;
// Now solve the two quadratic factors: (y^2 + h y + m)(y^2 - h y + n);
var roots1 = QuadraticRealPolynomial.computeRealRoots(1.0, h, m);
var roots2 = QuadraticRealPolynomial.computeRealRoots(1.0, -h, n);
if (roots1.length !== 0) {
roots1[0] += temp;
roots1[1] += temp;
if (roots2.length !== 0) {
roots2[0] += temp;
roots2[1] += temp;
if (roots1[1] <= roots2[0]) {
return [roots1[0], roots1[1], roots2[0], roots2[1]];
} else if (roots2[1] <= roots1[0]) {
return [roots2[0], roots2[1], roots1[0], roots1[1]];
} else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {
return [roots2[0], roots1[0], roots1[1], roots2[1]];
} else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {
return [roots1[0], roots2[0], roots2[1], roots1[1]];
} else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {
return [roots2[0], roots1[0], roots2[1], roots1[1]];
}
return [roots1[0], roots2[0], roots1[1], roots2[1]];
}
return roots1;
}
if (roots2.length !== 0) {
roots2[0] += temp;
roots2[1] += temp;
return roots2;
}
return [];
}
}
return [];
}
function neumark(a3, a2, a1, a0) {
var a1Squared = a1 * a1;
var a2Squared = a2 * a2;
var a3Squared = a3 * a3;
var p = -2.0 * a2;
var q = a1 * a3 + a2Squared - 4.0 * a0;
var r = a3Squared * a0 - a1 * a2 * a3 + a1Squared;
var cubicRoots = CubicRealPolynomial.computeRealRoots(1.0, p, q, r);
if (cubicRoots.length > 0) {
// Use the most positive root
var y = cubicRoots[0];
var temp = (a2 - y);
var tempSquared = temp * temp;
var g1 = a3 / 2.0;
var h1 = temp / 2.0;
var m = tempSquared - 4.0 * a0;
var mError = tempSquared + 4.0 * Math.abs(a0);
var n = a3Squared - 4.0 * y;
var nError = a3Squared + 4.0 * Math.abs(y);
var g2;
var h2;
if (y < 0.0 || (m * nError < n * mError)) {
var squareRootOfN = Math.sqrt(n);
g2 = squareRootOfN / 2.0;
h2 = squareRootOfN === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfN;
} else {
var squareRootOfM = Math.sqrt(m);
g2 = squareRootOfM === 0.0 ? 0.0 : (a3 * h1 - a1) / squareRootOfM;
h2 = squareRootOfM / 2.0;
}
var G;
var g;
if (g1 === 0.0 && g2 === 0.0) {
G = 0.0;
g = 0.0;
} else if (CesiumMath.sign(g1) === CesiumMath.sign(g2)) {
G = g1 + g2;
g = y / G;
} else {
g = g1 - g2;
G = y / g;
}
var H;
var h;
if (h1 === 0.0 && h2 === 0.0) {
H = 0.0;
h = 0.0;
} else if (CesiumMath.sign(h1) === CesiumMath.sign(h2)) {
H = h1 + h2;
h = a0 / H;
} else {
h = h1 - h2;
H = a0 / h;
}
// Now solve the two quadratic factors: (y^2 + G y + H)(y^2 + g y + h);
var roots1 = QuadraticRealPolynomial.computeRealRoots(1.0, G, H);
var roots2 = QuadraticRealPolynomial.computeRealRoots(1.0, g, h);
if (roots1.length !== 0) {
if (roots2.length !== 0) {
if (roots1[1] <= roots2[0]) {
return [roots1[0], roots1[1], roots2[0], roots2[1]];
} else if (roots2[1] <= roots1[0]) {
return [roots2[0], roots2[1], roots1[0], roots1[1]];
} else if (roots1[0] >= roots2[0] && roots1[1] <= roots2[1]) {
return [roots2[0], roots1[0], roots1[1], roots2[1]];
} else if (roots2[0] >= roots1[0] && roots2[1] <= roots1[1]) {
return [roots1[0], roots2[0], roots2[1], roots1[1]];
} else if (roots1[0] > roots2[0] && roots1[0] < roots2[1]) {
return [roots2[0], roots1[0], roots2[1], roots1[1]];
} else {
return [roots1[0], roots2[0], roots1[1], roots2[1]];
}
}
return roots1;
}
if (roots2.length !== 0) {
return roots2;
}
}
return [];
}
/**
* Provides the real valued roots of the quartic polynomial with the provided coefficients.
*
* @param {Number} a The coefficient of the 4th order monomial.
* @param {Number} b The coefficient of the 3rd order monomial.
* @param {Number} c The coefficient of the 2nd order monomial.
* @param {Number} d The coefficient of the 1st order monomial.
* @param {Number} e The coefficient of the 0th order monomial.
* @returns {Number[]} The real valued roots.
*/
QuarticRealPolynomial.computeRealRoots = function(a, b, c, d, e) {
if (typeof a !== 'number') {
throw new DeveloperError('a is a required number.');
}
if (typeof b !== 'number') {
throw new DeveloperError('b is a required number.');
}
if (typeof c !== 'number') {
throw new DeveloperError('c is a required number.');
}
if (typeof d !== 'number') {
throw new DeveloperError('d is a required number.');
}
if (typeof e !== 'number') {
throw new DeveloperError('e is a required number.');
}
if (Math.abs(a) < CesiumMath.EPSILON15) {
return CubicRealPolynomial.computeRealRoots(b, c, d, e);
}
var a3 = b / a;
var a2 = c / a;
var a1 = d / a;
var a0 = e / a;
var k = (a3 < 0.0) ? 1 : 0;
k += (a2 < 0.0) ? k + 1 : k;
k += (a1 < 0.0) ? k + 1 : k;
k += (a0 < 0.0) ? k + 1 : k;
switch (k) {
case 0:
return original(a3, a2, a1, a0);
case 1:
return neumark(a3, a2, a1, a0);
case 2:
return neumark(a3, a2, a1, a0);
case 3:
return original(a3, a2, a1, a0);
case 4:
return original(a3, a2, a1, a0);
case 5:
return neumark(a3, a2, a1, a0);
case 6:
return original(a3, a2, a1, a0);
case 7:
return original(a3, a2, a1, a0);
case 8:
return neumark(a3, a2, a1, a0);
case 9:
return original(a3, a2, a1, a0);
case 10:
return original(a3, a2, a1, a0);
case 11:
return neumark(a3, a2, a1, a0);
case 12:
return original(a3, a2, a1, a0);
case 13:
return original(a3, a2, a1, a0);
case 14:
return original(a3, a2, a1, a0);
case 15:
return original(a3, a2, a1, a0);
default:
return undefined;
}
};
return QuarticRealPolynomial;
});
/*global define*/
define('Core/Ray',[
'./Cartesian3',
'./defaultValue',
'./defined',
'./DeveloperError'
], function(
Cartesian3,
defaultValue,
defined,
DeveloperError) {
'use strict';
/**
* Represents a ray that extends infinitely from the provided origin in the provided direction.
* @alias Ray
* @constructor
*
* @param {Cartesian3} [origin=Cartesian3.ZERO] The origin of the ray.
* @param {Cartesian3} [direction=Cartesian3.ZERO] The direction of the ray.
*/
function Ray(origin, direction) {
direction = Cartesian3.clone(defaultValue(direction, Cartesian3.ZERO));
if (!Cartesian3.equals(direction, Cartesian3.ZERO)) {
Cartesian3.normalize(direction, direction);
}
/**
* The origin of the ray.
* @type {Cartesian3}
* @default {@link Cartesian3.ZERO}
*/
this.origin = Cartesian3.clone(defaultValue(origin, Cartesian3.ZERO));
/**
* The direction of the ray.
* @type {Cartesian3}
*/
this.direction = direction;
}
/**
* Computes the point along the ray given by r(t) = o + t*d,
* where o is the origin of the ray and d is the direction.
*
* @param {Ray} ray The ray.
* @param {Number} t A scalar value.
* @param {Cartesian3} [result] The object in which the result will be stored.
* @returns {Cartesian3} The modified result parameter, or a new instance if none was provided.
*
* @example
* //Get the first intersection point of a ray and an ellipsoid.
* var intersection = Cesium.IntersectionTests.rayEllipsoid(ray, ellipsoid);
* var point = Cesium.Ray.getPoint(ray, intersection.start);
*/
Ray.getPoint = function(ray, t, result) {
if (!defined(ray)){
throw new DeveloperError('ray is requred');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is a required number');
}
if (!defined(result)) {
result = new Cartesian3();
}
result = Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
return Ray;
});
/*global define*/
define('Core/IntersectionTests',[
'./Cartesian3',
'./Cartographic',
'./defaultValue',
'./defined',
'./DeveloperError',
'./Math',
'./Matrix3',
'./QuadraticRealPolynomial',
'./QuarticRealPolynomial',
'./Ray'
], function(
Cartesian3,
Cartographic,
defaultValue,
defined,
DeveloperError,
CesiumMath,
Matrix3,
QuadraticRealPolynomial,
QuarticRealPolynomial,
Ray) {
'use strict';
/**
* Functions for computing the intersection between geometries such as rays, planes, triangles, and ellipsoids.
*
* @exports IntersectionTests
*/
var IntersectionTests = {};
/**
* Computes the intersection of a ray and a plane.
*
* @param {Ray} ray The ray.
* @param {Plane} plane The plane.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.rayPlane = function(ray, plane, result) {
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
if (!defined(result)) {
result = new Cartesian3();
}
var origin = ray.origin;
var direction = ray.direction;
var normal = plane.normal;
var denominator = Cartesian3.dot(normal, direction);
if (Math.abs(denominator) < CesiumMath.EPSILON15) {
// Ray is parallel to plane. The ray may be in the polygon's plane.
return undefined;
}
var t = (-plane.distance - Cartesian3.dot(normal, origin)) / denominator;
if (t < 0) {
return undefined;
}
result = Cartesian3.multiplyByScalar(direction, t, result);
return Cartesian3.add(origin, result, result);
};
var scratchEdge0 = new Cartesian3();
var scratchEdge1 = new Cartesian3();
var scratchPVec = new Cartesian3();
var scratchTVec = new Cartesian3();
var scratchQVec = new Cartesian3();
/**
* Computes the intersection of a ray and a triangle as a parametric distance along the input ray.
*
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
*
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If true, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @returns {Number} The intersection as a parametric distance along the ray, or undefined if there is no intersection.
*/
IntersectionTests.rayTriangleParametric = function(ray, p0, p1, p2, cullBackFaces) {
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(p2)) {
throw new DeveloperError('p2 is required.');
}
cullBackFaces = defaultValue(cullBackFaces, false);
var origin = ray.origin;
var direction = ray.direction;
var edge0 = Cartesian3.subtract(p1, p0, scratchEdge0);
var edge1 = Cartesian3.subtract(p2, p0, scratchEdge1);
var p = Cartesian3.cross(direction, edge1, scratchPVec);
var det = Cartesian3.dot(edge0, p);
var tvec;
var q;
var u;
var v;
var t;
if (cullBackFaces) {
if (det < CesiumMath.EPSILON6) {
return undefined;
}
tvec = Cartesian3.subtract(origin, p0, scratchTVec);
u = Cartesian3.dot(tvec, p);
if (u < 0.0 || u > det) {
return undefined;
}
q = Cartesian3.cross(tvec, edge0, scratchQVec);
v = Cartesian3.dot(direction, q);
if (v < 0.0 || u + v > det) {
return undefined;
}
t = Cartesian3.dot(edge1, q) / det;
} else {
if (Math.abs(det) < CesiumMath.EPSILON6) {
return undefined;
}
var invDet = 1.0 / det;
tvec = Cartesian3.subtract(origin, p0, scratchTVec);
u = Cartesian3.dot(tvec, p) * invDet;
if (u < 0.0 || u > 1.0) {
return undefined;
}
q = Cartesian3.cross(tvec, edge0, scratchQVec);
v = Cartesian3.dot(direction, q) * invDet;
if (v < 0.0 || u + v > 1.0) {
return undefined;
}
t = Cartesian3.dot(edge1, q) * invDet;
}
return t;
};
/**
* Computes the intersection of a ray and a triangle as a Cartesian3 coordinate.
*
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
*
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If true, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @param {Cartesian3} [result] The Cartesian3 onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.rayTriangle = function(ray, p0, p1, p2, cullBackFaces, result) {
var t = IntersectionTests.rayTriangleParametric(ray, p0, p1, p2, cullBackFaces);
if (!defined(t) || t < 0.0) {
return undefined;
}
if (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
var scratchLineSegmentTriangleRay = new Ray();
/**
* Computes the intersection of a line segment and a triangle.
* @memberof IntersectionTests
*
* @param {Cartesian3} v0 The an end point of the line segment.
* @param {Cartesian3} v1 The other end point of the line segment.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If true, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @param {Cartesian3} [result] The Cartesian3 onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.lineSegmentTriangle = function(v0, v1, p0, p1, p2, cullBackFaces, result) {
if (!defined(v0)) {
throw new DeveloperError('v0 is required.');
}
if (!defined(v1)) {
throw new DeveloperError('v1 is required.');
}
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(p2)) {
throw new DeveloperError('p2 is required.');
}
var ray = scratchLineSegmentTriangleRay;
Cartesian3.clone(v0, ray.origin);
Cartesian3.subtract(v1, v0, ray.direction);
Cartesian3.normalize(ray.direction, ray.direction);
var t = IntersectionTests.rayTriangleParametric(ray, p0, p1, p2, cullBackFaces);
if (!defined(t) || t < 0.0 || t > Cartesian3.distance(v0, v1)) {
return undefined;
}
if (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
function solveQuadratic(a, b, c, result) {
var det = b * b - 4.0 * a * c;
if (det < 0.0) {
return undefined;
} else if (det > 0.0) {
var denom = 1.0 / (2.0 * a);
var disc = Math.sqrt(det);
var root0 = (-b + disc) * denom;
var root1 = (-b - disc) * denom;
if (root0 < root1) {
result.root0 = root0;
result.root1 = root1;
} else {
result.root0 = root1;
result.root1 = root0;
}
return result;
}
var root = -b / (2.0 * a);
if (root === 0.0) {
return undefined;
}
result.root0 = result.root1 = root;
return result;
}
var raySphereRoots = {
root0 : 0.0,
root1 : 0.0
};
function raySphere(ray, sphere, result) {
if (!defined(result)) {
result = {};
}
var origin = ray.origin;
var direction = ray.direction;
var center = sphere.center;
var radiusSquared = sphere.radius * sphere.radius;
var diff = Cartesian3.subtract(origin, center, scratchPVec);
var a = Cartesian3.dot(direction, direction);
var b = 2.0 * Cartesian3.dot(direction, diff);
var c = Cartesian3.magnitudeSquared(diff) - radiusSquared;
var roots = solveQuadratic(a, b, c, raySphereRoots);
if (!defined(roots)) {
return undefined;
}
result.start = roots.root0;
result.stop = roots.root1;
return result;
}
/**
* Computes the intersection points of a ray with a sphere.
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {BoundingSphere} sphere The sphere.
* @param {Object} [result] The result onto which to store the result.
* @returns {Object} An object with the first (start) and the second (stop) intersection scalars for points along the ray or undefined if there are no intersections.
*/
IntersectionTests.raySphere = function(ray, sphere, result) {
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
result = raySphere(ray, sphere, result);
if (!defined(result) || result.stop < 0.0) {
return undefined;
}
result.start = Math.max(result.start, 0.0);
return result;
};
var scratchLineSegmentRay = new Ray();
/**
* Computes the intersection points of a line segment with a sphere.
* @memberof IntersectionTests
*
* @param {Cartesian3} p0 An end point of the line segment.
* @param {Cartesian3} p1 The other end point of the line segment.
* @param {BoundingSphere} sphere The sphere.
* @param {Object} [result] The result onto which to store the result.
* @returns {Object} An object with the first (start) and the second (stop) intersection scalars for points along the line segment or undefined if there are no intersections.
*/
IntersectionTests.lineSegmentSphere = function(p0, p1, sphere, result) {
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
var ray = scratchLineSegmentRay;
Cartesian3.clone(p0, ray.origin);
var direction = Cartesian3.subtract(p1, p0, ray.direction);
var maxT = Cartesian3.magnitude(direction);
Cartesian3.normalize(direction, direction);
result = raySphere(ray, sphere, result);
if (!defined(result) || result.stop < 0.0 || result.start > maxT) {
return undefined;
}
result.start = Math.max(result.start, 0.0);
result.stop = Math.min(result.stop, maxT);
return result;
};
var scratchQ = new Cartesian3();
var scratchW = new Cartesian3();
/**
* Computes the intersection points of a ray with an ellipsoid.
*
* @param {Ray} ray The ray.
* @param {Ellipsoid} ellipsoid The ellipsoid.
* @returns {Object} An object with the first (start) and the second (stop) intersection scalars for points along the ray or undefined if there are no intersections.
*/
IntersectionTests.rayEllipsoid = function(ray, ellipsoid) {
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
var inverseRadii = ellipsoid.oneOverRadii;
var q = Cartesian3.multiplyComponents(inverseRadii, ray.origin, scratchQ);
var w = Cartesian3.multiplyComponents(inverseRadii, ray.direction, scratchW);
var q2 = Cartesian3.magnitudeSquared(q);
var qw = Cartesian3.dot(q, w);
var difference, w2, product, discriminant, temp;
if (q2 > 1.0) {
// Outside ellipsoid.
if (qw >= 0.0) {
// Looking outward or tangent (0 intersections).
return undefined;
}
// qw < 0.0.
var qw2 = qw * qw;
difference = q2 - 1.0; // Positively valued.
w2 = Cartesian3.magnitudeSquared(w);
product = w2 * difference;
if (qw2 < product) {
// Imaginary roots (0 intersections).
return undefined;
} else if (qw2 > product) {
// Distinct roots (2 intersections).
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Avoid cancellation.
var root0 = temp / w2;
var root1 = difference / temp;
if (root0 < root1) {
return {
start : root0,
stop : root1
};
}
return {
start : root1,
stop : root0
};
} else {
// qw2 == product. Repeated roots (2 intersections).
var root = Math.sqrt(difference / w2);
return {
start : root,
stop : root
};
}
} else if (q2 < 1.0) {
// Inside ellipsoid (2 intersections).
difference = q2 - 1.0; // Negatively valued.
w2 = Cartesian3.magnitudeSquared(w);
product = w2 * difference; // Negatively valued.
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Positively valued.
return {
start : 0.0,
stop : temp / w2
};
} else {
// q2 == 1.0. On ellipsoid.
if (qw < 0.0) {
// Looking inward.
w2 = Cartesian3.magnitudeSquared(w);
return {
start : 0.0,
stop : -qw / w2
};
}
// qw >= 0.0. Looking outward or tangent.
return undefined;
}
};
function addWithCancellationCheck(left, right, tolerance) {
var difference = left + right;
if ((CesiumMath.sign(left) !== CesiumMath.sign(right)) &&
Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance) {
return 0.0;
}
return difference;
}
function quadraticVectorExpression(A, b, c, x, w) {
var xSquared = x * x;
var wSquared = w * w;
var l2 = (A[Matrix3.COLUMN1ROW1] - A[Matrix3.COLUMN2ROW2]) * wSquared;
var l1 = w * (x * addWithCancellationCheck(A[Matrix3.COLUMN1ROW0], A[Matrix3.COLUMN0ROW1], CesiumMath.EPSILON15) + b.y);
var l0 = (A[Matrix3.COLUMN0ROW0] * xSquared + A[Matrix3.COLUMN2ROW2] * wSquared) + x * b.x + c;
var r1 = wSquared * addWithCancellationCheck(A[Matrix3.COLUMN2ROW1], A[Matrix3.COLUMN1ROW2], CesiumMath.EPSILON15);
var r0 = w * (x * addWithCancellationCheck(A[Matrix3.COLUMN2ROW0], A[Matrix3.COLUMN0ROW2]) + b.z);
var cosines;
var solutions = [];
if (r0 === 0.0 && r1 === 0.0) {
cosines = QuadraticRealPolynomial.computeRealRoots(l2, l1, l0);
if (cosines.length === 0) {
return solutions;
}
var cosine0 = cosines[0];
var sine0 = Math.sqrt(Math.max(1.0 - cosine0 * cosine0, 0.0));
solutions.push(new Cartesian3(x, w * cosine0, w * -sine0));
solutions.push(new Cartesian3(x, w * cosine0, w * sine0));
if (cosines.length === 2) {
var cosine1 = cosines[1];
var sine1 = Math.sqrt(Math.max(1.0 - cosine1 * cosine1, 0.0));
solutions.push(new Cartesian3(x, w * cosine1, w * -sine1));
solutions.push(new Cartesian3(x, w * cosine1, w * sine1));
}
return solutions;
}
var r0Squared = r0 * r0;
var r1Squared = r1 * r1;
var l2Squared = l2 * l2;
var r0r1 = r0 * r1;
var c4 = l2Squared + r1Squared;
var c3 = 2.0 * (l1 * l2 + r0r1);
var c2 = 2.0 * l0 * l2 + l1 * l1 - r1Squared + r0Squared;
var c1 = 2.0 * (l0 * l1 - r0r1);
var c0 = l0 * l0 - r0Squared;
if (c4 === 0.0 && c3 === 0.0 && c2 === 0.0 && c1 === 0.0) {
return solutions;
}
cosines = QuarticRealPolynomial.computeRealRoots(c4, c3, c2, c1, c0);
var length = cosines.length;
if (length === 0) {
return solutions;
}
for ( var i = 0; i < length; ++i) {
var cosine = cosines[i];
var cosineSquared = cosine * cosine;
var sineSquared = Math.max(1.0 - cosineSquared, 0.0);
var sine = Math.sqrt(sineSquared);
//var left = l2 * cosineSquared + l1 * cosine + l0;
var left;
if (CesiumMath.sign(l2) === CesiumMath.sign(l0)) {
left = addWithCancellationCheck(l2 * cosineSquared + l0, l1 * cosine, CesiumMath.EPSILON12);
} else if (CesiumMath.sign(l0) === CesiumMath.sign(l1 * cosine)) {
left = addWithCancellationCheck(l2 * cosineSquared, l1 * cosine + l0, CesiumMath.EPSILON12);
} else {
left = addWithCancellationCheck(l2 * cosineSquared + l1 * cosine, l0, CesiumMath.EPSILON12);
}
var right = addWithCancellationCheck(r1 * cosine, r0, CesiumMath.EPSILON15);
var product = left * right;
if (product < 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * sine));
} else if (product > 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * -sine));
} else if (sine !== 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * -sine));
solutions.push(new Cartesian3(x, w * cosine, w * sine));
++i;
} else {
solutions.push(new Cartesian3(x, w * cosine, w * sine));
}
}
return solutions;
}
var firstAxisScratch = new Cartesian3();
var secondAxisScratch = new Cartesian3();
var thirdAxisScratch = new Cartesian3();
var referenceScratch = new Cartesian3();
var bCart = new Cartesian3();
var bScratch = new Matrix3();
var btScratch = new Matrix3();
var diScratch = new Matrix3();
var dScratch = new Matrix3();
var cScratch = new Matrix3();
var tempMatrix = new Matrix3();
var aScratch = new Matrix3();
var sScratch = new Cartesian3();
var closestScratch = new Cartesian3();
var surfPointScratch = new Cartographic();
/**
* Provides the point along the ray which is nearest to the ellipsoid.
*
* @param {Ray} ray The ray.
* @param {Ellipsoid} ellipsoid The ellipsoid.
* @returns {Cartesian3} The nearest planetodetic point on the ray.
*/
IntersectionTests.grazingAltitudeLocation = function(ray, ellipsoid) {
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
var position = ray.origin;
var direction = ray.direction;
if (!Cartesian3.equals(position, Cartesian3.ZERO)) {
var normal = ellipsoid.geodeticSurfaceNormal(position, firstAxisScratch);
if (Cartesian3.dot(direction, normal) >= 0.0) { // The location provided is the closest point in altitude
return position;
}
}
var intersects = defined(this.rayEllipsoid(ray, ellipsoid));
// Compute the scaled direction vector.
var f = ellipsoid.transformPositionToScaledSpace(direction, firstAxisScratch);
// Constructs a basis from the unit scaled direction vector. Construct its rotation and transpose.
var firstAxis = Cartesian3.normalize(f, f);
var reference = Cartesian3.mostOrthogonalAxis(f, referenceScratch);
var secondAxis = Cartesian3.normalize(Cartesian3.cross(reference, firstAxis, secondAxisScratch), secondAxisScratch);
var thirdAxis = Cartesian3.normalize(Cartesian3.cross(firstAxis, secondAxis, thirdAxisScratch), thirdAxisScratch);
var B = bScratch;
B[0] = firstAxis.x;
B[1] = firstAxis.y;
B[2] = firstAxis.z;
B[3] = secondAxis.x;
B[4] = secondAxis.y;
B[5] = secondAxis.z;
B[6] = thirdAxis.x;
B[7] = thirdAxis.y;
B[8] = thirdAxis.z;
var B_T = Matrix3.transpose(B, btScratch);
// Get the scaling matrix and its inverse.
var D_I = Matrix3.fromScale(ellipsoid.radii, diScratch);
var D = Matrix3.fromScale(ellipsoid.oneOverRadii, dScratch);
var C = cScratch;
C[0] = 0.0;
C[1] = -direction.z;
C[2] = direction.y;
C[3] = direction.z;
C[4] = 0.0;
C[5] = -direction.x;
C[6] = -direction.y;
C[7] = direction.x;
C[8] = 0.0;
var temp = Matrix3.multiply(Matrix3.multiply(B_T, D, tempMatrix), C, tempMatrix);
var A = Matrix3.multiply(Matrix3.multiply(temp, D_I, aScratch), B, aScratch);
var b = Matrix3.multiplyByVector(temp, position, bCart);
// Solve for the solutions to the expression in standard form:
var solutions = quadraticVectorExpression(A, Cartesian3.negate(b, firstAxisScratch), 0.0, 0.0, 1.0);
var s;
var altitude;
var length = solutions.length;
if (length > 0) {
var closest = Cartesian3.clone(Cartesian3.ZERO, closestScratch);
var maximumValue = Number.NEGATIVE_INFINITY;
for ( var i = 0; i < length; ++i) {
s = Matrix3.multiplyByVector(D_I, Matrix3.multiplyByVector(B, solutions[i], sScratch), sScratch);
var v = Cartesian3.normalize(Cartesian3.subtract(s, position, referenceScratch), referenceScratch);
var dotProduct = Cartesian3.dot(v, direction);
if (dotProduct > maximumValue) {
maximumValue = dotProduct;
closest = Cartesian3.clone(s, closest);
}
}
var surfacePoint = ellipsoid.cartesianToCartographic(closest, surfPointScratch);
maximumValue = CesiumMath.clamp(maximumValue, 0.0, 1.0);
altitude = Cartesian3.magnitude(Cartesian3.subtract(closest, position, referenceScratch)) * Math.sqrt(1.0 - maximumValue * maximumValue);
altitude = intersects ? -altitude : altitude;
surfacePoint.height = altitude;
return ellipsoid.cartographicToCartesian(surfacePoint, new Cartesian3());
}
return undefined;
};
var lineSegmentPlaneDifference = new Cartesian3();
/**
* Computes the intersection of a line segment and a plane.
*
* @param {Cartesian3} endPoint0 An end point of the line segment.
* @param {Cartesian3} endPoint1 The other end point of the line segment.
* @param {Plane} plane The plane.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersection.
*
* @example
* var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* var normal = ellipsoid.geodeticSurfaceNormal(origin);
* var plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* var p0 = new Cesium.Cartesian3(...);
* var p1 = new Cesium.Cartesian3(...);
*
* // find the intersection of the line segment from p0 to p1 and the tangent plane at origin.
* var intersection = Cesium.IntersectionTests.lineSegmentPlane(p0, p1, plane);
*/
IntersectionTests.lineSegmentPlane = function(endPoint0, endPoint1, plane, result) {
if (!defined(endPoint0)) {
throw new DeveloperError('endPoint0 is required.');
}
if (!defined(endPoint1)) {
throw new DeveloperError('endPoint1 is required.');
}
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
if (!defined(result)) {
result = new Cartesian3();
}
var difference = Cartesian3.subtract(endPoint1, endPoint0, lineSegmentPlaneDifference);
var normal = plane.normal;
var nDotDiff = Cartesian3.dot(normal, difference);
// check if the segment and plane are parallel
if (Math.abs(nDotDiff) < CesiumMath.EPSILON6) {
return undefined;
}
var nDotP0 = Cartesian3.dot(normal, endPoint0);
var t = -(plane.distance + nDotP0) / nDotDiff;
// intersection only if t is in [0, 1]
if (t < 0.0 || t > 1.0) {
return undefined;
}
// intersection is endPoint0 + t * (endPoint1 - endPoint0)
Cartesian3.multiplyByScalar(difference, t, result);
Cartesian3.add(endPoint0, result, result);
return result;
};
/**
* Computes the intersection of a triangle and a plane
*
* @param {Cartesian3} p0 First point of the triangle
* @param {Cartesian3} p1 Second point of the triangle
* @param {Cartesian3} p2 Third point of the triangle
* @param {Plane} plane Intersection plane
* @returns {Object} An object with properties positions and indices, which are arrays that represent three triangles that do not cross the plane. (Undefined if no intersection exists)
*
* @example
* var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* var normal = ellipsoid.geodeticSurfaceNormal(origin);
* var plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* var p0 = new Cesium.Cartesian3(...);
* var p1 = new Cesium.Cartesian3(...);
* var p2 = new Cesium.Cartesian3(...);
*
* // convert the triangle composed of points (p0, p1, p2) to three triangles that don't cross the plane
* var triangles = Cesium.IntersectionTests.trianglePlaneIntersection(p0, p1, p2, plane);
*/
IntersectionTests.trianglePlaneIntersection = function(p0, p1, p2, plane) {
if ((!defined(p0)) ||
(!defined(p1)) ||
(!defined(p2)) ||
(!defined(plane))) {
throw new DeveloperError('p0, p1, p2, and plane are required.');
}
var planeNormal = plane.normal;
var planeD = plane.distance;
var p0Behind = (Cartesian3.dot(planeNormal, p0) + planeD) < 0.0;
var p1Behind = (Cartesian3.dot(planeNormal, p1) + planeD) < 0.0;
var p2Behind = (Cartesian3.dot(planeNormal, p2) + planeD) < 0.0;
// Given these dots products, the calls to lineSegmentPlaneIntersection
// always have defined results.
var numBehind = 0;
numBehind += p0Behind ? 1 : 0;
numBehind += p1Behind ? 1 : 0;
numBehind += p2Behind ? 1 : 0;
var u1, u2;
if (numBehind === 1 || numBehind === 2) {
u1 = new Cartesian3();
u2 = new Cartesian3();
}
if (numBehind === 1) {
if (p0Behind) {
IntersectionTests.lineSegmentPlane(p0, p1, plane, u1);
IntersectionTests.lineSegmentPlane(p0, p2, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
0, 3, 4,
// In front
1, 2, 4,
1, 4, 3
]
};
} else if (p1Behind) {
IntersectionTests.lineSegmentPlane(p1, p2, plane, u1);
IntersectionTests.lineSegmentPlane(p1, p0, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
1, 3, 4,
// In front
2, 0, 4,
2, 4, 3
]
};
} else if (p2Behind) {
IntersectionTests.lineSegmentPlane(p2, p0, plane, u1);
IntersectionTests.lineSegmentPlane(p2, p1, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
2, 3, 4,
// In front
0, 1, 4,
0, 4, 3
]
};
}
} else if (numBehind === 2) {
if (!p0Behind) {
IntersectionTests.lineSegmentPlane(p1, p0, plane, u1);
IntersectionTests.lineSegmentPlane(p2, p0, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
1, 2, 4,
1, 4, 3,
// In front
0, 3, 4
]
};
} else if (!p1Behind) {
IntersectionTests.lineSegmentPlane(p2, p1, plane, u1);
IntersectionTests.lineSegmentPlane(p0, p1, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
2, 0, 4,
2, 4, 3,
// In front
1, 3, 4
]
};
} else if (!p2Behind) {
IntersectionTests.lineSegmentPlane(p0, p2, plane, u1);
IntersectionTests.lineSegmentPlane(p1, p2, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
0, 1, 4,
0, 4, 3,
// In front
2, 3, 4
]
};
}
}
// if numBehind is 3, the triangle is completely behind the plane;
// otherwise, it is completely in front (numBehind is 0).
return undefined;
};
return IntersectionTests;
});
/*global define*/
define('Core/Plane',[
'./Cartesian3',
'./defined',
'./DeveloperError',
'./freezeObject'
], function(
Cartesian3,
defined,
DeveloperError,
freezeObject) {
'use strict';
/**
* A plane in Hessian Normal Form defined by
*
* ax + by + cz + d = 0
*
* where (a, b, c) is the plane's normal, d is the signed
* distance to the plane, and (x, y, z) is any point on
* the plane.
*
* @alias Plane
* @constructor
*
* @param {Cartesian3} normal The plane's normal (normalized).
* @param {Number} distance The shortest distance from the origin to the plane. The sign of
* distance determines which side of the plane the origin
* is on. If distance is positive, the origin is in the half-space
* in the direction of the normal; if negative, the origin is in the half-space
* opposite to the normal; if zero, the plane passes through the origin.
*
* @example
* // The plane x=0
* var plane = new Cesium.Plane(Cesium.Cartesian3.UNIT_X, 0.0);
*/
function Plane(normal, distance) {
if (!defined(normal)) {
throw new DeveloperError('normal is required.');
}
if (!defined(distance)) {
throw new DeveloperError('distance is required.');
}
/**
* The plane's normal.
*
* @type {Cartesian3}
*/
this.normal = Cartesian3.clone(normal);
/**
* The shortest distance from the origin to the plane. The sign of
* distance determines which side of the plane the origin
* is on. If distance is positive, the origin is in the half-space
* in the direction of the normal; if negative, the origin is in the half-space
* opposite to the normal; if zero, the plane passes through the origin.
*
* @type {Number}
*/
this.distance = distance;
}
/**
* Creates a plane from a normal and a point on the plane.
*
* @param {Cartesian3} point The point on the plane.
* @param {Cartesian3} normal The plane's normal (normalized).
* @param {Plane} [result] The object onto which to store the result.
* @returns {Plane} A new plane instance or the modified result parameter.
*
* @example
* var point = Cesium.Cartesian3.fromDegrees(-72.0, 40.0);
* var normal = ellipsoid.geodeticSurfaceNormal(point);
* var tangentPlane = Cesium.Plane.fromPointNormal(point, normal);
*/
Plane.fromPointNormal = function(point, normal, result) {
if (!defined(point)) {
throw new DeveloperError('point is required.');
}
if (!defined(normal)) {
throw new DeveloperError('normal is required.');
}
var distance = -Cartesian3.dot(normal, point);
if (!defined(result)) {
return new Plane(normal, distance);
}
Cartesian3.clone(normal, result.normal);
result.distance = distance;
return result;
};
var scratchNormal = new Cartesian3();
/**
* Creates a plane from the general equation
*
* @param {Cartesian4} coefficients The plane's normal (normalized).
* @param {Plane} [result] The object onto which to store the result.
* @returns {Plane} A new plane instance or the modified result parameter.
*/
Plane.fromCartesian4 = function(coefficients, result) {
if (!defined(coefficients)) {
throw new DeveloperError('coefficients is required.');
}
var normal = Cartesian3.fromCartesian4(coefficients, scratchNormal);
var distance = coefficients.w;
if (!defined(result)) {
return new Plane(normal, distance);
} else {
Cartesian3.clone(normal, result.normal);
result.distance = distance;
return result;
}
};
/**
* Computes the signed shortest distance of a point to a plane.
* The sign of the distance determines which side of the plane the point
* is on. If the distance is positive, the point is in the half-space
* in the direction of the normal; if negative, the point is in the half-space
* opposite to the normal; if zero, the plane passes through the point.
*
* @param {Plane} plane The plane.
* @param {Cartesian3} point The point.
* @returns {Number} The signed shortest distance of the point to the plane.
*/
Plane.getPointDistance = function(plane, point) {
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
if (!defined(point)) {
throw new DeveloperError('point is required.');
}
return Cartesian3.dot(plane.normal, point) + plane.distance;
};
/**
* A constant initialized to the XY plane passing through the origin, with normal in positive Z.
*
* @type {Plane}
* @constant
*/
Plane.ORIGIN_XY_PLANE = freezeObject(new Plane(Cartesian3.UNIT_Z, 0.0));
/**
* A constant initialized to the YZ plane passing through the origin, with normal in positive X.
*
* @type {Plane}
* @constant
*/
Plane.ORIGIN_YZ_PLANE = freezeObject(new Plane(Cartesian3.UNIT_X, 0.0));
/**
* A constant initialized to the ZX plane passing through the origin, with normal in positive Y.
*
* @type {Plane}
* @constant
*/
Plane.ORIGIN_ZX_PLANE = freezeObject(new Plane(Cartesian3.UNIT_Y, 0.0));
return Plane;
});
/*global define*/
define('Core/Tipsify',[
'./defaultValue',
'./defined',
'./DeveloperError'
], function(
defaultValue,
defined,
DeveloperError) {
'use strict';
/**
* Encapsulates an algorithm to optimize triangles for the post
* vertex-shader cache. This is based on the 2007 SIGGRAPH paper
* 'Fast Triangle Reordering for Vertex Locality and Reduced Overdraw.'
* The runtime is linear but several passes are made.
*
* @exports Tipsify
*
* @see
* Fast Triangle Reordering for Vertex Locality and Reduced Overdraw
* by Sander, Nehab, and Barczak
*
* @private
*/
var Tipsify = {};
/**
* Calculates the average cache miss ratio (ACMR) for a given set of indices.
*
* @param {Object} options Object with the following properties:
* @param {Number[]} options.indices Lists triads of numbers corresponding to the indices of the vertices
* in the vertex buffer that define the geometry's triangles.
* @param {Number} [options.maximumIndex] The maximum value of the elements in args.indices.
* If not supplied, this value will be computed.
* @param {Number} [options.cacheSize=24] The number of vertices that can be stored in the cache at any one time.
* @returns {Number} The average cache miss ratio (ACMR).
*
* @exception {DeveloperError} indices length must be a multiple of three.
* @exception {DeveloperError} cacheSize must be greater than two.
*
* @example
* var indices = [0, 1, 2, 3, 4, 5];
* var maxIndex = 5;
* var cacheSize = 3;
* var acmr = Cesium.Tipsify.calculateACMR({indices : indices, maxIndex : maxIndex, cacheSize : cacheSize});
*/
Tipsify.calculateACMR = function(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var indices = options.indices;
var maximumIndex = options.maximumIndex;
var cacheSize = defaultValue(options.cacheSize, 24);
if (!defined(indices)) {
throw new DeveloperError('indices is required.');
}
var numIndices = indices.length;
if (numIndices < 3 || numIndices % 3 !== 0) {
throw new DeveloperError('indices length must be a multiple of three.');
}
if (maximumIndex <= 0) {
throw new DeveloperError('maximumIndex must be greater than zero.');
}
if (cacheSize < 3) {
throw new DeveloperError('cacheSize must be greater than two.');
}
// Compute the maximumIndex if not given
if (!defined(maximumIndex)) {
maximumIndex = 0;
var currentIndex = 0;
var intoIndices = indices[currentIndex];
while (currentIndex < numIndices) {
if (intoIndices > maximumIndex) {
maximumIndex = intoIndices;
}
++currentIndex;
intoIndices = indices[currentIndex];
}
}
// Vertex time stamps
var vertexTimeStamps = [];
for ( var i = 0; i < maximumIndex + 1; i++) {
vertexTimeStamps[i] = 0;
}
// Cache processing
var s = cacheSize + 1;
for ( var j = 0; j < numIndices; ++j) {
if ((s - vertexTimeStamps[indices[j]]) > cacheSize) {
vertexTimeStamps[indices[j]] = s;
++s;
}
}
return (s - cacheSize + 1) / (numIndices / 3);
};
/**
* Optimizes triangles for the post-vertex shader cache.
*
* @param {Number[]} options.indices Lists triads of numbers corresponding to the indices of the vertices
* in the vertex buffer that define the geometry's triangles.
* @param {Number} [options.maximumIndex] The maximum value of the elements in args.indices.
* If not supplied, this value will be computed.
* @param {Number} [options.cacheSize=24] The number of vertices that can be stored in the cache at any one time.
* @returns {Number[]} A list of the input indices in an optimized order.
*
* @exception {DeveloperError} indices length must be a multiple of three.
* @exception {DeveloperError} cacheSize must be greater than two.
*
* @example
* var indices = [0, 1, 2, 3, 4, 5];
* var maxIndex = 5;
* var cacheSize = 3;
* var reorderedIndices = Cesium.Tipsify.tipsify({indices : indices, maxIndex : maxIndex, cacheSize : cacheSize});
*/
Tipsify.tipsify = function(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var indices = options.indices;
var maximumIndex = options.maximumIndex;
var cacheSize = defaultValue(options.cacheSize, 24);
var cursor;
function skipDeadEnd(vertices, deadEnd, indices, maximumIndexPlusOne) {
while (deadEnd.length >= 1) {
// while the stack is not empty
var d = deadEnd[deadEnd.length - 1]; // top of the stack
deadEnd.splice(deadEnd.length - 1, 1); // pop the stack
if (vertices[d].numLiveTriangles > 0) {
return d;
}
}
while (cursor < maximumIndexPlusOne) {
if (vertices[cursor].numLiveTriangles > 0) {
++cursor;
return cursor - 1;
}
++cursor;
}
return -1;
}
function getNextVertex(indices, cacheSize, oneRing, vertices, s, deadEnd, maximumIndexPlusOne) {
var n = -1;
var p;
var m = -1;
var itOneRing = 0;
while (itOneRing < oneRing.length) {
var index = oneRing[itOneRing];
if (vertices[index].numLiveTriangles) {
p = 0;
if ((s - vertices[index].timeStamp + (2 * vertices[index].numLiveTriangles)) <= cacheSize) {
p = s - vertices[index].timeStamp;
}
if ((p > m) || (m === -1)) {
m = p;
n = index;
}
}
++itOneRing;
}
if (n === -1) {
return skipDeadEnd(vertices, deadEnd, indices, maximumIndexPlusOne);
}
return n;
}
if (!defined(indices)) {
throw new DeveloperError('indices is required.');
}
var numIndices = indices.length;
if (numIndices < 3 || numIndices % 3 !== 0) {
throw new DeveloperError('indices length must be a multiple of three.');
}
if (maximumIndex <= 0) {
throw new DeveloperError('maximumIndex must be greater than zero.');
}
if (cacheSize < 3) {
throw new DeveloperError('cacheSize must be greater than two.');
}
// Determine maximum index
var maximumIndexPlusOne = 0;
var currentIndex = 0;
var intoIndices = indices[currentIndex];
var endIndex = numIndices;
if (defined(maximumIndex)) {
maximumIndexPlusOne = maximumIndex + 1;
} else {
while (currentIndex < endIndex) {
if (intoIndices > maximumIndexPlusOne) {
maximumIndexPlusOne = intoIndices;
}
++currentIndex;
intoIndices = indices[currentIndex];
}
if (maximumIndexPlusOne === -1) {
return 0;
}
++maximumIndexPlusOne;
}
// Vertices
var vertices = [];
for ( var i = 0; i < maximumIndexPlusOne; i++) {
vertices[i] = {
numLiveTriangles : 0,
timeStamp : 0,
vertexTriangles : []
};
}
currentIndex = 0;
var triangle = 0;
while (currentIndex < endIndex) {
vertices[indices[currentIndex]].vertexTriangles.push(triangle);
++(vertices[indices[currentIndex]]).numLiveTriangles;
vertices[indices[currentIndex + 1]].vertexTriangles.push(triangle);
++(vertices[indices[currentIndex + 1]]).numLiveTriangles;
vertices[indices[currentIndex + 2]].vertexTriangles.push(triangle);
++(vertices[indices[currentIndex + 2]]).numLiveTriangles;
++triangle;
currentIndex += 3;
}
// Starting index
var f = 0;
// Time Stamp
var s = cacheSize + 1;
cursor = 1;
// Process
var oneRing = [];
var deadEnd = []; //Stack
var vertex;
var intoVertices;
var currentOutputIndex = 0;
var outputIndices = [];
var numTriangles = numIndices / 3;
var triangleEmitted = [];
for (i = 0; i < numTriangles; i++) {
triangleEmitted[i] = false;
}
var index;
var limit;
while (f !== -1) {
oneRing = [];
intoVertices = vertices[f];
limit = intoVertices.vertexTriangles.length;
for ( var k = 0; k < limit; ++k) {
triangle = intoVertices.vertexTriangles[k];
if (!triangleEmitted[triangle]) {
triangleEmitted[triangle] = true;
currentIndex = triangle + triangle + triangle;
for ( var j = 0; j < 3; ++j) {
// Set this index as a possible next index
index = indices[currentIndex];
oneRing.push(index);
deadEnd.push(index);
// Output index
outputIndices[currentOutputIndex] = index;
++currentOutputIndex;
// Cache processing
vertex = vertices[index];
--vertex.numLiveTriangles;
if ((s - vertex.timeStamp) > cacheSize) {
vertex.timeStamp = s;
++s;
}
++currentIndex;
}
}
}
f = getNextVertex(indices, cacheSize, oneRing, vertices, s, deadEnd, maximumIndexPlusOne);
}
return outputIndices;
};
return Tipsify;
});
/*global define*/
define('Core/GeometryPipeline',[
'./AttributeCompression',
'./barycentricCoordinates',
'./BoundingSphere',
'./Cartesian2',
'./Cartesian3',
'./Cartesian4',
'./Cartographic',
'./ComponentDatatype',
'./defaultValue',
'./defined',
'./DeveloperError',
'./EncodedCartesian3',
'./GeographicProjection',
'./Geometry',
'./GeometryAttribute',
'./GeometryType',
'./IndexDatatype',
'./Intersect',
'./IntersectionTests',
'./Math',
'./Matrix3',
'./Matrix4',
'./Plane',
'./PrimitiveType',
'./Tipsify'
], function(
AttributeCompression,
barycentricCoordinates,
BoundingSphere,
Cartesian2,
Cartesian3,
Cartesian4,
Cartographic,
ComponentDatatype,
defaultValue,
defined,
DeveloperError,
EncodedCartesian3,
GeographicProjection,
Geometry,
GeometryAttribute,
GeometryType,
IndexDatatype,
Intersect,
IntersectionTests,
CesiumMath,
Matrix3,
Matrix4,
Plane,
PrimitiveType,
Tipsify) {
'use strict';
/**
* Content pipeline functions for geometries.
*
* @exports GeometryPipeline
*
* @see Geometry
*/
var GeometryPipeline = {};
function addTriangle(lines, index, i0, i1, i2) {
lines[index++] = i0;
lines[index++] = i1;
lines[index++] = i1;
lines[index++] = i2;
lines[index++] = i2;
lines[index] = i0;
}
function trianglesToLines(triangles) {
var count = triangles.length;
var size = (count / 3) * 6;
var lines = IndexDatatype.createTypedArray(count, size);
var index = 0;
for ( var i = 0; i < count; i += 3, index += 6) {
addTriangle(lines, index, triangles[i], triangles[i + 1], triangles[i + 2]);
}
return lines;
}
function triangleStripToLines(triangles) {
var count = triangles.length;
if (count >= 3) {
var size = (count - 2) * 6;
var lines = IndexDatatype.createTypedArray(count, size);
addTriangle(lines, 0, triangles[0], triangles[1], triangles[2]);
var index = 6;
for ( var i = 3; i < count; ++i, index += 6) {
addTriangle(lines, index, triangles[i - 1], triangles[i], triangles[i - 2]);
}
return lines;
}
return new Uint16Array();
}
function triangleFanToLines(triangles) {
if (triangles.length > 0) {
var count = triangles.length - 1;
var size = (count - 1) * 6;
var lines = IndexDatatype.createTypedArray(count, size);
var base = triangles[0];
var index = 0;
for ( var i = 1; i < count; ++i, index += 6) {
addTriangle(lines, index, base, triangles[i], triangles[i + 1]);
}
return lines;
}
return new Uint16Array();
}
/**
* Converts a geometry's triangle indices to line indices. If the geometry has an indices
* and its primitiveType is TRIANGLES, TRIANGLE_STRIP,
* TRIANGLE_FAN, it is converted to LINES; otherwise, the geometry is not changed.
*
* This is commonly used to create a wireframe geometry for visual debugging.
*
*
* @param {Geometry} geometry The geometry to modify.
* @returns {Geometry} The modified geometry argument, with its triangle indices converted to lines.
*
* @exception {DeveloperError} geometry.primitiveType must be TRIANGLES, TRIANGLE_STRIP, or TRIANGLE_FAN.
*
* @example
* geometry = Cesium.GeometryPipeline.toWireframe(geometry);
*/
GeometryPipeline.toWireframe = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var indices = geometry.indices;
if (defined(indices)) {
switch (geometry.primitiveType) {
case PrimitiveType.TRIANGLES:
geometry.indices = trianglesToLines(indices);
break;
case PrimitiveType.TRIANGLE_STRIP:
geometry.indices = triangleStripToLines(indices);
break;
case PrimitiveType.TRIANGLE_FAN:
geometry.indices = triangleFanToLines(indices);
break;
default:
throw new DeveloperError('geometry.primitiveType must be TRIANGLES, TRIANGLE_STRIP, or TRIANGLE_FAN.');
}
geometry.primitiveType = PrimitiveType.LINES;
}
return geometry;
};
/**
* Creates a new {@link Geometry} with LINES representing the provided
* attribute (attributeName) for the provided geometry. This is used to
* visualize vector attributes like normals, binormals, and tangents.
*
* @param {Geometry} geometry The Geometry instance with the attribute.
* @param {String} [attributeName='normal'] The name of the attribute.
* @param {Number} [length=10000.0] The length of each line segment in meters. This can be negative to point the vector in the opposite direction.
* @returns {Geometry} A new Geometry instance with line segments for the vector.
*
* @exception {DeveloperError} geometry.attributes must have an attribute with the same name as the attributeName parameter.
*
* @example
* var geometry = Cesium.GeometryPipeline.createLineSegmentsForVectors(instance.geometry, 'binormal', 100000.0);
*/
GeometryPipeline.createLineSegmentsForVectors = function(geometry, attributeName, length) {
attributeName = defaultValue(attributeName, 'normal');
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
if (!defined(geometry.attributes.position)) {
throw new DeveloperError('geometry.attributes.position is required.');
}
if (!defined(geometry.attributes[attributeName])) {
throw new DeveloperError('geometry.attributes must have an attribute with the same name as the attributeName parameter, ' + attributeName + '.');
}
length = defaultValue(length, 10000.0);
var positions = geometry.attributes.position.values;
var vectors = geometry.attributes[attributeName].values;
var positionsLength = positions.length;
var newPositions = new Float64Array(2 * positionsLength);
var j = 0;
for (var i = 0; i < positionsLength; i += 3) {
newPositions[j++] = positions[i];
newPositions[j++] = positions[i + 1];
newPositions[j++] = positions[i + 2];
newPositions[j++] = positions[i] + (vectors[i] * length);
newPositions[j++] = positions[i + 1] + (vectors[i + 1] * length);
newPositions[j++] = positions[i + 2] + (vectors[i + 2] * length);
}
var newBoundingSphere;
var bs = geometry.boundingSphere;
if (defined(bs)) {
newBoundingSphere = new BoundingSphere(bs.center, bs.radius + length);
}
return new Geometry({
attributes : {
position : new GeometryAttribute({
componentDatatype : ComponentDatatype.DOUBLE,
componentsPerAttribute : 3,
values : newPositions
})
},
primitiveType : PrimitiveType.LINES,
boundingSphere : newBoundingSphere
});
};
/**
* Creates an object that maps attribute names to unique locations (indices)
* for matching vertex attributes and shader programs.
*
* @param {Geometry} geometry The geometry, which is not modified, to create the object for.
* @returns {Object} An object with attribute name / index pairs.
*
* @example
* var attributeLocations = Cesium.GeometryPipeline.createAttributeLocations(geometry);
* // Example output
* // {
* // 'position' : 0,
* // 'normal' : 1
* // }
*/
GeometryPipeline.createAttributeLocations = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
// There can be a WebGL performance hit when attribute 0 is disabled, so
// assign attribute locations to well-known attributes.
var semantics = [
'position',
'positionHigh',
'positionLow',
// From VertexFormat.position - after 2D projection and high-precision encoding
'position3DHigh',
'position3DLow',
'position2DHigh',
'position2DLow',
// From Primitive
'pickColor',
// From VertexFormat
'normal',
'st',
'binormal',
'tangent',
// From compressing texture coordinates and normals
'compressedAttributes'
];
var attributes = geometry.attributes;
var indices = {};
var j = 0;
var i;
var len = semantics.length;
// Attribute locations for well-known attributes
for (i = 0; i < len; ++i) {
var semantic = semantics[i];
if (defined(attributes[semantic])) {
indices[semantic] = j++;
}
}
// Locations for custom attributes
for (var name in attributes) {
if (attributes.hasOwnProperty(name) && (!defined(indices[name]))) {
indices[name] = j++;
}
}
return indices;
};
/**
* Reorders a geometry's attributes and indices to achieve better performance from the GPU's pre-vertex-shader cache.
*
* @param {Geometry} geometry The geometry to modify.
* @returns {Geometry} The modified geometry argument, with its attributes and indices reordered for the GPU's pre-vertex-shader cache.
*
* @exception {DeveloperError} Each attribute array in geometry.attributes must have the same number of attributes.
*
*
* @example
* geometry = Cesium.GeometryPipeline.reorderForPreVertexCache(geometry);
*
* @see GeometryPipeline.reorderForPostVertexCache
*/
GeometryPipeline.reorderForPreVertexCache = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var numVertices = Geometry.computeNumberOfVertices(geometry);
var indices = geometry.indices;
if (defined(indices)) {
var indexCrossReferenceOldToNew = new Int32Array(numVertices);
for ( var i = 0; i < numVertices; i++) {
indexCrossReferenceOldToNew[i] = -1;
}
// Construct cross reference and reorder indices
var indicesIn = indices;
var numIndices = indicesIn.length;
var indicesOut = IndexDatatype.createTypedArray(numVertices, numIndices);
var intoIndicesIn = 0;
var intoIndicesOut = 0;
var nextIndex = 0;
var tempIndex;
while (intoIndicesIn < numIndices) {
tempIndex = indexCrossReferenceOldToNew[indicesIn[intoIndicesIn]];
if (tempIndex !== -1) {
indicesOut[intoIndicesOut] = tempIndex;
} else {
tempIndex = indicesIn[intoIndicesIn];
indexCrossReferenceOldToNew[tempIndex] = nextIndex;
indicesOut[intoIndicesOut] = nextIndex;
++nextIndex;
}
++intoIndicesIn;
++intoIndicesOut;
}
geometry.indices = indicesOut;
// Reorder attributes
var attributes = geometry.attributes;
for ( var property in attributes) {
if (attributes.hasOwnProperty(property) &&
defined(attributes[property]) &&
defined(attributes[property].values)) {
var attribute = attributes[property];
var elementsIn = attribute.values;
var intoElementsIn = 0;
var numComponents = attribute.componentsPerAttribute;
var elementsOut = ComponentDatatype.createTypedArray(attribute.componentDatatype, nextIndex * numComponents);
while (intoElementsIn < numVertices) {
var temp = indexCrossReferenceOldToNew[intoElementsIn];
if (temp !== -1) {
for (i = 0; i < numComponents; i++) {
elementsOut[numComponents * temp + i] = elementsIn[numComponents * intoElementsIn + i];
}
}
++intoElementsIn;
}
attribute.values = elementsOut;
}
}
}
return geometry;
};
/**
* Reorders a geometry's indices to achieve better performance from the GPU's
* post vertex-shader cache by using the Tipsify algorithm. If the geometry primitiveType
* is not TRIANGLES or the geometry does not have an indices, this function has no effect.
*
* @param {Geometry} geometry The geometry to modify.
* @param {Number} [cacheCapacity=24] The number of vertices that can be held in the GPU's vertex cache.
* @returns {Geometry} The modified geometry argument, with its indices reordered for the post-vertex-shader cache.
*
* @exception {DeveloperError} cacheCapacity must be greater than two.
*
*
* @example
* geometry = Cesium.GeometryPipeline.reorderForPostVertexCache(geometry);
*
* @see GeometryPipeline.reorderForPreVertexCache
* @see {@link http://gfx.cs.princ0eton.edu/pubs/Sander_2007_%3ETR/tipsy.pdf|Fast Triangle Reordering for Vertex Locality and Reduced Overdraw}
* by Sander, Nehab, and Barczak
*/
GeometryPipeline.reorderForPostVertexCache = function(geometry, cacheCapacity) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var indices = geometry.indices;
if ((geometry.primitiveType === PrimitiveType.TRIANGLES) && (defined(indices))) {
var numIndices = indices.length;
var maximumIndex = 0;
for ( var j = 0; j < numIndices; j++) {
if (indices[j] > maximumIndex) {
maximumIndex = indices[j];
}
}
geometry.indices = Tipsify.tipsify({
indices : indices,
maximumIndex : maximumIndex,
cacheSize : cacheCapacity
});
}
return geometry;
};
function copyAttributesDescriptions(attributes) {
var newAttributes = {};
for ( var attribute in attributes) {
if (attributes.hasOwnProperty(attribute) &&
defined(attributes[attribute]) &&
defined(attributes[attribute].values)) {
var attr = attributes[attribute];
newAttributes[attribute] = new GeometryAttribute({
componentDatatype : attr.componentDatatype,
componentsPerAttribute : attr.componentsPerAttribute,
normalize : attr.normalize,
values : []
});
}
}
return newAttributes;
}
function copyVertex(destinationAttributes, sourceAttributes, index) {
for ( var attribute in sourceAttributes) {
if (sourceAttributes.hasOwnProperty(attribute) &&
defined(sourceAttributes[attribute]) &&
defined(sourceAttributes[attribute].values)) {
var attr = sourceAttributes[attribute];
for ( var k = 0; k < attr.componentsPerAttribute; ++k) {
destinationAttributes[attribute].values.push(attr.values[(index * attr.componentsPerAttribute) + k]);
}
}
}
}
/**
* Splits a geometry into multiple geometries, if necessary, to ensure that indices in the
* indices fit into unsigned shorts. This is used to meet the WebGL requirements
* when unsigned int indices are not supported.
*
* If the geometry does not have any indices, this function has no effect.
*
*
* @param {Geometry} geometry The geometry to be split into multiple geometries.
* @returns {Geometry[]} An array of geometries, each with indices that fit into unsigned shorts.
*
* @exception {DeveloperError} geometry.primitiveType must equal to PrimitiveType.TRIANGLES, PrimitiveType.LINES, or PrimitiveType.POINTS
* @exception {DeveloperError} All geometry attribute lists must have the same number of attributes.
*
* @example
* var geometries = Cesium.GeometryPipeline.fitToUnsignedShortIndices(geometry);
*/
GeometryPipeline.fitToUnsignedShortIndices = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
if ((defined(geometry.indices)) &&
((geometry.primitiveType !== PrimitiveType.TRIANGLES) &&
(geometry.primitiveType !== PrimitiveType.LINES) &&
(geometry.primitiveType !== PrimitiveType.POINTS))) {
throw new DeveloperError('geometry.primitiveType must equal to PrimitiveType.TRIANGLES, PrimitiveType.LINES, or PrimitiveType.POINTS.');
}
var geometries = [];
// If there's an index list and more than 64K attributes, it is possible that
// some indices are outside the range of unsigned short [0, 64K - 1]
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (defined(geometry.indices) && (numberOfVertices >= CesiumMath.SIXTY_FOUR_KILOBYTES)) {
var oldToNewIndex = [];
var newIndices = [];
var currentIndex = 0;
var newAttributes = copyAttributesDescriptions(geometry.attributes);
var originalIndices = geometry.indices;
var numberOfIndices = originalIndices.length;
var indicesPerPrimitive;
if (geometry.primitiveType === PrimitiveType.TRIANGLES) {
indicesPerPrimitive = 3;
} else if (geometry.primitiveType === PrimitiveType.LINES) {
indicesPerPrimitive = 2;
} else if (geometry.primitiveType === PrimitiveType.POINTS) {
indicesPerPrimitive = 1;
}
for ( var j = 0; j < numberOfIndices; j += indicesPerPrimitive) {
for (var k = 0; k < indicesPerPrimitive; ++k) {
var x = originalIndices[j + k];
var i = oldToNewIndex[x];
if (!defined(i)) {
i = currentIndex++;
oldToNewIndex[x] = i;
copyVertex(newAttributes, geometry.attributes, x);
}
newIndices.push(i);
}
if (currentIndex + indicesPerPrimitive >= CesiumMath.SIXTY_FOUR_KILOBYTES) {
geometries.push(new Geometry({
attributes : newAttributes,
indices : newIndices,
primitiveType : geometry.primitiveType,
boundingSphere : geometry.boundingSphere,
boundingSphereCV : geometry.boundingSphereCV
}));
// Reset for next vertex-array
oldToNewIndex = [];
newIndices = [];
currentIndex = 0;
newAttributes = copyAttributesDescriptions(geometry.attributes);
}
}
if (newIndices.length !== 0) {
geometries.push(new Geometry({
attributes : newAttributes,
indices : newIndices,
primitiveType : geometry.primitiveType,
boundingSphere : geometry.boundingSphere,
boundingSphereCV : geometry.boundingSphereCV
}));
}
} else {
// No need to split into multiple geometries
geometries.push(geometry);
}
return geometries;
};
var scratchProjectTo2DCartesian3 = new Cartesian3();
var scratchProjectTo2DCartographic = new Cartographic();
/**
* Projects a geometry's 3D position attribute to 2D, replacing the position
* attribute with separate position3D and position2D attributes.
*
* If the geometry does not have a position, this function has no effect.
*
*
* @param {Geometry} geometry The geometry to modify.
* @param {String} attributeName The name of the attribute.
* @param {String} attributeName3D The name of the attribute in 3D.
* @param {String} attributeName2D The name of the attribute in 2D.
* @param {Object} [projection=new GeographicProjection()] The projection to use.
* @returns {Geometry} The modified geometry argument with position3D and position2D attributes.
*
* @exception {DeveloperError} geometry must have attribute matching the attributeName argument.
* @exception {DeveloperError} The attribute componentDatatype must be ComponentDatatype.DOUBLE.
* @exception {DeveloperError} Could not project a point to 2D.
*
* @example
* geometry = Cesium.GeometryPipeline.projectTo2D(geometry, 'position', 'position3D', 'position2D');
*/
GeometryPipeline.projectTo2D = function(geometry, attributeName, attributeName3D, attributeName2D, projection) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
if (!defined(attributeName)) {
throw new DeveloperError('attributeName is required.');
}
if (!defined(attributeName3D)) {
throw new DeveloperError('attributeName3D is required.');
}
if (!defined(attributeName2D)) {
throw new DeveloperError('attributeName2D is required.');
}
if (!defined(geometry.attributes[attributeName])) {
throw new DeveloperError('geometry must have attribute matching the attributeName argument: ' + attributeName + '.');
}
if (geometry.attributes[attributeName].componentDatatype !== ComponentDatatype.DOUBLE) {
throw new DeveloperError('The attribute componentDatatype must be ComponentDatatype.DOUBLE.');
}
var attribute = geometry.attributes[attributeName];
projection = (defined(projection)) ? projection : new GeographicProjection();
var ellipsoid = projection.ellipsoid;
// Project original values to 2D.
var values3D = attribute.values;
var projectedValues = new Float64Array(values3D.length);
var index = 0;
for ( var i = 0; i < values3D.length; i += 3) {
var value = Cartesian3.fromArray(values3D, i, scratchProjectTo2DCartesian3);
var lonLat = ellipsoid.cartesianToCartographic(value, scratchProjectTo2DCartographic);
if (!defined(lonLat)) {
throw new DeveloperError('Could not project point (' + value.x + ', ' + value.y + ', ' + value.z + ') to 2D.');
}
var projectedLonLat = projection.project(lonLat, scratchProjectTo2DCartesian3);
projectedValues[index++] = projectedLonLat.x;
projectedValues[index++] = projectedLonLat.y;
projectedValues[index++] = projectedLonLat.z;
}
// Rename original cartesians to WGS84 cartesians.
geometry.attributes[attributeName3D] = attribute;
// Replace original cartesians with 2D projected cartesians
geometry.attributes[attributeName2D] = new GeometryAttribute({
componentDatatype : ComponentDatatype.DOUBLE,
componentsPerAttribute : 3,
values : projectedValues
});
delete geometry.attributes[attributeName];
return geometry;
};
var encodedResult = {
high : 0.0,
low : 0.0
};
/**
* Encodes floating-point geometry attribute values as two separate attributes to improve
* rendering precision.
*
* This is commonly used to create high-precision position vertex attributes.
*
*
* @param {Geometry} geometry The geometry to modify.
* @param {String} attributeName The name of the attribute.
* @param {String} attributeHighName The name of the attribute for the encoded high bits.
* @param {String} attributeLowName The name of the attribute for the encoded low bits.
* @returns {Geometry} The modified geometry argument, with its encoded attribute.
*
* @exception {DeveloperError} geometry must have attribute matching the attributeName argument.
* @exception {DeveloperError} The attribute componentDatatype must be ComponentDatatype.DOUBLE.
*
* @example
* geometry = Cesium.GeometryPipeline.encodeAttribute(geometry, 'position3D', 'position3DHigh', 'position3DLow');
*/
GeometryPipeline.encodeAttribute = function(geometry, attributeName, attributeHighName, attributeLowName) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
if (!defined(attributeName)) {
throw new DeveloperError('attributeName is required.');
}
if (!defined(attributeHighName)) {
throw new DeveloperError('attributeHighName is required.');
}
if (!defined(attributeLowName)) {
throw new DeveloperError('attributeLowName is required.');
}
if (!defined(geometry.attributes[attributeName])) {
throw new DeveloperError('geometry must have attribute matching the attributeName argument: ' + attributeName + '.');
}
if (geometry.attributes[attributeName].componentDatatype !== ComponentDatatype.DOUBLE) {
throw new DeveloperError('The attribute componentDatatype must be ComponentDatatype.DOUBLE.');
}
var attribute = geometry.attributes[attributeName];
var values = attribute.values;
var length = values.length;
var highValues = new Float32Array(length);
var lowValues = new Float32Array(length);
for (var i = 0; i < length; ++i) {
EncodedCartesian3.encode(values[i], encodedResult);
highValues[i] = encodedResult.high;
lowValues[i] = encodedResult.low;
}
var componentsPerAttribute = attribute.componentsPerAttribute;
geometry.attributes[attributeHighName] = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : componentsPerAttribute,
values : highValues
});
geometry.attributes[attributeLowName] = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : componentsPerAttribute,
values : lowValues
});
delete geometry.attributes[attributeName];
return geometry;
};
var scratchCartesian3 = new Cartesian3();
function transformPoint(matrix, attribute) {
if (defined(attribute)) {
var values = attribute.values;
var length = values.length;
for (var i = 0; i < length; i += 3) {
Cartesian3.unpack(values, i, scratchCartesian3);
Matrix4.multiplyByPoint(matrix, scratchCartesian3, scratchCartesian3);
Cartesian3.pack(scratchCartesian3, values, i);
}
}
}
function transformVector(matrix, attribute) {
if (defined(attribute)) {
var values = attribute.values;
var length = values.length;
for (var i = 0; i < length; i += 3) {
Cartesian3.unpack(values, i, scratchCartesian3);
Matrix3.multiplyByVector(matrix, scratchCartesian3, scratchCartesian3);
scratchCartesian3 = Cartesian3.normalize(scratchCartesian3, scratchCartesian3);
Cartesian3.pack(scratchCartesian3, values, i);
}
}
}
var inverseTranspose = new Matrix4();
var normalMatrix = new Matrix3();
/**
* Transforms a geometry instance to world coordinates. This changes
* the instance's modelMatrix to {@link Matrix4.IDENTITY} and transforms the
* following attributes if they are present: position, normal,
* binormal, and tangent.
*
* @param {GeometryInstance} instance The geometry instance to modify.
* @returns {GeometryInstance} The modified instance argument, with its attributes transforms to world coordinates.
*
* @example
* Cesium.GeometryPipeline.transformToWorldCoordinates(instance);
*/
GeometryPipeline.transformToWorldCoordinates = function(instance) {
if (!defined(instance)) {
throw new DeveloperError('instance is required.');
}
var modelMatrix = instance.modelMatrix;
if (Matrix4.equals(modelMatrix, Matrix4.IDENTITY)) {
// Already in world coordinates
return instance;
}
var attributes = instance.geometry.attributes;
// Transform attributes in known vertex formats
transformPoint(modelMatrix, attributes.position);
transformPoint(modelMatrix, attributes.prevPosition);
transformPoint(modelMatrix, attributes.nextPosition);
if ((defined(attributes.normal)) ||
(defined(attributes.binormal)) ||
(defined(attributes.tangent))) {
Matrix4.inverse(modelMatrix, inverseTranspose);
Matrix4.transpose(inverseTranspose, inverseTranspose);
Matrix4.getRotation(inverseTranspose, normalMatrix);
transformVector(normalMatrix, attributes.normal);
transformVector(normalMatrix, attributes.binormal);
transformVector(normalMatrix, attributes.tangent);
}
var boundingSphere = instance.geometry.boundingSphere;
if (defined(boundingSphere)) {
instance.geometry.boundingSphere = BoundingSphere.transform(boundingSphere, modelMatrix, boundingSphere);
}
instance.modelMatrix = Matrix4.clone(Matrix4.IDENTITY);
return instance;
};
function findAttributesInAllGeometries(instances, propertyName) {
var length = instances.length;
var attributesInAllGeometries = {};
var attributes0 = instances[0][propertyName].attributes;
var name;
for (name in attributes0) {
if (attributes0.hasOwnProperty(name) &&
defined(attributes0[name]) &&
defined(attributes0[name].values)) {
var attribute = attributes0[name];
var numberOfComponents = attribute.values.length;
var inAllGeometries = true;
// Does this same attribute exist in all geometries?
for (var i = 1; i < length; ++i) {
var otherAttribute = instances[i][propertyName].attributes[name];
if ((!defined(otherAttribute)) ||
(attribute.componentDatatype !== otherAttribute.componentDatatype) ||
(attribute.componentsPerAttribute !== otherAttribute.componentsPerAttribute) ||
(attribute.normalize !== otherAttribute.normalize)) {
inAllGeometries = false;
break;
}
numberOfComponents += otherAttribute.values.length;
}
if (inAllGeometries) {
attributesInAllGeometries[name] = new GeometryAttribute({
componentDatatype : attribute.componentDatatype,
componentsPerAttribute : attribute.componentsPerAttribute,
normalize : attribute.normalize,
values : ComponentDatatype.createTypedArray(attribute.componentDatatype, numberOfComponents)
});
}
}
}
return attributesInAllGeometries;
}
var tempScratch = new Cartesian3();
function combineGeometries(instances, propertyName) {
var length = instances.length;
var name;
var i;
var j;
var k;
var m = instances[0].modelMatrix;
var haveIndices = (defined(instances[0][propertyName].indices));
var primitiveType = instances[0][propertyName].primitiveType;
for (i = 1; i < length; ++i) {
if (!Matrix4.equals(instances[i].modelMatrix, m)) {
throw new DeveloperError('All instances must have the same modelMatrix.');
}
if ((defined(instances[i][propertyName].indices)) !== haveIndices) {
throw new DeveloperError('All instance geometries must have an indices or not have one.');
}
if (instances[i][propertyName].primitiveType !== primitiveType) {
throw new DeveloperError('All instance geometries must have the same primitiveType.');
}
}
// Find subset of attributes in all geometries
var attributes = findAttributesInAllGeometries(instances, propertyName);
var values;
var sourceValues;
var sourceValuesLength;
// Combine attributes from each geometry into a single typed array
for (name in attributes) {
if (attributes.hasOwnProperty(name)) {
values = attributes[name].values;
k = 0;
for (i = 0; i < length; ++i) {
sourceValues = instances[i][propertyName].attributes[name].values;
sourceValuesLength = sourceValues.length;
for (j = 0; j < sourceValuesLength; ++j) {
values[k++] = sourceValues[j];
}
}
}
}
// Combine index lists
var indices;
if (haveIndices) {
var numberOfIndices = 0;
for (i = 0; i < length; ++i) {
numberOfIndices += instances[i][propertyName].indices.length;
}
var numberOfVertices = Geometry.computeNumberOfVertices(new Geometry({
attributes : attributes,
primitiveType : PrimitiveType.POINTS
}));
var destIndices = IndexDatatype.createTypedArray(numberOfVertices, numberOfIndices);
var destOffset = 0;
var offset = 0;
for (i = 0; i < length; ++i) {
var sourceIndices = instances[i][propertyName].indices;
var sourceIndicesLen = sourceIndices.length;
for (k = 0; k < sourceIndicesLen; ++k) {
destIndices[destOffset++] = offset + sourceIndices[k];
}
offset += Geometry.computeNumberOfVertices(instances[i][propertyName]);
}
indices = destIndices;
}
// Create bounding sphere that includes all instances
var center = new Cartesian3();
var radius = 0.0;
var bs;
for (i = 0; i < length; ++i) {
bs = instances[i][propertyName].boundingSphere;
if (!defined(bs)) {
// If any geometries have an undefined bounding sphere, then so does the combined geometry
center = undefined;
break;
}
Cartesian3.add(bs.center, center, center);
}
if (defined(center)) {
Cartesian3.divideByScalar(center, length, center);
for (i = 0; i < length; ++i) {
bs = instances[i][propertyName].boundingSphere;
var tempRadius = Cartesian3.magnitude(Cartesian3.subtract(bs.center, center, tempScratch)) + bs.radius;
if (tempRadius > radius) {
radius = tempRadius;
}
}
}
return new Geometry({
attributes : attributes,
indices : indices,
primitiveType : primitiveType,
boundingSphere : (defined(center)) ? new BoundingSphere(center, radius) : undefined
});
}
/**
* Combines geometry from several {@link GeometryInstance} objects into one geometry.
* This concatenates the attributes, concatenates and adjusts the indices, and creates
* a bounding sphere encompassing all instances.
*
* If the instances do not have the same attributes, a subset of attributes common
* to all instances is used, and the others are ignored.
*
*
* This is used by {@link Primitive} to efficiently render a large amount of static data.
*
*
* @private
*
* @param {GeometryInstance[]} [instances] The array of {@link GeometryInstance} objects whose geometry will be combined.
* @returns {Geometry} A single geometry created from the provided geometry instances.
*
* @exception {DeveloperError} All instances must have the same modelMatrix.
* @exception {DeveloperError} All instance geometries must have an indices or not have one.
* @exception {DeveloperError} All instance geometries must have the same primitiveType.
*
*
* @example
* for (var i = 0; i < instances.length; ++i) {
* Cesium.GeometryPipeline.transformToWorldCoordinates(instances[i]);
* }
* var geometries = Cesium.GeometryPipeline.combineInstances(instances);
*
* @see GeometryPipeline.transformToWorldCoordinates
*/
GeometryPipeline.combineInstances = function(instances) {
if ((!defined(instances)) || (instances.length < 1)) {
throw new DeveloperError('instances is required and must have length greater than zero.');
}
var instanceGeometry = [];
var instanceSplitGeometry = [];
var length = instances.length;
for (var i = 0; i < length; ++i) {
var instance = instances[i];
if (defined(instance.geometry)) {
instanceGeometry.push(instance);
} else if (defined(instance.westHemisphereGeometry) && defined(instance.eastHemisphereGeometry)) {
instanceSplitGeometry.push(instance);
}
}
var geometries = [];
if (instanceGeometry.length > 0) {
geometries.push(combineGeometries(instanceGeometry, 'geometry'));
}
if (instanceSplitGeometry.length > 0) {
geometries.push(combineGeometries(instanceSplitGeometry, 'westHemisphereGeometry'));
geometries.push(combineGeometries(instanceSplitGeometry, 'eastHemisphereGeometry'));
}
return geometries;
};
var normal = new Cartesian3();
var v0 = new Cartesian3();
var v1 = new Cartesian3();
var v2 = new Cartesian3();
/**
* Computes per-vertex normals for a geometry containing TRIANGLES by averaging the normals of
* all triangles incident to the vertex. The result is a new normal attribute added to the geometry.
* This assumes a counter-clockwise winding order.
*
* @param {Geometry} geometry The geometry to modify.
* @returns {Geometry} The modified geometry argument with the computed normal attribute.
*
* @exception {DeveloperError} geometry.indices length must be greater than 0 and be a multiple of 3.
* @exception {DeveloperError} geometry.primitiveType must be {@link PrimitiveType.TRIANGLES}.
*
* @example
* Cesium.GeometryPipeline.computeNormal(geometry);
*/
GeometryPipeline.computeNormal = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
if (!defined(geometry.attributes.position) || !defined(geometry.attributes.position.values)) {
throw new DeveloperError('geometry.attributes.position.values is required.');
}
if (!defined(geometry.indices)) {
throw new DeveloperError('geometry.indices is required.');
}
if (geometry.indices.length < 2 || geometry.indices.length % 3 !== 0) {
throw new DeveloperError('geometry.indices length must be greater than 0 and be a multiple of 3.');
}
if (geometry.primitiveType !== PrimitiveType.TRIANGLES) {
throw new DeveloperError('geometry.primitiveType must be PrimitiveType.TRIANGLES.');
}
var indices = geometry.indices;
var attributes = geometry.attributes;
var vertices = attributes.position.values;
var numVertices = attributes.position.values.length / 3;
var numIndices = indices.length;
var normalsPerVertex = new Array(numVertices);
var normalsPerTriangle = new Array(numIndices / 3);
var normalIndices = new Array(numIndices);
for ( var i = 0; i < numVertices; i++) {
normalsPerVertex[i] = {
indexOffset : 0,
count : 0,
currentCount : 0
};
}
var j = 0;
for (i = 0; i < numIndices; i += 3) {
var i0 = indices[i];
var i1 = indices[i + 1];
var i2 = indices[i + 2];
var i03 = i0 * 3;
var i13 = i1 * 3;
var i23 = i2 * 3;
v0.x = vertices[i03];
v0.y = vertices[i03 + 1];
v0.z = vertices[i03 + 2];
v1.x = vertices[i13];
v1.y = vertices[i13 + 1];
v1.z = vertices[i13 + 2];
v2.x = vertices[i23];
v2.y = vertices[i23 + 1];
v2.z = vertices[i23 + 2];
normalsPerVertex[i0].count++;
normalsPerVertex[i1].count++;
normalsPerVertex[i2].count++;
Cartesian3.subtract(v1, v0, v1);
Cartesian3.subtract(v2, v0, v2);
normalsPerTriangle[j] = Cartesian3.cross(v1, v2, new Cartesian3());
j++;
}
var indexOffset = 0;
for (i = 0; i < numVertices; i++) {
normalsPerVertex[i].indexOffset += indexOffset;
indexOffset += normalsPerVertex[i].count;
}
j = 0;
var vertexNormalData;
for (i = 0; i < numIndices; i += 3) {
vertexNormalData = normalsPerVertex[indices[i]];
var index = vertexNormalData.indexOffset + vertexNormalData.currentCount;
normalIndices[index] = j;
vertexNormalData.currentCount++;
vertexNormalData = normalsPerVertex[indices[i + 1]];
index = vertexNormalData.indexOffset + vertexNormalData.currentCount;
normalIndices[index] = j;
vertexNormalData.currentCount++;
vertexNormalData = normalsPerVertex[indices[i + 2]];
index = vertexNormalData.indexOffset + vertexNormalData.currentCount;
normalIndices[index] = j;
vertexNormalData.currentCount++;
j++;
}
var normalValues = new Float32Array(numVertices * 3);
for (i = 0; i < numVertices; i++) {
var i3 = i * 3;
vertexNormalData = normalsPerVertex[i];
if (vertexNormalData.count > 0) {
Cartesian3.clone(Cartesian3.ZERO, normal);
for (j = 0; j < vertexNormalData.count; j++) {
Cartesian3.add(normal, normalsPerTriangle[normalIndices[vertexNormalData.indexOffset + j]], normal);
}
Cartesian3.normalize(normal, normal);
normalValues[i3] = normal.x;
normalValues[i3 + 1] = normal.y;
normalValues[i3 + 2] = normal.z;
} else {
normalValues[i3] = 0.0;
normalValues[i3 + 1] = 0.0;
normalValues[i3 + 2] = 1.0;
}
}
geometry.attributes.normal = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : normalValues
});
return geometry;
};
var normalScratch = new Cartesian3();
var normalScale = new Cartesian3();
var tScratch = new Cartesian3();
/**
* Computes per-vertex binormals and tangents for a geometry containing TRIANGLES.
* The result is new binormal and tangent attributes added to the geometry.
* This assumes a counter-clockwise winding order.
*
* Based on Computing Tangent Space Basis Vectors
* for an Arbitrary Mesh by Eric Lengyel.
*
*
* @param {Geometry} geometry The geometry to modify.
* @returns {Geometry} The modified geometry argument with the computed binormal and tangent attributes.
*
* @exception {DeveloperError} geometry.indices length must be greater than 0 and be a multiple of 3.
* @exception {DeveloperError} geometry.primitiveType must be {@link PrimitiveType.TRIANGLES}.
*
* @example
* Cesium.GeometryPipeline.computeBinormalAndTangent(geometry);
*/
GeometryPipeline.computeBinormalAndTangent = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var attributes = geometry.attributes;
var indices = geometry.indices;
if (!defined(attributes.position) || !defined(attributes.position.values)) {
throw new DeveloperError('geometry.attributes.position.values is required.');
}
if (!defined(attributes.normal) || !defined(attributes.normal.values)) {
throw new DeveloperError('geometry.attributes.normal.values is required.');
}
if (!defined(attributes.st) || !defined(attributes.st.values)) {
throw new DeveloperError('geometry.attributes.st.values is required.');
}
if (!defined(indices)) {
throw new DeveloperError('geometry.indices is required.');
}
if (indices.length < 2 || indices.length % 3 !== 0) {
throw new DeveloperError('geometry.indices length must be greater than 0 and be a multiple of 3.');
}
if (geometry.primitiveType !== PrimitiveType.TRIANGLES) {
throw new DeveloperError('geometry.primitiveType must be PrimitiveType.TRIANGLES.');
}
var vertices = geometry.attributes.position.values;
var normals = geometry.attributes.normal.values;
var st = geometry.attributes.st.values;
var numVertices = geometry.attributes.position.values.length / 3;
var numIndices = indices.length;
var tan1 = new Array(numVertices * 3);
for ( var i = 0; i < tan1.length; i++) {
tan1[i] = 0;
}
var i03;
var i13;
var i23;
for (i = 0; i < numIndices; i += 3) {
var i0 = indices[i];
var i1 = indices[i + 1];
var i2 = indices[i + 2];
i03 = i0 * 3;
i13 = i1 * 3;
i23 = i2 * 3;
var i02 = i0 * 2;
var i12 = i1 * 2;
var i22 = i2 * 2;
var ux = vertices[i03];
var uy = vertices[i03 + 1];
var uz = vertices[i03 + 2];
var wx = st[i02];
var wy = st[i02 + 1];
var t1 = st[i12 + 1] - wy;
var t2 = st[i22 + 1] - wy;
var r = 1.0 / ((st[i12] - wx) * t2 - (st[i22] - wx) * t1);
var sdirx = (t2 * (vertices[i13] - ux) - t1 * (vertices[i23] - ux)) * r;
var sdiry = (t2 * (vertices[i13 + 1] - uy) - t1 * (vertices[i23 + 1] - uy)) * r;
var sdirz = (t2 * (vertices[i13 + 2] - uz) - t1 * (vertices[i23 + 2] - uz)) * r;
tan1[i03] += sdirx;
tan1[i03 + 1] += sdiry;
tan1[i03 + 2] += sdirz;
tan1[i13] += sdirx;
tan1[i13 + 1] += sdiry;
tan1[i13 + 2] += sdirz;
tan1[i23] += sdirx;
tan1[i23 + 1] += sdiry;
tan1[i23 + 2] += sdirz;
}
var binormalValues = new Float32Array(numVertices * 3);
var tangentValues = new Float32Array(numVertices * 3);
for (i = 0; i < numVertices; i++) {
i03 = i * 3;
i13 = i03 + 1;
i23 = i03 + 2;
var n = Cartesian3.fromArray(normals, i03, normalScratch);
var t = Cartesian3.fromArray(tan1, i03, tScratch);
var scalar = Cartesian3.dot(n, t);
Cartesian3.multiplyByScalar(n, scalar, normalScale);
Cartesian3.normalize(Cartesian3.subtract(t, normalScale, t), t);
tangentValues[i03] = t.x;
tangentValues[i13] = t.y;
tangentValues[i23] = t.z;
Cartesian3.normalize(Cartesian3.cross(n, t, t), t);
binormalValues[i03] = t.x;
binormalValues[i13] = t.y;
binormalValues[i23] = t.z;
}
geometry.attributes.tangent = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : tangentValues
});
geometry.attributes.binormal = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : binormalValues
});
return geometry;
};
var scratchCartesian2 = new Cartesian2();
var toEncode1 = new Cartesian3();
var toEncode2 = new Cartesian3();
var toEncode3 = new Cartesian3();
/**
* Compresses and packs geometry normal attribute values to save memory.
*
* @param {Geometry} geometry The geometry to modify.
* @returns {Geometry} The modified geometry argument, with its normals compressed and packed.
*
* @example
* geometry = Cesium.GeometryPipeline.compressVertices(geometry);
*/
GeometryPipeline.compressVertices = function(geometry) {
if (!defined(geometry)) {
throw new DeveloperError('geometry is required.');
}
var normalAttribute = geometry.attributes.normal;
var stAttribute = geometry.attributes.st;
if (!defined(normalAttribute) && !defined(stAttribute)) {
return geometry;
}
var tangentAttribute = geometry.attributes.tangent;
var binormalAttribute = geometry.attributes.binormal;
var normals;
var st;
var tangents;
var binormals;
if (defined(normalAttribute)) {
normals = normalAttribute.values;
}
if (defined(stAttribute)) {
st = stAttribute.values;
}
if (defined(tangentAttribute)) {
tangents = tangentAttribute.values;
}
if (binormalAttribute) {
binormals = binormalAttribute.values;
}
var length = defined(normals) ? normals.length : st.length;
var numComponents = defined(normals) ? 3.0 : 2.0;
var numVertices = length / numComponents;
var compressedLength = numVertices;
var numCompressedComponents = defined(st) && defined(normals) ? 2.0 : 1.0;
numCompressedComponents += defined(tangents) || defined(binormals) ? 1.0 : 0.0;
compressedLength *= numCompressedComponents;
var compressedAttributes = new Float32Array(compressedLength);
var normalIndex = 0;
for (var i = 0; i < numVertices; ++i) {
if (defined(st)) {
Cartesian2.fromArray(st, i * 2.0, scratchCartesian2);
compressedAttributes[normalIndex++] = AttributeCompression.compressTextureCoordinates(scratchCartesian2);
}
var index = i * 3.0;
if (defined(normals) && defined(tangents) && defined(binormals)) {
Cartesian3.fromArray(normals, index, toEncode1);
Cartesian3.fromArray(tangents, index, toEncode2);
Cartesian3.fromArray(binormals, index, toEncode3);
AttributeCompression.octPack(toEncode1, toEncode2, toEncode3, scratchCartesian2);
compressedAttributes[normalIndex++] = scratchCartesian2.x;
compressedAttributes[normalIndex++] = scratchCartesian2.y;
} else {
if (defined(normals)) {
Cartesian3.fromArray(normals, index, toEncode1);
compressedAttributes[normalIndex++] = AttributeCompression.octEncodeFloat(toEncode1);
}
if (defined(tangents)) {
Cartesian3.fromArray(tangents, index, toEncode1);
compressedAttributes[normalIndex++] = AttributeCompression.octEncodeFloat(toEncode1);
}
if (defined(binormals)) {
Cartesian3.fromArray(binormals, index, toEncode1);
compressedAttributes[normalIndex++] = AttributeCompression.octEncodeFloat(toEncode1);
}
}
}
geometry.attributes.compressedAttributes = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : numCompressedComponents,
values : compressedAttributes
});
if (defined(normals)) {
delete geometry.attributes.normal;
}
if (defined(st)) {
delete geometry.attributes.st;
}
if (defined(tangents)) {
delete geometry.attributes.tangent;
}
if (defined(binormals)) {
delete geometry.attributes.binormal;
}
return geometry;
};
function indexTriangles(geometry) {
if (defined(geometry.indices)) {
return geometry;
}
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 3) {
throw new DeveloperError('The number of vertices must be at least three.');
}
if (numberOfVertices % 3 !== 0) {
throw new DeveloperError('The number of vertices must be a multiple of three.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, numberOfVertices);
for (var i = 0; i < numberOfVertices; ++i) {
indices[i] = i;
}
geometry.indices = indices;
return geometry;
}
function indexTriangleFan(geometry) {
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 3) {
throw new DeveloperError('The number of vertices must be at least three.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, (numberOfVertices - 2) * 3);
indices[0] = 1;
indices[1] = 0;
indices[2] = 2;
var indicesIndex = 3;
for (var i = 3; i < numberOfVertices; ++i) {
indices[indicesIndex++] = i - 1;
indices[indicesIndex++] = 0;
indices[indicesIndex++] = i;
}
geometry.indices = indices;
geometry.primitiveType = PrimitiveType.TRIANGLES;
return geometry;
}
function indexTriangleStrip(geometry) {
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 3) {
throw new DeveloperError('The number of vertices must be at least 3.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, (numberOfVertices - 2) * 3);
indices[0] = 0;
indices[1] = 1;
indices[2] = 2;
if (numberOfVertices > 3) {
indices[3] = 0;
indices[4] = 2;
indices[5] = 3;
}
var indicesIndex = 6;
for (var i = 3; i < numberOfVertices - 1; i += 2) {
indices[indicesIndex++] = i;
indices[indicesIndex++] = i - 1;
indices[indicesIndex++] = i + 1;
if (i + 2 < numberOfVertices) {
indices[indicesIndex++] = i;
indices[indicesIndex++] = i + 1;
indices[indicesIndex++] = i + 2;
}
}
geometry.indices = indices;
geometry.primitiveType = PrimitiveType.TRIANGLES;
return geometry;
}
function indexLines(geometry) {
if (defined(geometry.indices)) {
return geometry;
}
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 2) {
throw new DeveloperError('The number of vertices must be at least two.');
}
if (numberOfVertices % 2 !== 0) {
throw new DeveloperError('The number of vertices must be a multiple of 2.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, numberOfVertices);
for (var i = 0; i < numberOfVertices; ++i) {
indices[i] = i;
}
geometry.indices = indices;
return geometry;
}
function indexLineStrip(geometry) {
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 2) {
throw new DeveloperError('The number of vertices must be at least two.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, (numberOfVertices - 1) * 2);
indices[0] = 0;
indices[1] = 1;
var indicesIndex = 2;
for (var i = 2; i < numberOfVertices; ++i) {
indices[indicesIndex++] = i - 1;
indices[indicesIndex++] = i;
}
geometry.indices = indices;
geometry.primitiveType = PrimitiveType.LINES;
return geometry;
}
function indexLineLoop(geometry) {
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
if (numberOfVertices < 2) {
throw new DeveloperError('The number of vertices must be at least two.');
}
var indices = IndexDatatype.createTypedArray(numberOfVertices, numberOfVertices * 2);
indices[0] = 0;
indices[1] = 1;
var indicesIndex = 2;
for (var i = 2; i < numberOfVertices; ++i) {
indices[indicesIndex++] = i - 1;
indices[indicesIndex++] = i;
}
indices[indicesIndex++] = numberOfVertices - 1;
indices[indicesIndex] = 0;
geometry.indices = indices;
geometry.primitiveType = PrimitiveType.LINES;
return geometry;
}
function indexPrimitive(geometry) {
switch (geometry.primitiveType) {
case PrimitiveType.TRIANGLE_FAN:
return indexTriangleFan(geometry);
case PrimitiveType.TRIANGLE_STRIP:
return indexTriangleStrip(geometry);
case PrimitiveType.TRIANGLES:
return indexTriangles(geometry);
case PrimitiveType.LINE_STRIP:
return indexLineStrip(geometry);
case PrimitiveType.LINE_LOOP:
return indexLineLoop(geometry);
case PrimitiveType.LINES:
return indexLines(geometry);
}
return geometry;
}
function offsetPointFromXZPlane(p, isBehind) {
if (Math.abs(p.y) < CesiumMath.EPSILON6){
if (isBehind) {
p.y = -CesiumMath.EPSILON6;
} else {
p.y = CesiumMath.EPSILON6;
}
}
}
function offsetTriangleFromXZPlane(p0, p1, p2) {
if (p0.y !== 0.0 && p1.y !== 0.0 && p2.y !== 0.0) {
offsetPointFromXZPlane(p0, p0.y < 0.0);
offsetPointFromXZPlane(p1, p1.y < 0.0);
offsetPointFromXZPlane(p2, p2.y < 0.0);
return;
}
var p0y = Math.abs(p0.y);
var p1y = Math.abs(p1.y);
var p2y = Math.abs(p2.y);
var sign;
if (p0y > p1y) {
if (p0y > p2y) {
sign = CesiumMath.sign(p0.y);
} else {
sign = CesiumMath.sign(p2.y);
}
} else if (p1y > p2y) {
sign = CesiumMath.sign(p1.y);
} else {
sign = CesiumMath.sign(p2.y);
}
var isBehind = sign < 0.0;
offsetPointFromXZPlane(p0, isBehind);
offsetPointFromXZPlane(p1, isBehind);
offsetPointFromXZPlane(p2, isBehind);
}
var c3 = new Cartesian3();
function getXZIntersectionOffsetPoints(p, p1, u1, v1) {
Cartesian3.add(p, Cartesian3.multiplyByScalar(Cartesian3.subtract(p1, p, c3), p.y/(p.y-p1.y), c3), u1);
Cartesian3.clone(u1, v1);
offsetPointFromXZPlane(u1, true);
offsetPointFromXZPlane(v1, false);
}
var u1 = new Cartesian3();
var u2 = new Cartesian3();
var q1 = new Cartesian3();
var q2 = new Cartesian3();
var splitTriangleResult = {
positions : new Array(7),
indices : new Array(3 * 3)
};
function splitTriangle(p0, p1, p2) {
// In WGS84 coordinates, for a triangle approximately on the
// ellipsoid to cross the IDL, first it needs to be on the
// negative side of the plane x = 0.
if ((p0.x >= 0.0) || (p1.x >= 0.0) || (p2.x >= 0.0)) {
return undefined;
}
offsetTriangleFromXZPlane(p0, p1, p2);
var p0Behind = p0.y < 0.0;
var p1Behind = p1.y < 0.0;
var p2Behind = p2.y < 0.0;
var numBehind = 0;
numBehind += p0Behind ? 1 : 0;
numBehind += p1Behind ? 1 : 0;
numBehind += p2Behind ? 1 : 0;
var indices = splitTriangleResult.indices;
if (numBehind === 1) {
indices[1] = 3;
indices[2] = 4;
indices[5] = 6;
indices[7] = 6;
indices[8] = 5;
if (p0Behind) {
getXZIntersectionOffsetPoints(p0, p1, u1, q1);
getXZIntersectionOffsetPoints(p0, p2, u2, q2);
indices[0] = 0;
indices[3] = 1;
indices[4] = 2;
indices[6] = 1;
} else if (p1Behind) {
getXZIntersectionOffsetPoints(p1, p2, u1, q1);
getXZIntersectionOffsetPoints(p1, p0, u2, q2);
indices[0] = 1;
indices[3] = 2;
indices[4] = 0;
indices[6] = 2;
} else if (p2Behind) {
getXZIntersectionOffsetPoints(p2, p0, u1, q1);
getXZIntersectionOffsetPoints(p2, p1, u2, q2);
indices[0] = 2;
indices[3] = 0;
indices[4] = 1;
indices[6] = 0;
}
} else if (numBehind === 2) {
indices[2] = 4;
indices[4] = 4;
indices[5] = 3;
indices[7] = 5;
indices[8] = 6;
if (!p0Behind) {
getXZIntersectionOffsetPoints(p0, p1, u1, q1);
getXZIntersectionOffsetPoints(p0, p2, u2, q2);
indices[0] = 1;
indices[1] = 2;
indices[3] = 1;
indices[6] = 0;
} else if (!p1Behind) {
getXZIntersectionOffsetPoints(p1, p2, u1, q1);
getXZIntersectionOffsetPoints(p1, p0, u2, q2);
indices[0] = 2;
indices[1] = 0;
indices[3] = 2;
indices[6] = 1;
} else if (!p2Behind) {
getXZIntersectionOffsetPoints(p2, p0, u1, q1);
getXZIntersectionOffsetPoints(p2, p1, u2, q2);
indices[0] = 0;
indices[1] = 1;
indices[3] = 0;
indices[6] = 2;
}
}
var positions = splitTriangleResult.positions;
positions[0] = p0;
positions[1] = p1;
positions[2] = p2;
positions.length = 3;
if (numBehind === 1 || numBehind === 2) {
positions[3] = u1;
positions[4] = u2;
positions[5] = q1;
positions[6] = q2;
positions.length = 7;
}
return splitTriangleResult;
}
function updateGeometryAfterSplit(geometry, computeBoundingSphere) {
var attributes = geometry.attributes;
if (attributes.position.values.length === 0) {
return undefined;
}
for (var property in attributes) {
if (attributes.hasOwnProperty(property) &&
defined(attributes[property]) &&
defined(attributes[property].values)) {
var attribute = attributes[property];
attribute.values = ComponentDatatype.createTypedArray(attribute.componentDatatype, attribute.values);
}
}
var numberOfVertices = Geometry.computeNumberOfVertices(geometry);
geometry.indices = IndexDatatype.createTypedArray(numberOfVertices, geometry.indices);
if (computeBoundingSphere) {
geometry.boundingSphere = BoundingSphere.fromVertices(attributes.position.values);
}
return geometry;
}
function copyGeometryForSplit(geometry) {
var attributes = geometry.attributes;
var copiedAttributes = {};
for (var property in attributes) {
if (attributes.hasOwnProperty(property) &&
defined(attributes[property]) &&
defined(attributes[property].values)) {
var attribute = attributes[property];
copiedAttributes[property] = new GeometryAttribute({
componentDatatype : attribute.componentDatatype,
componentsPerAttribute : attribute.componentsPerAttribute,
normalize : attribute.normalize,
values : []
});
}
}
return new Geometry({
attributes : copiedAttributes,
indices : [],
primitiveType : geometry.primitiveType
});
}
function updateInstanceAfterSplit(instance, westGeometry, eastGeometry) {
var computeBoundingSphere = defined(instance.geometry.boundingSphere);
westGeometry = updateGeometryAfterSplit(westGeometry, computeBoundingSphere);
eastGeometry = updateGeometryAfterSplit(eastGeometry, computeBoundingSphere);
if (defined(eastGeometry) && !defined(westGeometry)) {
instance.geometry = eastGeometry;
} else if (!defined(eastGeometry) && defined(westGeometry)) {
instance.geometry = westGeometry;
} else {
instance.westHemisphereGeometry = westGeometry;
instance.eastHemisphereGeometry = eastGeometry;
instance.geometry = undefined;
}
}
var p0Scratch = new Cartesian3();
var p1Scratch = new Cartesian3();
var p2Scratch = new Cartesian3();
var barycentricScratch = new Cartesian3();
var s0Scratch = new Cartesian2();
var s1Scratch = new Cartesian2();
var s2Scratch = new Cartesian2();
function computeTriangleAttributes(i0, i1, i2, point, positions, normals, binormals, tangents, texCoords, currentAttributes, insertedIndex) {
if (!defined(normals) && !defined(binormals) && !defined(tangents) && !defined(texCoords)) {
return;
}
var p0 = Cartesian3.fromArray(positions, i0 * 3, p0Scratch);
var p1 = Cartesian3.fromArray(positions, i1 * 3, p1Scratch);
var p2 = Cartesian3.fromArray(positions, i2 * 3, p2Scratch);
var coords = barycentricCoordinates(point, p0, p1, p2, barycentricScratch);
if (defined(normals)) {
var n0 = Cartesian3.fromArray(normals, i0 * 3, p0Scratch);
var n1 = Cartesian3.fromArray(normals, i1 * 3, p1Scratch);
var n2 = Cartesian3.fromArray(normals, i2 * 3, p2Scratch);
Cartesian3.multiplyByScalar(n0, coords.x, n0);
Cartesian3.multiplyByScalar(n1, coords.y, n1);
Cartesian3.multiplyByScalar(n2, coords.z, n2);
var normal = Cartesian3.add(n0, n1, n0);
Cartesian3.add(normal, n2, normal);
Cartesian3.normalize(normal, normal);
Cartesian3.pack(normal, currentAttributes.normal.values, insertedIndex * 3);
}
if (defined(binormals)) {
var b0 = Cartesian3.fromArray(binormals, i0 * 3, p0Scratch);
var b1 = Cartesian3.fromArray(binormals, i1 * 3, p1Scratch);
var b2 = Cartesian3.fromArray(binormals, i2 * 3, p2Scratch);
Cartesian3.multiplyByScalar(b0, coords.x, b0);
Cartesian3.multiplyByScalar(b1, coords.y, b1);
Cartesian3.multiplyByScalar(b2, coords.z, b2);
var binormal = Cartesian3.add(b0, b1, b0);
Cartesian3.add(binormal, b2, binormal);
Cartesian3.normalize(binormal, binormal);
Cartesian3.pack(binormal, currentAttributes.binormal.values, insertedIndex * 3);
}
if (defined(tangents)) {
var t0 = Cartesian3.fromArray(tangents, i0 * 3, p0Scratch);
var t1 = Cartesian3.fromArray(tangents, i1 * 3, p1Scratch);
var t2 = Cartesian3.fromArray(tangents, i2 * 3, p2Scratch);
Cartesian3.multiplyByScalar(t0, coords.x, t0);
Cartesian3.multiplyByScalar(t1, coords.y, t1);
Cartesian3.multiplyByScalar(t2, coords.z, t2);
var tangent = Cartesian3.add(t0, t1, t0);
Cartesian3.add(tangent, t2, tangent);
Cartesian3.normalize(tangent, tangent);
Cartesian3.pack(tangent, currentAttributes.tangent.values, insertedIndex * 3);
}
if (defined(texCoords)) {
var s0 = Cartesian2.fromArray(texCoords, i0 * 2, s0Scratch);
var s1 = Cartesian2.fromArray(texCoords, i1 * 2, s1Scratch);
var s2 = Cartesian2.fromArray(texCoords, i2 * 2, s2Scratch);
Cartesian2.multiplyByScalar(s0, coords.x, s0);
Cartesian2.multiplyByScalar(s1, coords.y, s1);
Cartesian2.multiplyByScalar(s2, coords.z, s2);
var texCoord = Cartesian2.add(s0, s1, s0);
Cartesian2.add(texCoord, s2, texCoord);
Cartesian2.pack(texCoord, currentAttributes.st.values, insertedIndex * 2);
}
}
function insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, currentIndex, point) {
var insertIndex = currentAttributes.position.values.length / 3;
if (currentIndex !== -1) {
var prevIndex = indices[currentIndex];
var newIndex = currentIndexMap[prevIndex];
if (newIndex === -1) {
currentIndexMap[prevIndex] = insertIndex;
currentAttributes.position.values.push(point.x, point.y, point.z);
currentIndices.push(insertIndex);
return insertIndex;
}
currentIndices.push(newIndex);
return newIndex;
}
currentAttributes.position.values.push(point.x, point.y, point.z);
currentIndices.push(insertIndex);
return insertIndex;
}
function splitLongitudeTriangles(instance) {
var geometry = instance.geometry;
var attributes = geometry.attributes;
var positions = attributes.position.values;
var normals = (defined(attributes.normal)) ? attributes.normal.values : undefined;
var binormals = (defined(attributes.binormal)) ? attributes.binormal.values : undefined;
var tangents = (defined(attributes.tangent)) ? attributes.tangent.values : undefined;
var texCoords = (defined(attributes.st)) ? attributes.st.values : undefined;
var indices = geometry.indices;
var eastGeometry = copyGeometryForSplit(geometry);
var westGeometry = copyGeometryForSplit(geometry);
var currentAttributes;
var currentIndices;
var currentIndexMap;
var insertedIndex;
var i;
var westGeometryIndexMap = [];
westGeometryIndexMap.length = positions.length / 3;
var eastGeometryIndexMap = [];
eastGeometryIndexMap.length = positions.length / 3;
for (i = 0; i < westGeometryIndexMap.length; ++i) {
westGeometryIndexMap[i] = -1;
eastGeometryIndexMap[i] = -1;
}
var len = indices.length;
for (i = 0; i < len; i += 3) {
var i0 = indices[i];
var i1 = indices[i + 1];
var i2 = indices[i + 2];
var p0 = Cartesian3.fromArray(positions, i0 * 3);
var p1 = Cartesian3.fromArray(positions, i1 * 3);
var p2 = Cartesian3.fromArray(positions, i2 * 3);
var result = splitTriangle(p0, p1, p2);
if (defined(result) && result.positions.length > 3) {
var resultPositions = result.positions;
var resultIndices = result.indices;
var resultLength = resultIndices.length;
for (var j = 0; j < resultLength; ++j) {
var resultIndex = resultIndices[j];
var point = resultPositions[resultIndex];
if (point.y < 0.0) {
currentAttributes = westGeometry.attributes;
currentIndices = westGeometry.indices;
currentIndexMap = westGeometryIndexMap;
} else {
currentAttributes = eastGeometry.attributes;
currentIndices = eastGeometry.indices;
currentIndexMap = eastGeometryIndexMap;
}
insertedIndex = insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, resultIndex < 3 ? i + resultIndex : -1, point);
computeTriangleAttributes(i0, i1, i2, point, positions, normals, binormals, tangents, texCoords, currentAttributes, insertedIndex);
}
} else {
if (defined(result)) {
p0 = result.positions[0];
p1 = result.positions[1];
p2 = result.positions[2];
}
if (p0.y < 0.0) {
currentAttributes = westGeometry.attributes;
currentIndices = westGeometry.indices;
currentIndexMap = westGeometryIndexMap;
} else {
currentAttributes = eastGeometry.attributes;
currentIndices = eastGeometry.indices;
currentIndexMap = eastGeometryIndexMap;
}
insertedIndex = insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, i, p0);
computeTriangleAttributes(i0, i1, i2, p0, positions, normals, binormals, tangents, texCoords, currentAttributes, insertedIndex);
insertedIndex = insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, i + 1, p1);
computeTriangleAttributes(i0, i1, i2, p1, positions, normals, binormals, tangents, texCoords, currentAttributes, insertedIndex);
insertedIndex = insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, i + 2, p2);
computeTriangleAttributes(i0, i1, i2, p2, positions, normals, binormals, tangents, texCoords, currentAttributes, insertedIndex);
}
}
updateInstanceAfterSplit(instance, westGeometry, eastGeometry);
}
var xzPlane = Plane.fromPointNormal(Cartesian3.ZERO, Cartesian3.UNIT_Y);
var offsetScratch = new Cartesian3();
var offsetPointScratch = new Cartesian3();
function splitLongitudeLines(instance) {
var geometry = instance.geometry;
var attributes = geometry.attributes;
var positions = attributes.position.values;
var indices = geometry.indices;
var eastGeometry = copyGeometryForSplit(geometry);
var westGeometry = copyGeometryForSplit(geometry);
var i;
var length = indices.length;
var westGeometryIndexMap = [];
westGeometryIndexMap.length = positions.length / 3;
var eastGeometryIndexMap = [];
eastGeometryIndexMap.length = positions.length / 3;
for (i = 0; i < westGeometryIndexMap.length; ++i) {
westGeometryIndexMap[i] = -1;
eastGeometryIndexMap[i] = -1;
}
for (i = 0; i < length; i += 2) {
var i0 = indices[i];
var i1 = indices[i + 1];
var p0 = Cartesian3.fromArray(positions, i0 * 3, p0Scratch);
var p1 = Cartesian3.fromArray(positions, i1 * 3, p1Scratch);
if (Math.abs(p0.y) < CesiumMath.EPSILON6){
if (p0.y < 0.0) {
p0.y = -CesiumMath.EPSILON6;
} else {
p0.y = CesiumMath.EPSILON6;
}
}
if (Math.abs(p1.y) < CesiumMath.EPSILON6){
if (p1.y < 0.0) {
p1.y = -CesiumMath.EPSILON6;
} else {
p1.y = CesiumMath.EPSILON6;
}
}
var p0Attributes = eastGeometry.attributes;
var p0Indices = eastGeometry.indices;
var p0IndexMap = eastGeometryIndexMap;
var p1Attributes = westGeometry.attributes;
var p1Indices = westGeometry.indices;
var p1IndexMap = westGeometryIndexMap;
var intersection = IntersectionTests.lineSegmentPlane(p0, p1, xzPlane, p2Scratch);
if (defined(intersection)) {
// move point on the xz-plane slightly away from the plane
var offset = Cartesian3.multiplyByScalar(Cartesian3.UNIT_Y, 5.0 * CesiumMath.EPSILON9, offsetScratch);
if (p0.y < 0.0) {
Cartesian3.negate(offset, offset);
p0Attributes = westGeometry.attributes;
p0Indices = westGeometry.indices;
p0IndexMap = westGeometryIndexMap;
p1Attributes = eastGeometry.attributes;
p1Indices = eastGeometry.indices;
p1IndexMap = eastGeometryIndexMap;
}
var offsetPoint = Cartesian3.add(intersection, offset, offsetPointScratch);
insertSplitPoint(p0Attributes, p0Indices, p0IndexMap, indices, i, p0);
insertSplitPoint(p0Attributes, p0Indices, p0IndexMap, indices, -1, offsetPoint);
Cartesian3.negate(offset, offset);
Cartesian3.add(intersection, offset, offsetPoint);
insertSplitPoint(p1Attributes, p1Indices, p1IndexMap, indices, -1, offsetPoint);
insertSplitPoint(p1Attributes, p1Indices, p1IndexMap, indices, i + 1, p1);
} else {
var currentAttributes;
var currentIndices;
var currentIndexMap;
if (p0.y < 0.0) {
currentAttributes = westGeometry.attributes;
currentIndices = westGeometry.indices;
currentIndexMap = westGeometryIndexMap;
} else {
currentAttributes = eastGeometry.attributes;
currentIndices = eastGeometry.indices;
currentIndexMap = eastGeometryIndexMap;
}
insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, i, p0);
insertSplitPoint(currentAttributes, currentIndices, currentIndexMap, indices, i + 1, p1);
}
}
updateInstanceAfterSplit(instance, westGeometry, eastGeometry);
}
var cartesian2Scratch0 = new Cartesian2();
var cartesian2Scratch1 = new Cartesian2();
var cartesian3Scratch0 = new Cartesian3();
var cartesian3Scratch2 = new Cartesian3();
var cartesian3Scratch3 = new Cartesian3();
var cartesian3Scratch4 = new Cartesian3();
var cartesian3Scratch5 = new Cartesian3();
var cartesian3Scratch6 = new Cartesian3();
var cartesian4Scratch0 = new Cartesian4();
function updateAdjacencyAfterSplit(geometry) {
var attributes = geometry.attributes;
var positions = attributes.position.values;
var prevPositions = attributes.prevPosition.values;
var nextPositions = attributes.nextPosition.values;
var length = positions.length;
for (var j = 0; j < length; j += 3) {
var position = Cartesian3.unpack(positions, j, cartesian3Scratch0);
if (position.x > 0.0) {
continue;
}
var prevPosition = Cartesian3.unpack(prevPositions, j, cartesian3Scratch2);
if ((position.y < 0.0 && prevPosition.y > 0.0) || (position.y > 0.0 && prevPosition.y < 0.0)) {
if (j - 3 > 0) {
prevPositions[j] = positions[j - 3];
prevPositions[j + 1] = positions[j - 2];
prevPositions[j + 2] = positions[j - 1];
} else {
Cartesian3.pack(position, prevPositions, j);
}
}
var nextPosition = Cartesian3.unpack(nextPositions, j, cartesian3Scratch3);
if ((position.y < 0.0 && nextPosition.y > 0.0) || (position.y > 0.0 && nextPosition.y < 0.0)) {
if (j + 3 < length) {
nextPositions[j] = positions[j + 3];
nextPositions[j + 1] = positions[j + 4];
nextPositions[j + 2] = positions[j + 5];
} else {
Cartesian3.pack(position, nextPositions, j);
}
}
}
}
var offsetScalar = 5.0 * CesiumMath.EPSILON9;
var coplanarOffset = CesiumMath.EPSILON6;
function splitLongitudePolyline(instance) {
var geometry = instance.geometry;
var attributes = geometry.attributes;
var positions = attributes.position.values;
var prevPositions = attributes.prevPosition.values;
var nextPositions = attributes.nextPosition.values;
var expandAndWidths = attributes.expandAndWidth.values;
var texCoords = (defined(attributes.st)) ? attributes.st.values : undefined;
var colors = (defined(attributes.color)) ? attributes.color.values : undefined;
var eastGeometry = copyGeometryForSplit(geometry);
var westGeometry = copyGeometryForSplit(geometry);
var i;
var j;
var index;
var intersectionFound = false;
var length = positions.length / 3;
for (i = 0; i < length; i += 4) {
var i0 = i;
var i2 = i + 2;
var p0 = Cartesian3.fromArray(positions, i0 * 3, cartesian3Scratch0);
var p2 = Cartesian3.fromArray(positions, i2 * 3, cartesian3Scratch2);
// Offset points that are close to the 180 longitude and change the previous/next point
// to be the same offset point so it can be projected to 2D. There is special handling in the
// shader for when position == prevPosition || position == nextPosition.
if (Math.abs(p0.y) < coplanarOffset) {
p0.y = coplanarOffset * (p2.y < 0.0 ? -1.0 : 1.0);
positions[i * 3 + 1] = p0.y;
positions[(i + 1) * 3 + 1] = p0.y;
for (j = i0 * 3; j < i0 * 3 + 4 * 3; j += 3) {
prevPositions[j] = positions[i * 3];
prevPositions[j + 1] = positions[i * 3 + 1];
prevPositions[j + 2] = positions[i * 3 + 2];
}
}
// Do the same but for when the line crosses 180 longitude in the opposite direction.
if (Math.abs(p2.y) < coplanarOffset) {
p2.y = coplanarOffset * (p0.y < 0.0 ? -1.0 : 1.0);
positions[(i + 2) * 3 + 1] = p2.y;
positions[(i + 3) * 3 + 1] = p2.y;
for (j = i0 * 3; j < i0 * 3 + 4 * 3; j += 3) {
nextPositions[j] = positions[(i + 2) * 3];
nextPositions[j + 1] = positions[(i + 2) * 3 + 1];
nextPositions[j + 2] = positions[(i + 2) * 3 + 2];
}
}
var p0Attributes = eastGeometry.attributes;
var p0Indices = eastGeometry.indices;
var p2Attributes = westGeometry.attributes;
var p2Indices = westGeometry.indices;
var intersection = IntersectionTests.lineSegmentPlane(p0, p2, xzPlane, cartesian3Scratch4);
if (defined(intersection)) {
intersectionFound = true;
// move point on the xz-plane slightly away from the plane
var offset = Cartesian3.multiplyByScalar(Cartesian3.UNIT_Y, offsetScalar, cartesian3Scratch5);
if (p0.y < 0.0) {
Cartesian3.negate(offset, offset);
p0Attributes = westGeometry.attributes;
p0Indices = westGeometry.indices;
p2Attributes = eastGeometry.attributes;
p2Indices = eastGeometry.indices;
}
var offsetPoint = Cartesian3.add(intersection, offset, cartesian3Scratch6);
p0Attributes.position.values.push(p0.x, p0.y, p0.z, p0.x, p0.y, p0.z);
p0Attributes.position.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p0Attributes.position.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p0Attributes.prevPosition.values.push(prevPositions[i0 * 3], prevPositions[i0 * 3 + 1], prevPositions[i0 * 3 + 2]);
p0Attributes.prevPosition.values.push(prevPositions[i0 * 3 + 3], prevPositions[i0 * 3 + 4], prevPositions[i0 * 3 + 5]);
p0Attributes.prevPosition.values.push(p0.x, p0.y, p0.z, p0.x, p0.y, p0.z);
p0Attributes.nextPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p0Attributes.nextPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p0Attributes.nextPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p0Attributes.nextPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
Cartesian3.negate(offset, offset);
Cartesian3.add(intersection, offset, offsetPoint);
p2Attributes.position.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.position.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.position.values.push(p2.x, p2.y, p2.z, p2.x, p2.y, p2.z);
p2Attributes.prevPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.prevPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.prevPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.prevPosition.values.push(offsetPoint.x, offsetPoint.y, offsetPoint.z);
p2Attributes.nextPosition.values.push(p2.x, p2.y, p2.z, p2.x, p2.y, p2.z);
p2Attributes.nextPosition.values.push(nextPositions[i2 * 3], nextPositions[i2 * 3 + 1], nextPositions[i2 * 3 + 2]);
p2Attributes.nextPosition.values.push(nextPositions[i2 * 3 + 3], nextPositions[i2 * 3 + 4], nextPositions[i2 * 3 + 5]);
var ew0 = Cartesian2.fromArray(expandAndWidths, i0 * 2, cartesian2Scratch0);
var width = Math.abs(ew0.y);
p0Attributes.expandAndWidth.values.push(-1, width, 1, width);
p0Attributes.expandAndWidth.values.push(-1, -width, 1, -width);
p2Attributes.expandAndWidth.values.push(-1, width, 1, width);
p2Attributes.expandAndWidth.values.push(-1, -width, 1, -width);
var t = Cartesian3.magnitudeSquared(Cartesian3.subtract(intersection, p0, cartesian3Scratch3));
t /= Cartesian3.magnitudeSquared(Cartesian3.subtract(p2, p0, cartesian3Scratch3));
if (defined(colors)) {
var c0 = Cartesian4.fromArray(colors, i0 * 4, cartesian4Scratch0);
var c2 = Cartesian4.fromArray(colors, i2 * 4, cartesian4Scratch0);
var r = CesiumMath.lerp(c0.x, c2.x, t);
var g = CesiumMath.lerp(c0.y, c2.y, t);
var b = CesiumMath.lerp(c0.z, c2.z, t);
var a = CesiumMath.lerp(c0.w, c2.w, t);
for (j = i0 * 4; j < i0 * 4 + 2 * 4; ++j) {
p0Attributes.color.values.push(colors[j]);
}
p0Attributes.color.values.push(r, g, b, a);
p0Attributes.color.values.push(r, g, b, a);
p2Attributes.color.values.push(r, g, b, a);
p2Attributes.color.values.push(r, g, b, a);
for (j = i2 * 4; j < i2 * 4 + 2 * 4; ++j) {
p2Attributes.color.values.push(colors[j]);
}
}
if (defined(texCoords)) {
var s0 = Cartesian2.fromArray(texCoords, i0 * 2, cartesian2Scratch0);
var s3 = Cartesian2.fromArray(texCoords, (i + 3) * 2, cartesian2Scratch1);
var sx = CesiumMath.lerp(s0.x, s3.x, t);
for (j = i0 * 2; j < i0 * 2 + 2 * 2; ++j) {
p0Attributes.st.values.push(texCoords[j]);
}
p0Attributes.st.values.push(sx, s0.y);
p0Attributes.st.values.push(sx, s3.y);
p2Attributes.st.values.push(sx, s0.y);
p2Attributes.st.values.push(sx, s3.y);
for (j = i2 * 2; j < i2 * 2 + 2 * 2; ++j) {
p2Attributes.st.values.push(texCoords[j]);
}
}
index = p0Attributes.position.values.length / 3 - 4;
p0Indices.push(index, index + 2, index + 1);
p0Indices.push(index + 1, index + 2, index + 3);
index = p2Attributes.position.values.length / 3 - 4;
p2Indices.push(index, index + 2, index + 1);
p2Indices.push(index + 1, index + 2, index + 3);
} else {
var currentAttributes;
var currentIndices;
if (p0.y < 0.0) {
currentAttributes = westGeometry.attributes;
currentIndices = westGeometry.indices;
} else {
currentAttributes = eastGeometry.attributes;
currentIndices = eastGeometry.indices;
}
currentAttributes.position.values.push(p0.x, p0.y, p0.z);
currentAttributes.position.values.push(p0.x, p0.y, p0.z);
currentAttributes.position.values.push(p2.x, p2.y, p2.z);
currentAttributes.position.values.push(p2.x, p2.y, p2.z);
for (j = i * 3; j < i * 3 + 4 * 3; ++j) {
currentAttributes.prevPosition.values.push(prevPositions[j]);
currentAttributes.nextPosition.values.push(nextPositions[j]);
}
for (j = i * 2; j < i * 2 + 4 * 2; ++j) {
currentAttributes.expandAndWidth.values.push(expandAndWidths[j]);
if (defined(texCoords)) {
currentAttributes.st.values.push(texCoords[j]);
}
}
if (defined(colors)) {
for (j = i * 4; j < i * 4 + 4 * 4; ++j) {
currentAttributes.color.values.push(colors[j]);
}
}
index = currentAttributes.position.values.length / 3 - 4;
currentIndices.push(index, index + 2, index + 1);
currentIndices.push(index + 1, index + 2, index + 3);
}
}
if (intersectionFound) {
updateAdjacencyAfterSplit(westGeometry);
updateAdjacencyAfterSplit(eastGeometry);
}
updateInstanceAfterSplit(instance, westGeometry, eastGeometry);
}
/**
* Splits the instances's geometry, by introducing new vertices and indices,that
* intersect the International Date Line and Prime Meridian so that no primitives cross longitude
* -180/180 degrees. This is not required for 3D drawing, but is required for
* correcting drawing in 2D and Columbus view.
*
* @private
*
* @param {GeometryInstance} instance The instance to modify.
* @returns {GeometryInstance} The modified instance argument, with it's geometry split at the International Date Line.
*
* @example
* instance = Cesium.GeometryPipeline.splitLongitude(instance);
*/
GeometryPipeline.splitLongitude = function(instance) {
if (!defined(instance)) {
throw new DeveloperError('instance is required.');
}
var geometry = instance.geometry;
var boundingSphere = geometry.boundingSphere;
if (defined(boundingSphere)) {
var minX = boundingSphere.center.x - boundingSphere.radius;
if (minX > 0 || BoundingSphere.intersectPlane(boundingSphere, Plane.ORIGIN_ZX_PLANE) !== Intersect.INTERSECTING) {
return instance;
}
}
if (geometry.geometryType !== GeometryType.NONE) {
switch (geometry.geometryType) {
case GeometryType.POLYLINES:
splitLongitudePolyline(instance);
break;
case GeometryType.TRIANGLES:
splitLongitudeTriangles(instance);
break;
case GeometryType.LINES:
splitLongitudeLines(instance);
break;
}
} else {
indexPrimitive(geometry);
if (geometry.primitiveType === PrimitiveType.TRIANGLES) {
splitLongitudeTriangles(instance);
} else if (geometry.primitiveType === PrimitiveType.LINES) {
splitLongitudeLines(instance);
}
}
return instance;
};
return GeometryPipeline;
});
/*global define*/
define('Core/Matrix2',[
'./Cartesian2',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./freezeObject'
], function(
Cartesian2,
defaultValue,
defined,
defineProperties,
DeveloperError,
freezeObject) {
'use strict';
/**
* A 2x2 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix2
* @constructor
*
* @param {Number} [column0Row0=0.0] The value for column 0, row 0.
* @param {Number} [column1Row0=0.0] The value for column 1, row 0.
* @param {Number} [column0Row1=0.0] The value for column 0, row 1.
* @param {Number} [column1Row1=0.0] The value for column 1, row 1.
*
* @see Matrix2.fromColumnMajorArray
* @see Matrix2.fromRowMajorArray
* @see Matrix2.fromScale
* @see Matrix2.fromUniformScale
* @see Matrix3
* @see Matrix4
*/
function Matrix2(column0Row0, column1Row0, column0Row1, column1Row1) {
this[0] = defaultValue(column0Row0, 0.0);
this[1] = defaultValue(column0Row1, 0.0);
this[2] = defaultValue(column1Row0, 0.0);
this[3] = defaultValue(column1Row1, 0.0);
}
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Matrix2.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Matrix2} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Matrix2.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value[0];
array[startingIndex++] = value[1];
array[startingIndex++] = value[2];
array[startingIndex++] = value[3];
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Matrix2} [result] The object into which to store the result.
* @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.
*/
Matrix2.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Matrix2();
}
result[0] = array[startingIndex++];
result[1] = array[startingIndex++];
result[2] = array[startingIndex++];
result[3] = array[startingIndex++];
return result;
};
/**
* Duplicates a Matrix2 instance.
*
* @param {Matrix2} matrix The matrix to duplicate.
* @param {Matrix2} [result] The object onto which to store the result.
* @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided. (Returns undefined if matrix is undefined)
*/
Matrix2.clone = function(values, result) {
if (!defined(values)) {
return undefined;
}
if (!defined(result)) {
return new Matrix2(values[0], values[2],
values[1], values[3]);
}
result[0] = values[0];
result[1] = values[1];
result[2] = values[2];
result[3] = values[3];
return result;
};
/**
* Creates a Matrix2 from 4 consecutive elements in an array.
*
* @param {Number[]} array The array whose 4 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
* @param {Matrix2} [result] The object onto which to store the result.
* @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.
*
* @example
* // Create the Matrix2:
* // [1.0, 2.0]
* // [1.0, 2.0]
*
* var v = [1.0, 1.0, 2.0, 2.0];
* var m = Cesium.Matrix2.fromArray(v);
*
* // Create same Matrix2 with using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 1.0, 2.0, 2.0];
* var m2 = Cesium.Matrix2.fromArray(v2, 2);
*/
Matrix2.fromArray = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Matrix2();
}
result[0] = array[startingIndex];
result[1] = array[startingIndex + 1];
result[2] = array[startingIndex + 2];
result[3] = array[startingIndex + 3];
return result;
};
/**
* Creates a Matrix2 instance from a column-major order array.
*
* @param {Number[]} values The column-major order array.
* @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.
*/
Matrix2.fromColumnMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values parameter is required');
}
return Matrix2.clone(values, result);
};
/**
* Creates a Matrix2 instance from a row-major order array.
* The resulting matrix will be in column-major order.
*
* @param {Number[]} values The row-major order array.
* @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.
*/
Matrix2.fromRowMajorArray = function(values, result) {
if (!defined(values)) {
throw new DeveloperError('values is required.');
}
if (!defined(result)) {
return new Matrix2(values[0], values[1],
values[2], values[3]);
}
result[0] = values[0];
result[1] = values[2];
result[2] = values[1];
result[3] = values[3];
return result;
};
/**
* Computes a Matrix2 instance representing a non-uniform scale.
*
* @param {Cartesian2} scale The x and y scale factors.
* @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.
*
* @example
* // Creates
* // [7.0, 0.0]
* // [0.0, 8.0]
* var m = Cesium.Matrix2.fromScale(new Cesium.Cartesian2(7.0, 8.0));
*/
Matrix2.fromScale = function(scale, result) {
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix2(
scale.x, 0.0,
0.0, scale.y);
}
result[0] = scale.x;
result[1] = 0.0;
result[2] = 0.0;
result[3] = scale.y;
return result;
};
/**
* Computes a Matrix2 instance representing a uniform scale.
*
* @param {Number} scale The uniform scale factor.
* @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.
*
* @example
* // Creates
* // [2.0, 0.0]
* // [0.0, 2.0]
* var m = Cesium.Matrix2.fromUniformScale(2.0);
*/
Matrix2.fromUniformScale = function(scale, result) {
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required.');
}
if (!defined(result)) {
return new Matrix2(
scale, 0.0,
0.0, scale);
}
result[0] = scale;
result[1] = 0.0;
result[2] = 0.0;
result[3] = scale;
return result;
};
/**
* Creates a rotation matrix.
*
* @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix2} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix2} The modified result parameter, or a new Matrix2 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise.
* var p = new Cesium.Cartesian2(5, 6);
* var m = Cesium.Matrix2.fromRotation(Cesium.Math.toRadians(45.0));
* var rotated = Cesium.Matrix2.multiplyByVector(m, p, new Cesium.Cartesian2());
*/
Matrix2.fromRotation = function(angle, result) {
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
var cosAngle = Math.cos(angle);
var sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix2(
cosAngle, -sinAngle,
sinAngle, cosAngle);
}
result[0] = cosAngle;
result[1] = sinAngle;
result[2] = -sinAngle;
result[3] = cosAngle;
return result;
};
/**
* Creates an Array from the provided Matrix2 instance.
* The array will be in column-major order.
*
* @param {Matrix2} matrix The matrix to use..
* @param {Number[]} [result] The Array onto which to store the result.
* @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
*/
Matrix2.toArray = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
return [matrix[0], matrix[1], matrix[2], matrix[3]];
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
return result;
};
/**
* Computes the array index of the element at the provided row and column.
*
* @param {Number} row The zero-based index of the row.
* @param {Number} column The zero-based index of the column.
* @returns {Number} The index of the element at the provided row and column.
*
* @exception {DeveloperError} row must be 0 or 1.
* @exception {DeveloperError} column must be 0 or 1.
*
* @example
* var myMatrix = new Cesium.Matrix2();
* var column1Row0Index = Cesium.Matrix2.getElementIndex(1, 0);
* var column1Row0 = myMatrix[column1Row0Index]
* myMatrix[column1Row0Index] = 10.0;
*/
Matrix2.getElementIndex = function(column, row) {
if (typeof row !== 'number' || row < 0 || row > 1) {
throw new DeveloperError('row must be 0 or 1.');
}
if (typeof column !== 'number' || column < 0 || column > 1) {
throw new DeveloperError('column must be 0 or 1.');
}
return column * 2 + row;
};
/**
* Retrieves a copy of the matrix column at the provided index as a Cartesian2 instance.
*
* @param {Matrix2} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to retrieve.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*
* @exception {DeveloperError} index must be 0 or 1.
*/
Matrix2.getColumn = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 1) {
throw new DeveloperError('index must be 0 or 1.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var startIndex = index * 2;
var x = matrix[startIndex];
var y = matrix[startIndex + 1];
result.x = x;
result.y = y;
return result;
};
/**
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian2 instance.
*
* @param {Matrix2} matrix The matrix to use.
* @param {Number} index The zero-based index of the column to set.
* @param {Cartesian2} cartesian The Cartesian whose values will be assigned to the specified column.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*
* @exception {DeveloperError} index must be 0 or 1.
*/
Matrix2.setColumn = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 1) {
throw new DeveloperError('index must be 0 or 1.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix2.clone(matrix, result);
var startIndex = index * 2;
result[startIndex] = cartesian.x;
result[startIndex + 1] = cartesian.y;
return result;
};
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian2 instance.
*
* @param {Matrix2} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to retrieve.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*
* @exception {DeveloperError} index must be 0 or 1.
*/
Matrix2.getRow = function(matrix, index, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 1) {
throw new DeveloperError('index must be 0 or 1.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = matrix[index];
var y = matrix[index + 2];
result.x = x;
result.y = y;
return result;
};
/**
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian2 instance.
*
* @param {Matrix2} matrix The matrix to use.
* @param {Number} index The zero-based index of the row to set.
* @param {Cartesian2} cartesian The Cartesian whose values will be assigned to the specified row.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*
* @exception {DeveloperError} index must be 0 or 1.
*/
Matrix2.setRow = function(matrix, index, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 1) {
throw new DeveloperError('index must be 0 or 1.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result = Matrix2.clone(matrix, result);
result[index] = cartesian.x;
result[index + 2] = cartesian.y;
return result;
};
var scratchColumn = new Cartesian2();
/**
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
*
* @param {Matrix2} matrix The matrix.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Matrix2.getScale = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = Cartesian2.magnitude(Cartesian2.fromElements(matrix[0], matrix[1], scratchColumn));
result.y = Cartesian2.magnitude(Cartesian2.fromElements(matrix[2], matrix[3], scratchColumn));
return result;
};
var scratchScale = new Cartesian2();
/**
* Computes the maximum scale assuming the matrix is an affine transformation.
* The maximum scale is the maximum length of the column vectors.
*
* @param {Matrix2} matrix The matrix.
* @returns {Number} The maximum scale.
*/
Matrix2.getMaximumScale = function(matrix) {
Matrix2.getScale(matrix, scratchScale);
return Cartesian2.maximumComponent(scratchScale);
};
/**
* Computes the product of two matrices.
*
* @param {Matrix2} left The first matrix.
* @param {Matrix2} right The second matrix.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.multiply = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = left[0] * right[0] + left[2] * right[1];
var column1Row0 = left[0] * right[2] + left[2] * right[3];
var column0Row1 = left[1] * right[0] + left[3] * right[1];
var column1Row1 = left[1] * right[2] + left[3] * right[3];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column1Row0;
result[3] = column1Row1;
return result;
};
/**
* Computes the sum of two matrices.
*
* @param {Matrix2} left The first matrix.
* @param {Matrix2} right The second matrix.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] + right[0];
result[1] = left[1] + right[1];
result[2] = left[2] + right[2];
result[3] = left[3] + right[3];
return result;
};
/**
* Computes the difference of two matrices.
*
* @param {Matrix2} left The first matrix.
* @param {Matrix2} right The second matrix.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = left[0] - right[0];
result[1] = left[1] - right[1];
result[2] = left[2] - right[2];
result[3] = left[3] - right[3];
return result;
};
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix2} matrix The matrix.
* @param {Cartesian2} cartesian The column.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Matrix2.multiplyByVector = function(matrix, cartesian, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = matrix[0] * cartesian.x + matrix[2] * cartesian.y;
var y = matrix[1] * cartesian.x + matrix[3] * cartesian.y;
result.x = x;
result.y = y;
return result;
};
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix2} matrix The matrix.
* @param {Number} scalar The number to multiply by.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.multiplyByScalar = function(matrix, scalar, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
return result;
};
/**
* Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
*
* @param {Matrix2} matrix The matrix on the left-hand side.
* @param {Cartesian2} scale The non-uniform scale on the right-hand side.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix2.multiply(m, Cesium.Matrix2.fromScale(scale), m);
* Cesium.Matrix2.multiplyByScale(m, scale, m);
*
* @see Matrix2.fromScale
* @see Matrix2.multiplyByUniformScale
*/
Matrix2.multiplyByScale = function(matrix, scale, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = matrix[0] * scale.x;
result[1] = matrix[1] * scale.x;
result[2] = matrix[2] * scale.y;
result[3] = matrix[3] * scale.y;
return result;
};
/**
* Creates a negated copy of the provided matrix.
*
* @param {Matrix2} matrix The matrix to negate.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.negate = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
return result;
};
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix2} matrix The matrix to transpose.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.transpose = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var column0Row0 = matrix[0];
var column0Row1 = matrix[2];
var column1Row0 = matrix[1];
var column1Row1 = matrix[3];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column1Row0;
result[3] = column1Row1;
return result;
};
/**
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
*
* @param {Matrix2} matrix The matrix with signed elements.
* @param {Matrix2} result The object onto which to store the result.
* @returns {Matrix2} The modified result parameter.
*/
Matrix2.abs = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result[0] = Math.abs(matrix[0]);
result[1] = Math.abs(matrix[1]);
result[2] = Math.abs(matrix[2]);
result[3] = Math.abs(matrix[3]);
return result;
};
/**
* Compares the provided matrices componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix2} [left] The first matrix.
* @param {Matrix2} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Matrix2.equals = function(left, right) {
return (left === right) ||
(defined(left) &&
defined(right) &&
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[3] === right[3]);
};
/**
* @private
*/
Matrix2.equalsArray = function(matrix, array, offset) {
return matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3];
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix2} [left] The first matrix.
* @param {Matrix2} [right] The second matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Matrix2.equalsEpsilon = function(left, right, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon must be a number');
}
return (left === right) ||
(defined(left) &&
defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon);
};
/**
* An immutable Matrix2 instance initialized to the identity matrix.
*
* @type {Matrix2}
* @constant
*/
Matrix2.IDENTITY = freezeObject(new Matrix2(1.0, 0.0,
0.0, 1.0));
/**
* An immutable Matrix2 instance initialized to the zero matrix.
*
* @type {Matrix2}
* @constant
*/
Matrix2.ZERO = freezeObject(new Matrix2(0.0, 0.0,
0.0, 0.0));
/**
* The index into Matrix2 for column 0, row 0.
*
* @type {Number}
* @constant
*
* @example
* var matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN0ROW0] = 5.0; // set column 0, row 0 to 5.0
*/
Matrix2.COLUMN0ROW0 = 0;
/**
* The index into Matrix2 for column 0, row 1.
*
* @type {Number}
* @constant
*
* @example
* var matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN0ROW1] = 5.0; // set column 0, row 1 to 5.0
*/
Matrix2.COLUMN0ROW1 = 1;
/**
* The index into Matrix2 for column 1, row 0.
*
* @type {Number}
* @constant
*
* @example
* var matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN1ROW0] = 5.0; // set column 1, row 0 to 5.0
*/
Matrix2.COLUMN1ROW0 = 2;
/**
* The index into Matrix2 for column 1, row 1.
*
* @type {Number}
* @constant
*
* @example
* var matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN1ROW1] = 5.0; // set column 1, row 1 to 5.0
*/
Matrix2.COLUMN1ROW1 = 3;
defineProperties(Matrix2.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix2.prototype
*
* @type {Number}
*/
length : {
get : function() {
return Matrix2.packedLength;
}
}
});
/**
* Duplicates the provided Matrix2 instance.
*
* @param {Matrix2} [result] The object onto which to store the result.
* @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.
*/
Matrix2.prototype.clone = function(result) {
return Matrix2.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix2} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix2.prototype.equals = function(right) {
return Matrix2.equals(this, right);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix2} [right] The right hand side matrix.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix2.prototype.equalsEpsilon = function(right, epsilon) {
return Matrix2.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1)'.
*/
Matrix2.prototype.toString = function() {
return '(' + this[0] + ', ' + this[2] + ')\n' +
'(' + this[1] + ', ' + this[3] + ')';
};
return Matrix2;
});
/*global define*/
define('ThirdParty/earcut-2.1.1',[], function() {
'use strict';
function earcut(data, holeIndices, dim) {
dim = dim || 2;
var hasHoles = holeIndices && holeIndices.length,
outerLen = hasHoles ? holeIndices[0] * dim : data.length,
outerNode = linkedList(data, 0, outerLen, dim, true),
triangles = [];
if (!outerNode) return triangles;
var minX, minY, maxX, maxY, x, y, size;
if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim);
// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
if (data.length > 80 * dim) {
minX = maxX = data[0];
minY = maxY = data[1];
for (var i = dim; i < outerLen; i += dim) {
x = data[i];
y = data[i + 1];
if (x < minX) minX = x;
if (y < minY) minY = y;
if (x > maxX) maxX = x;
if (y > maxY) maxY = y;
}
// minX, minY and size are later used to transform coords into integers for z-order calculation
size = Math.max(maxX - minX, maxY - minY);
}
earcutLinked(outerNode, triangles, dim, minX, minY, size);
return triangles;
}
// create a circular doubly linked list from polygon points in the specified winding order
function linkedList(data, start, end, dim, clockwise) {
var i, last;
if (clockwise === (signedArea(data, start, end, dim) > 0)) {
for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last);
} else {
for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last);
}
if (last && equals(last, last.next)) {
removeNode(last);
last = last.next;
}
return last;
}
// eliminate colinear or duplicate points
function filterPoints(start, end) {
if (!start) return start;
if (!end) end = start;
var p = start,
again;
do {
again = false;
if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {
removeNode(p);
p = end = p.prev;
if (p === p.next) return null;
again = true;
} else {
p = p.next;
}
} while (again || p !== end);
return end;
}
// main ear slicing loop which triangulates a polygon (given as a linked list)
function earcutLinked(ear, triangles, dim, minX, minY, size, pass) {
if (!ear) return;
// interlink polygon nodes in z-order
if (!pass && size) indexCurve(ear, minX, minY, size);
var stop = ear,
prev, next;
// iterate through ears, slicing them one by one
while (ear.prev !== ear.next) {
prev = ear.prev;
next = ear.next;
if (size ? isEarHashed(ear, minX, minY, size) : isEar(ear)) {
// cut off the triangle
triangles.push(prev.i / dim);
triangles.push(ear.i / dim);
triangles.push(next.i / dim);
removeNode(ear);
// skipping the next vertice leads to less sliver triangles
ear = next.next;
stop = next.next;
continue;
}
ear = next;
// if we looped through the whole remaining polygon and can't find any more ears
if (ear === stop) {
// try filtering points and slicing again
if (!pass) {
earcutLinked(filterPoints(ear), triangles, dim, minX, minY, size, 1);
// if this didn't work, try curing all small self-intersections locally
} else if (pass === 1) {
ear = cureLocalIntersections(ear, triangles, dim);
earcutLinked(ear, triangles, dim, minX, minY, size, 2);
// as a last resort, try splitting the remaining polygon into two
} else if (pass === 2) {
splitEarcut(ear, triangles, dim, minX, minY, size);
}
break;
}
}
}
// check whether a polygon node forms a valid ear with adjacent nodes
function isEar(ear) {
var a = ear.prev,
b = ear,
c = ear.next;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
// now make sure we don't have other points inside the potential ear
var p = ear.next.next;
while (p !== ear.prev) {
if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.next;
}
return true;
}
function isEarHashed(ear, minX, minY, size) {
var a = ear.prev,
b = ear,
c = ear.next;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
// triangle bbox; min & max are calculated like this for speed
var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x),
minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y),
maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x),
maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y);
// z-order range for the current triangle bbox;
var minZ = zOrder(minTX, minTY, minX, minY, size),
maxZ = zOrder(maxTX, maxTY, minX, minY, size);
// first look for points inside the triangle in increasing z-order
var p = ear.nextZ;
while (p && p.z <= maxZ) {
if (p !== ear.prev && p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.nextZ;
}
// then look for points in decreasing z-order
p = ear.prevZ;
while (p && p.z >= minZ) {
if (p !== ear.prev && p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.prevZ;
}
return true;
}
// go through all polygon nodes and cure small local self-intersections
function cureLocalIntersections(start, triangles, dim) {
var p = start;
do {
var a = p.prev,
b = p.next.next;
if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {
triangles.push(a.i / dim);
triangles.push(p.i / dim);
triangles.push(b.i / dim);
// remove two nodes involved
removeNode(p);
removeNode(p.next);
p = start = b;
}
p = p.next;
} while (p !== start);
return p;
}
// try splitting polygon into two and triangulate them independently
function splitEarcut(start, triangles, dim, minX, minY, size) {
// look for a valid diagonal that divides the polygon into two
var a = start;
do {
var b = a.next.next;
while (b !== a.prev) {
if (a.i !== b.i && isValidDiagonal(a, b)) {
// split the polygon in two by the diagonal
var c = splitPolygon(a, b);
// filter colinear points around the cuts
a = filterPoints(a, a.next);
c = filterPoints(c, c.next);
// run earcut on each half
earcutLinked(a, triangles, dim, minX, minY, size);
earcutLinked(c, triangles, dim, minX, minY, size);
return;
}
b = b.next;
}
a = a.next;
} while (a !== start);
}
// link every hole into the outer loop, producing a single-ring polygon without holes
function eliminateHoles(data, holeIndices, outerNode, dim) {
var queue = [],
i, len, start, end, list;
for (i = 0, len = holeIndices.length; i < len; i++) {
start = holeIndices[i] * dim;
end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
list = linkedList(data, start, end, dim, false);
if (list === list.next) list.steiner = true;
queue.push(getLeftmost(list));
}
queue.sort(compareX);
// process holes from left to right
for (i = 0; i < queue.length; i++) {
eliminateHole(queue[i], outerNode);
outerNode = filterPoints(outerNode, outerNode.next);
}
return outerNode;
}
function compareX(a, b) {
return a.x - b.x;
}
// find a bridge between vertices that connects hole with an outer ring and and link it
function eliminateHole(hole, outerNode) {
outerNode = findHoleBridge(hole, outerNode);
if (outerNode) {
var b = splitPolygon(outerNode, hole);
filterPoints(b, b.next);
}
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
function findHoleBridge(hole, outerNode) {
var p = outerNode,
hx = hole.x,
hy = hole.y,
qx = -Infinity,
m;
// find a segment intersected by a ray from the hole's leftmost point to the left;
// segment's endpoint with lesser x will be potential connection point
do {
if (hy <= p.y && hy >= p.next.y) {
var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);
if (x <= hx && x > qx) {
qx = x;
if (x === hx) {
if (hy === p.y) return p;
if (hy === p.next.y) return p.next;
}
m = p.x < p.next.x ? p : p.next;
}
}
p = p.next;
} while (p !== outerNode);
if (!m) return null;
if (hx === qx) return m.prev; // hole touches outer segment; pick lower endpoint
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point
var stop = m,
mx = m.x,
my = m.y,
tanMin = Infinity,
tan;
p = m.next;
while (p !== stop) {
if (hx >= p.x && p.x >= mx &&
pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) {
tan = Math.abs(hy - p.y) / (hx - p.x); // tangential
if ((tan < tanMin || (tan === tanMin && p.x > m.x)) && locallyInside(p, hole)) {
m = p;
tanMin = tan;
}
}
p = p.next;
}
return m;
}
// interlink polygon nodes in z-order
function indexCurve(start, minX, minY, size) {
var p = start;
do {
if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, size);
p.prevZ = p.prev;
p.nextZ = p.next;
p = p.next;
} while (p !== start);
p.prevZ.nextZ = null;
p.prevZ = null;
sortLinked(p);
}
// Simon Tatham's linked list merge sort algorithm
// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
function sortLinked(list) {
var i, p, q, e, tail, numMerges, pSize, qSize,
inSize = 1;
do {
p = list;
list = null;
tail = null;
numMerges = 0;
while (p) {
numMerges++;
q = p;
pSize = 0;
for (i = 0; i < inSize; i++) {
pSize++;
q = q.nextZ;
if (!q) break;
}
qSize = inSize;
while (pSize > 0 || (qSize > 0 && q)) {
if (pSize === 0) {
e = q;
q = q.nextZ;
qSize--;
} else if (qSize === 0 || !q) {
e = p;
p = p.nextZ;
pSize--;
} else if (p.z <= q.z) {
e = p;
p = p.nextZ;
pSize--;
} else {
e = q;
q = q.nextZ;
qSize--;
}
if (tail) tail.nextZ = e;
else list = e;
e.prevZ = tail;
tail = e;
}
p = q;
}
tail.nextZ = null;
inSize *= 2;
} while (numMerges > 1);
return list;
}
// z-order of a point given coords and size of the data bounding box
function zOrder(x, y, minX, minY, size) {
// coords are transformed into non-negative 15-bit integer range
x = 32767 * (x - minX) / size;
y = 32767 * (y - minY) / size;
x = (x | (x << 8)) & 0x00FF00FF;
x = (x | (x << 4)) & 0x0F0F0F0F;
x = (x | (x << 2)) & 0x33333333;
x = (x | (x << 1)) & 0x55555555;
y = (y | (y << 8)) & 0x00FF00FF;
y = (y | (y << 4)) & 0x0F0F0F0F;
y = (y | (y << 2)) & 0x33333333;
y = (y | (y << 1)) & 0x55555555;
return x | (y << 1);
}
// find the leftmost node of a polygon ring
function getLeftmost(start) {
var p = start,
leftmost = start;
do {
if (p.x < leftmost.x) leftmost = p;
p = p.next;
} while (p !== start);
return leftmost;
}
// check if a point lies within a convex triangle
function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
}
// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
function isValidDiagonal(a, b) {
return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) &&
locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b);
}
// signed area of a triangle
function area(p, q, r) {
return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
}
// check if two points are equal
function equals(p1, p2) {
return p1.x === p2.x && p1.y === p2.y;
}
// check if two segments intersect
function intersects(p1, q1, p2, q2) {
if ((equals(p1, q1) && equals(p2, q2)) ||
(equals(p1, q2) && equals(p2, q1))) return true;
return area(p1, q1, p2) > 0 !== area(p1, q1, q2) > 0 &&
area(p2, q2, p1) > 0 !== area(p2, q2, q1) > 0;
}
// check if a polygon diagonal intersects any polygon segments
function intersectsPolygon(a, b) {
var p = a;
do {
if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i &&
intersects(p, p.next, a, b)) return true;
p = p.next;
} while (p !== a);
return false;
}
// check if a polygon diagonal is locally inside the polygon
function locallyInside(a, b) {
return area(a.prev, a, a.next) < 0 ?
area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 :
area(a, b, a.prev) < 0 || area(a, a.next, b) < 0;
}
// check if the middle point of a polygon diagonal is inside the polygon
function middleInside(a, b) {
var p = a,
inside = false,
px = (a.x + b.x) / 2,
py = (a.y + b.y) / 2;
do {
if (((p.y > py) !== (p.next.y > py)) && (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x))
inside = !inside;
p = p.next;
} while (p !== a);
return inside;
}
// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two;
// if one belongs to the outer ring and another to a hole, it merges it into a single ring
function splitPolygon(a, b) {
var a2 = new Node(a.i, a.x, a.y),
b2 = new Node(b.i, b.x, b.y),
an = a.next,
bp = b.prev;
a.next = b;
b.prev = a;
a2.next = an;
an.prev = a2;
b2.next = a2;
a2.prev = b2;
bp.next = b2;
b2.prev = bp;
return b2;
}
// create a node and optionally link it with previous one (in a circular doubly linked list)
function insertNode(i, x, y, last) {
var p = new Node(i, x, y);
if (!last) {
p.prev = p;
p.next = p;
} else {
p.next = last.next;
p.prev = last;
last.next.prev = p;
last.next = p;
}
return p;
}
function removeNode(p) {
p.next.prev = p.prev;
p.prev.next = p.next;
if (p.prevZ) p.prevZ.nextZ = p.nextZ;
if (p.nextZ) p.nextZ.prevZ = p.prevZ;
}
function Node(i, x, y) {
// vertice index in coordinates array
this.i = i;
// vertex coordinates
this.x = x;
this.y = y;
// previous and next vertice nodes in a polygon ring
this.prev = null;
this.next = null;
// z-order curve value
this.z = null;
// previous and next nodes in z-order
this.prevZ = null;
this.nextZ = null;
// indicates whether this is a steiner point
this.steiner = false;
}
// return a percentage difference between the polygon area and its triangulation area;
// used to verify correctness of triangulation
earcut.deviation = function (data, holeIndices, dim, triangles) {
var hasHoles = holeIndices && holeIndices.length;
var outerLen = hasHoles ? holeIndices[0] * dim : data.length;
var polygonArea = Math.abs(signedArea(data, 0, outerLen, dim));
if (hasHoles) {
for (var i = 0, len = holeIndices.length; i < len; i++) {
var start = holeIndices[i] * dim;
var end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
polygonArea -= Math.abs(signedArea(data, start, end, dim));
}
}
var trianglesArea = 0;
for (i = 0; i < triangles.length; i += 3) {
var a = triangles[i] * dim;
var b = triangles[i + 1] * dim;
var c = triangles[i + 2] * dim;
trianglesArea += Math.abs(
(data[a] - data[c]) * (data[b + 1] - data[a + 1]) -
(data[a] - data[b]) * (data[c + 1] - data[a + 1]));
}
return polygonArea === 0 && trianglesArea === 0 ? 0 :
Math.abs((trianglesArea - polygonArea) / polygonArea);
};
function signedArea(data, start, end, dim) {
var sum = 0;
for (var i = start, j = end - dim; i < end; i += dim) {
sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
j = i;
}
return sum;
}
// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts
earcut.flatten = function (data) {
var dim = data[0][0].length,
result = {vertices: [], holes: [], dimensions: dim},
holeIndex = 0;
for (var i = 0; i < data.length; i++) {
for (var j = 0; j < data[i].length; j++) {
for (var d = 0; d < dim; d++) result.vertices.push(data[i][j][d]);
}
if (i > 0) {
holeIndex += data[i - 1].length;
result.holes.push(holeIndex);
}
}
return result;
};
return earcut;
});
/*global define*/
define('Core/WindingOrder',[
'./freezeObject',
'./WebGLConstants'
], function(
freezeObject,
WebGLConstants) {
'use strict';
/**
* Winding order defines the order of vertices for a triangle to be considered front-facing.
*
* @exports WindingOrder
*/
var WindingOrder = {
/**
* Vertices are in clockwise order.
*
* @type {Number}
* @constant
*/
CLOCKWISE : WebGLConstants.CW,
/**
* Vertices are in counter-clockwise order.
*
* @type {Number}
* @constant
*/
COUNTER_CLOCKWISE : WebGLConstants.CCW,
/**
* @private
*/
validate : function(windingOrder) {
return windingOrder === WindingOrder.CLOCKWISE ||
windingOrder === WindingOrder.COUNTER_CLOCKWISE;
}
};
return freezeObject(WindingOrder);
});
/*global define*/
define('Core/PolygonPipeline',[
'../ThirdParty/earcut-2.1.1',
'./Cartesian2',
'./Cartesian3',
'./ComponentDatatype',
'./defaultValue',
'./defined',
'./DeveloperError',
'./Ellipsoid',
'./Geometry',
'./GeometryAttribute',
'./Math',
'./PrimitiveType',
'./WindingOrder'
], function(
earcut,
Cartesian2,
Cartesian3,
ComponentDatatype,
defaultValue,
defined,
DeveloperError,
Ellipsoid,
Geometry,
GeometryAttribute,
CesiumMath,
PrimitiveType,
WindingOrder) {
'use strict';
var scaleToGeodeticHeightN = new Cartesian3();
var scaleToGeodeticHeightP = new Cartesian3();
/**
* @private
*/
var PolygonPipeline = {};
/**
* @exception {DeveloperError} At least three positions are required.
*/
PolygonPipeline.computeArea2D = function(positions) {
if (!defined(positions)) {
throw new DeveloperError('positions is required.');
}
if (positions.length < 3) {
throw new DeveloperError('At least three positions are required.');
}
var length = positions.length;
var area = 0.0;
for ( var i0 = length - 1, i1 = 0; i1 < length; i0 = i1++) {
var v0 = positions[i0];
var v1 = positions[i1];
area += (v0.x * v1.y) - (v1.x * v0.y);
}
return area * 0.5;
};
/**
* @returns {WindingOrder} The winding order.
*
* @exception {DeveloperError} At least three positions are required.
*/
PolygonPipeline.computeWindingOrder2D = function(positions) {
var area = PolygonPipeline.computeArea2D(positions);
return (area > 0.0) ? WindingOrder.COUNTER_CLOCKWISE : WindingOrder.CLOCKWISE;
};
/**
* Triangulate a polygon.
*
* @param {Cartesian2[]} positions Cartesian2 array containing the vertices of the polygon
* @param {Number[]} [holes] An array of the staring indices of the holes.
* @returns {Number[]} Index array representing triangles that fill the polygon
*/
PolygonPipeline.triangulate = function(positions, holes) {
if (!defined(positions)) {
throw new DeveloperError('positions is required.');
}
var flattenedPositions = Cartesian2.packArray(positions);
return earcut(flattenedPositions, holes, 2);
};
var subdivisionV0Scratch = new Cartesian3();
var subdivisionV1Scratch = new Cartesian3();
var subdivisionV2Scratch = new Cartesian3();
var subdivisionS0Scratch = new Cartesian3();
var subdivisionS1Scratch = new Cartesian3();
var subdivisionS2Scratch = new Cartesian3();
var subdivisionMidScratch = new Cartesian3();
/**
* Subdivides positions and raises points to the surface of the ellipsoid.
*
* @param {Ellipsoid} ellipsoid The ellipsoid the polygon in on.
* @param {Cartesian3[]} positions An array of {@link Cartesian3} positions of the polygon.
* @param {Number[]} indices An array of indices that determines the triangles in the polygon.
* @param {Number} [granularity=CesiumMath.RADIANS_PER_DEGREE] The distance, in radians, between each latitude and longitude. Determines the number of positions in the buffer.
*
* @exception {DeveloperError} At least three indices are required.
* @exception {DeveloperError} The number of indices must be divisable by three.
* @exception {DeveloperError} Granularity must be greater than zero.
*/
PolygonPipeline.computeSubdivision = function(ellipsoid, positions, indices, granularity) {
granularity = defaultValue(granularity, CesiumMath.RADIANS_PER_DEGREE);
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
if (!defined(positions)) {
throw new DeveloperError('positions is required.');
}
if (!defined(indices)) {
throw new DeveloperError('indices is required.');
}
if (indices.length < 3) {
throw new DeveloperError('At least three indices are required.');
}
if (indices.length % 3 !== 0) {
throw new DeveloperError('The number of indices must be divisable by three.');
}
if (granularity <= 0.0) {
throw new DeveloperError('granularity must be greater than zero.');
}
// triangles that need (or might need) to be subdivided.
var triangles = indices.slice(0);
// New positions due to edge splits are appended to the positions list.
var i;
var length = positions.length;
var subdividedPositions = new Array(length * 3);
var q = 0;
for (i = 0; i < length; i++) {
var item = positions[i];
subdividedPositions[q++] = item.x;
subdividedPositions[q++] = item.y;
subdividedPositions[q++] = item.z;
}
var subdividedIndices = [];
// Used to make sure shared edges are not split more than once.
var edges = {};
var radius = ellipsoid.maximumRadius;
var minDistance = CesiumMath.chordLength(granularity, radius);
var minDistanceSqrd = minDistance * minDistance;
while (triangles.length > 0) {
var i2 = triangles.pop();
var i1 = triangles.pop();
var i0 = triangles.pop();
var v0 = Cartesian3.fromArray(subdividedPositions, i0 * 3, subdivisionV0Scratch);
var v1 = Cartesian3.fromArray(subdividedPositions, i1 * 3, subdivisionV1Scratch);
var v2 = Cartesian3.fromArray(subdividedPositions, i2 * 3, subdivisionV2Scratch);
var s0 = Cartesian3.multiplyByScalar(Cartesian3.normalize(v0, subdivisionS0Scratch), radius, subdivisionS0Scratch);
var s1 = Cartesian3.multiplyByScalar(Cartesian3.normalize(v1, subdivisionS1Scratch), radius, subdivisionS1Scratch);
var s2 = Cartesian3.multiplyByScalar(Cartesian3.normalize(v2, subdivisionS2Scratch), radius, subdivisionS2Scratch);
var g0 = Cartesian3.magnitudeSquared(Cartesian3.subtract(s0, s1, subdivisionMidScratch));
var g1 = Cartesian3.magnitudeSquared(Cartesian3.subtract(s1, s2, subdivisionMidScratch));
var g2 = Cartesian3.magnitudeSquared(Cartesian3.subtract(s2, s0, subdivisionMidScratch));
var max = Math.max(g0, g1, g2);
var edge;
var mid;
// if the max length squared of a triangle edge is greater than the chord length of squared
// of the granularity, subdivide the triangle
if (max > minDistanceSqrd) {
if (g0 === max) {
edge = Math.min(i0, i1) + ' ' + Math.max(i0, i1);
i = edges[edge];
if (!defined(i)) {
mid = Cartesian3.add(v0, v1, subdivisionMidScratch);
Cartesian3.multiplyByScalar(mid, 0.5, mid);
subdividedPositions.push(mid.x, mid.y, mid.z);
i = subdividedPositions.length / 3 - 1;
edges[edge] = i;
}
triangles.push(i0, i, i2);
triangles.push(i, i1, i2);
} else if (g1 === max) {
edge = Math.min(i1, i2) + ' ' + Math.max(i1, i2);
i = edges[edge];
if (!defined(i)) {
mid = Cartesian3.add(v1, v2, subdivisionMidScratch);
Cartesian3.multiplyByScalar(mid, 0.5, mid);
subdividedPositions.push(mid.x, mid.y, mid.z);
i = subdividedPositions.length / 3 - 1;
edges[edge] = i;
}
triangles.push(i1, i, i0);
triangles.push(i, i2, i0);
} else if (g2 === max) {
edge = Math.min(i2, i0) + ' ' + Math.max(i2, i0);
i = edges[edge];
if (!defined(i)) {
mid = Cartesian3.add(v2, v0, subdivisionMidScratch);
Cartesian3.multiplyByScalar(mid, 0.5, mid);
subdividedPositions.push(mid.x, mid.y, mid.z);
i = subdividedPositions.length / 3 - 1;
edges[edge] = i;
}
triangles.push(i2, i, i1);
triangles.push(i, i0, i1);
}
} else {
subdividedIndices.push(i0);
subdividedIndices.push(i1);
subdividedIndices.push(i2);
}
}
return new Geometry({
attributes : {
position : new GeometryAttribute({
componentDatatype : ComponentDatatype.DOUBLE,
componentsPerAttribute : 3,
values : subdividedPositions
})
},
indices : subdividedIndices,
primitiveType : PrimitiveType.TRIANGLES
});
};
/**
* Scales each position of a geometry's position attribute to a height, in place.
*
* @param {Number[]} positions The array of numbers representing the positions to be scaled
* @param {Number} [height=0.0] The desired height to add to the positions
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the positions lie.
* @param {Boolean} [scaleToSurface=true] true if the positions need to be scaled to the surface before the height is added.
* @returns {Number[]} The input array of positions, scaled to height
*/
PolygonPipeline.scaleToGeodeticHeight = function(positions, height, ellipsoid, scaleToSurface) {
ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);
var n = scaleToGeodeticHeightN;
var p = scaleToGeodeticHeightP;
height = defaultValue(height, 0.0);
scaleToSurface = defaultValue(scaleToSurface, true);
if (defined(positions)) {
var length = positions.length;
for ( var i = 0; i < length; i += 3) {
Cartesian3.fromArray(positions, i, p);
if (scaleToSurface) {
p = ellipsoid.scaleToGeodeticSurface(p, p);
}
if (height !== 0) {
n = ellipsoid.geodeticSurfaceNormal(p, n);
Cartesian3.multiplyByScalar(n, height, n);
Cartesian3.add(p, n, p);
}
positions[i] = p.x;
positions[i + 1] = p.y;
positions[i + 2] = p.z;
}
}
return positions;
};
return PolygonPipeline;
});
/*global define*/
define('Core/Quaternion',[
'./Cartesian3',
'./defaultValue',
'./defined',
'./DeveloperError',
'./FeatureDetection',
'./freezeObject',
'./Math',
'./Matrix3'
], function(
Cartesian3,
defaultValue,
defined,
DeveloperError,
FeatureDetection,
freezeObject,
CesiumMath,
Matrix3) {
'use strict';
/**
* A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space.
* @alias Quaternion
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
* @param {Number} [w=0.0] The W component.
*
* @see PackableForInterpolation
*/
function Quaternion(x, y, z, w) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = defaultValue(z, 0.0);
/**
* The W component.
* @type {Number}
* @default 0.0
*/
this.w = defaultValue(w, 0.0);
}
var fromAxisAngleScratch = new Cartesian3();
/**
* Computes a quaternion representing a rotation around an axis.
*
* @param {Cartesian3} axis The axis of rotation.
* @param {Number} angle The angle in radians to rotate around the axis.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.fromAxisAngle = function(axis, angle, result) {
if (!defined(axis)) {
throw new DeveloperError('axis is required.');
}
if (typeof angle !== 'number') {
throw new DeveloperError('angle is required and must be a number.');
}
var halfAngle = angle / 2.0;
var s = Math.sin(halfAngle);
fromAxisAngleScratch = Cartesian3.normalize(axis, fromAxisAngleScratch);
var x = fromAxisAngleScratch.x * s;
var y = fromAxisAngleScratch.y * s;
var z = fromAxisAngleScratch.z * s;
var w = Math.cos(halfAngle);
if (!defined(result)) {
return new Quaternion(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
var fromRotationMatrixNext = [1, 2, 0];
var fromRotationMatrixQuat = new Array(3);
/**
* Computes a Quaternion from the provided Matrix3 instance.
*
* @param {Matrix3} matrix The rotation matrix.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*
* @see Matrix3.fromQuaternion
*/
Quaternion.fromRotationMatrix = function(matrix, result) {
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
var root;
var x;
var y;
var z;
var w;
var m00 = matrix[Matrix3.COLUMN0ROW0];
var m11 = matrix[Matrix3.COLUMN1ROW1];
var m22 = matrix[Matrix3.COLUMN2ROW2];
var trace = m00 + m11 + m22;
if (trace > 0.0) {
// |w| > 1/2, may as well choose w > 1/2
root = Math.sqrt(trace + 1.0); // 2w
w = 0.5 * root;
root = 0.5 / root; // 1/(4w)
x = (matrix[Matrix3.COLUMN1ROW2] - matrix[Matrix3.COLUMN2ROW1]) * root;
y = (matrix[Matrix3.COLUMN2ROW0] - matrix[Matrix3.COLUMN0ROW2]) * root;
z = (matrix[Matrix3.COLUMN0ROW1] - matrix[Matrix3.COLUMN1ROW0]) * root;
} else {
// |w| <= 1/2
var next = fromRotationMatrixNext;
var i = 0;
if (m11 > m00) {
i = 1;
}
if (m22 > m00 && m22 > m11) {
i = 2;
}
var j = next[i];
var k = next[j];
root = Math.sqrt(matrix[Matrix3.getElementIndex(i, i)] - matrix[Matrix3.getElementIndex(j, j)] - matrix[Matrix3.getElementIndex(k, k)] + 1.0);
var quat = fromRotationMatrixQuat;
quat[i] = 0.5 * root;
root = 0.5 / root;
w = (matrix[Matrix3.getElementIndex(k, j)] - matrix[Matrix3.getElementIndex(j, k)]) * root;
quat[j] = (matrix[Matrix3.getElementIndex(j, i)] + matrix[Matrix3.getElementIndex(i, j)]) * root;
quat[k] = (matrix[Matrix3.getElementIndex(k, i)] + matrix[Matrix3.getElementIndex(i, k)]) * root;
x = -quat[0];
y = -quat[1];
z = -quat[2];
}
if (!defined(result)) {
return new Quaternion(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
var scratchHPRQuaternion = new Quaternion();
/**
* Computes a rotation from the given heading, pitch and roll angles. Heading is the rotation about the
* negative z axis. Pitch is the rotation about the negative y axis. Roll is the rotation about
* the positive x axis.
*
* @param {Number} heading The heading angle in radians.
* @param {Number} pitch The pitch angle in radians.
* @param {Number} roll The roll angle in radians.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if none was provided.
*/
Quaternion.fromHeadingPitchRoll = function(heading, pitch, roll, result) {
if (!defined(heading)) {
throw new DeveloperError('heading is required.');
}
if (!defined(pitch)) {
throw new DeveloperError('pitch is required.');
}
if (!defined(roll)) {
throw new DeveloperError('roll is required.');
}
var rollQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_X, roll, scratchHPRQuaternion);
var pitchQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_Y, -pitch, result);
result = Quaternion.multiply(pitchQuaternion, rollQuaternion, pitchQuaternion);
var headingQuaternion = Quaternion.fromAxisAngle(Cartesian3.UNIT_Z, -heading, scratchHPRQuaternion);
return Quaternion.multiply(headingQuaternion, result, result);
};
var sampledQuaternionAxis = new Cartesian3();
var sampledQuaternionRotation = new Cartesian3();
var sampledQuaternionTempQuaternion = new Quaternion();
var sampledQuaternionQuaternion0 = new Quaternion();
var sampledQuaternionQuaternion0Conjugate = new Quaternion();
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Quaternion.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Quaternion} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Quaternion.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex++] = value.z;
array[startingIndex] = value.w;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Quaternion} [result] The object into which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Quaternion();
}
result.x = array[startingIndex];
result.y = array[startingIndex + 1];
result.z = array[startingIndex + 2];
result.w = array[startingIndex + 3];
return result;
};
/**
* The number of elements used to store the object into an array in its interpolatable form.
* @type {Number}
*/
Quaternion.packedInterpolationLength = 3;
/**
* Converts a packed array into a form suitable for interpolation.
*
* @param {Number[]} packedArray The packed array.
* @param {Number} [startingIndex=0] The index of the first element to be converted.
* @param {Number} [lastIndex=packedArray.length] The index of the last element to be converted.
* @param {Number[]} result The object into which to store the result.
*/
Quaternion.convertPackedArrayForInterpolation = function(packedArray, startingIndex, lastIndex, result) {
Quaternion.unpack(packedArray, lastIndex * 4, sampledQuaternionQuaternion0Conjugate);
Quaternion.conjugate(sampledQuaternionQuaternion0Conjugate, sampledQuaternionQuaternion0Conjugate);
for (var i = 0, len = lastIndex - startingIndex + 1; i < len; i++) {
var offset = i * 3;
Quaternion.unpack(packedArray, (startingIndex + i) * 4, sampledQuaternionTempQuaternion);
Quaternion.multiply(sampledQuaternionTempQuaternion, sampledQuaternionQuaternion0Conjugate, sampledQuaternionTempQuaternion);
if (sampledQuaternionTempQuaternion.w < 0) {
Quaternion.negate(sampledQuaternionTempQuaternion, sampledQuaternionTempQuaternion);
}
Quaternion.computeAxis(sampledQuaternionTempQuaternion, sampledQuaternionAxis);
var angle = Quaternion.computeAngle(sampledQuaternionTempQuaternion);
result[offset] = sampledQuaternionAxis.x * angle;
result[offset + 1] = sampledQuaternionAxis.y * angle;
result[offset + 2] = sampledQuaternionAxis.z * angle;
}
};
/**
* Retrieves an instance from a packed array converted with {@link convertPackedArrayForInterpolation}.
*
* @param {Number[]} array The array previously packed for interpolation.
* @param {Number[]} sourceArray The original packed array.
* @param {Number} [startingIndex=0] The startingIndex used to convert the array.
* @param {Number} [lastIndex=packedArray.length] The lastIndex used to convert the array.
* @param {Quaternion} [result] The object into which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.unpackInterpolationResult = function(array, sourceArray, firstIndex, lastIndex, result) {
if (!defined(result)) {
result = new Quaternion();
}
Cartesian3.fromArray(array, 0, sampledQuaternionRotation);
var magnitude = Cartesian3.magnitude(sampledQuaternionRotation);
Quaternion.unpack(sourceArray, lastIndex * 4, sampledQuaternionQuaternion0);
if (magnitude === 0) {
Quaternion.clone(Quaternion.IDENTITY, sampledQuaternionTempQuaternion);
} else {
Quaternion.fromAxisAngle(sampledQuaternionRotation, magnitude, sampledQuaternionTempQuaternion);
}
return Quaternion.multiply(sampledQuaternionTempQuaternion, sampledQuaternionQuaternion0, result);
};
/**
* Duplicates a Quaternion instance.
*
* @param {Quaternion} quaternion The quaternion to duplicate.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided. (Returns undefined if quaternion is undefined)
*/
Quaternion.clone = function(quaternion, result) {
if (!defined(quaternion)) {
return undefined;
}
if (!defined(result)) {
return new Quaternion(quaternion.x, quaternion.y, quaternion.z, quaternion.w);
}
result.x = quaternion.x;
result.y = quaternion.y;
result.z = quaternion.z;
result.w = quaternion.w;
return result;
};
/**
* Computes the conjugate of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.conjugate = function(quaternion, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = -quaternion.x;
result.y = -quaternion.y;
result.z = -quaternion.z;
result.w = quaternion.w;
return result;
};
/**
* Computes magnitude squared for the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @returns {Number} The magnitude squared.
*/
Quaternion.magnitudeSquared = function(quaternion) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
return quaternion.x * quaternion.x + quaternion.y * quaternion.y + quaternion.z * quaternion.z + quaternion.w * quaternion.w;
};
/**
* Computes magnitude for the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @returns {Number} The magnitude.
*/
Quaternion.magnitude = function(quaternion) {
return Math.sqrt(Quaternion.magnitudeSquared(quaternion));
};
/**
* Computes the normalized form of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to normalize.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.normalize = function(quaternion, result) {
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var inverseMagnitude = 1.0 / Quaternion.magnitude(quaternion);
var x = quaternion.x * inverseMagnitude;
var y = quaternion.y * inverseMagnitude;
var z = quaternion.z * inverseMagnitude;
var w = quaternion.w * inverseMagnitude;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes the inverse of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to normalize.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.inverse = function(quaternion, result) {
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var magnitudeSquared = Quaternion.magnitudeSquared(quaternion);
result = Quaternion.conjugate(quaternion, result);
return Quaternion.multiplyByScalar(result, 1.0 / magnitudeSquared, result);
};
/**
* Computes the componentwise sum of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.add = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
result.w = left.w + right.w;
return result;
};
/**
* Computes the componentwise difference of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.subtract = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
result.w = left.w - right.w;
return result;
};
/**
* Negates the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to be negated.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.negate = function(quaternion, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = -quaternion.x;
result.y = -quaternion.y;
result.z = -quaternion.z;
result.w = -quaternion.w;
return result;
};
/**
* Computes the dot (scalar) product of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @returns {Number} The dot product.
*/
Quaternion.dot = function(left, right) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
return left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w;
};
/**
* Computes the product of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.multiply = function(left, right, result) {
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var leftX = left.x;
var leftY = left.y;
var leftZ = left.z;
var leftW = left.w;
var rightX = right.x;
var rightY = right.y;
var rightZ = right.z;
var rightW = right.w;
var x = leftW * rightX + leftX * rightW + leftY * rightZ - leftZ * rightY;
var y = leftW * rightY - leftX * rightZ + leftY * rightW + leftZ * rightX;
var z = leftW * rightZ + leftX * rightY - leftY * rightX + leftZ * rightW;
var w = leftW * rightW - leftX * rightX - leftY * rightY - leftZ * rightZ;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Multiplies the provided quaternion componentwise by the provided scalar.
*
* @param {Quaternion} quaternion The quaternion to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.multiplyByScalar = function(quaternion, scalar, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = quaternion.x * scalar;
result.y = quaternion.y * scalar;
result.z = quaternion.z * scalar;
result.w = quaternion.w * scalar;
return result;
};
/**
* Divides the provided quaternion componentwise by the provided scalar.
*
* @param {Quaternion} quaternion The quaternion to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.divideByScalar = function(quaternion, scalar, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
result.x = quaternion.x / scalar;
result.y = quaternion.y / scalar;
result.z = quaternion.z / scalar;
result.w = quaternion.w / scalar;
return result;
};
/**
* Computes the axis of rotation of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to use.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Quaternion.computeAxis = function(quaternion, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var w = quaternion.w;
if (Math.abs(w - 1.0) < CesiumMath.EPSILON6) {
result.x = result.y = result.z = 0;
return result;
}
var scalar = 1.0 / Math.sqrt(1.0 - (w * w));
result.x = quaternion.x * scalar;
result.y = quaternion.y * scalar;
result.z = quaternion.z * scalar;
return result;
};
/**
* Computes the angle of rotation of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to use.
* @returns {Number} The angle of rotation.
*/
Quaternion.computeAngle = function(quaternion) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required');
}
if (Math.abs(quaternion.w - 1.0) < CesiumMath.EPSILON6) {
return 0.0;
}
return 2.0 * Math.acos(quaternion.w);
};
var lerpScratch = new Quaternion();
/**
* Computes the linear interpolation or extrapolation at t using the provided quaternions.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.lerp = function(start, end, t, result) {
if (!defined(start)) {
throw new DeveloperError('start is required.');
}
if (!defined(end)) {
throw new DeveloperError('end is required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
lerpScratch = Quaternion.multiplyByScalar(end, t, lerpScratch);
result = Quaternion.multiplyByScalar(start, 1.0 - t, result);
return Quaternion.add(lerpScratch, result, result);
};
var slerpEndNegated = new Quaternion();
var slerpScaledP = new Quaternion();
var slerpScaledR = new Quaternion();
/**
* Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#fastSlerp
*/
Quaternion.slerp = function(start, end, t, result) {
if (!defined(start)) {
throw new DeveloperError('start is required.');
}
if (!defined(end)) {
throw new DeveloperError('end is required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var dot = Quaternion.dot(start, end);
// The angle between start must be acute. Since q and -q represent
// the same rotation, negate q to get the acute angle.
var r = end;
if (dot < 0.0) {
dot = -dot;
r = slerpEndNegated = Quaternion.negate(end, slerpEndNegated);
}
// dot > 0, as the dot product approaches 1, the angle between the
// quaternions vanishes. use linear interpolation.
if (1.0 - dot < CesiumMath.EPSILON6) {
return Quaternion.lerp(start, r, t, result);
}
var theta = Math.acos(dot);
slerpScaledP = Quaternion.multiplyByScalar(start, Math.sin((1 - t) * theta), slerpScaledP);
slerpScaledR = Quaternion.multiplyByScalar(r, Math.sin(t * theta), slerpScaledR);
result = Quaternion.add(slerpScaledP, slerpScaledR, result);
return Quaternion.multiplyByScalar(result, 1.0 / Math.sin(theta), result);
};
/**
* The logarithmic quaternion function.
*
* @param {Quaternion} quaternion The unit quaternion.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Quaternion.log = function(quaternion, result) {
if (!defined(quaternion)) {
throw new DeveloperError('quaternion is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var theta = CesiumMath.acosClamped(quaternion.w);
var thetaOverSinTheta = 0.0;
if (theta !== 0.0) {
thetaOverSinTheta = theta / Math.sin(theta);
}
return Cartesian3.multiplyByScalar(quaternion, thetaOverSinTheta, result);
};
/**
* The exponential quaternion function.
*
* @param {Cartesian3} cartesian The cartesian.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.exp = function(cartesian, result) {
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var theta = Cartesian3.magnitude(cartesian);
var sinThetaOverTheta = 0.0;
if (theta !== 0.0) {
sinThetaOverTheta = Math.sin(theta) / theta;
}
result.x = cartesian.x * sinThetaOverTheta;
result.y = cartesian.y * sinThetaOverTheta;
result.z = cartesian.z * sinThetaOverTheta;
result.w = Math.cos(theta);
return result;
};
var squadScratchCartesian0 = new Cartesian3();
var squadScratchCartesian1 = new Cartesian3();
var squadScratchQuaternion0 = new Quaternion();
var squadScratchQuaternion1 = new Quaternion();
/**
* Computes an inner quadrangle point.
* This will compute quaternions that ensure a squad curve is C1.
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} q2 The third quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#squad
*/
Quaternion.computeInnerQuadrangle = function(q0, q1, q2, result) {
if (!defined(q0) || !defined(q1) || !defined(q2)) {
throw new DeveloperError('q0, q1, and q2 are required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var qInv = Quaternion.conjugate(q1, squadScratchQuaternion0);
Quaternion.multiply(qInv, q2, squadScratchQuaternion1);
var cart0 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian0);
Quaternion.multiply(qInv, q0, squadScratchQuaternion1);
var cart1 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian1);
Cartesian3.add(cart0, cart1, cart0);
Cartesian3.multiplyByScalar(cart0, 0.25, cart0);
Cartesian3.negate(cart0, cart0);
Quaternion.exp(cart0, squadScratchQuaternion0);
return Quaternion.multiply(q1, squadScratchQuaternion0, result);
};
/**
* Computes the spherical quadrangle interpolation between quaternions.
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} s0 The first inner quadrangle.
* @param {Quaternion} s1 The second inner quadrangle.
* @param {Number} t The time in [0,1] used to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
*
* @example
* // 1. compute the squad interpolation between two quaternions on a curve
* var s0 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new Cesium.Quaternion());
* var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new Cesium.Quaternion());
* var q = Cesium.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t, new Cesium.Quaternion());
*
* // 2. compute the squad interpolation as above but where the first quaternion is a end point.
* var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[0], quaternions[1], quaternions[2], new Cesium.Quaternion());
* var q = Cesium.Quaternion.squad(quaternions[0], quaternions[1], quaternions[0], s1, t, new Cesium.Quaternion());
*
* @see Quaternion#computeInnerQuadrangle
*/
Quaternion.squad = function(q0, q1, s0, s1, t, result) {
if (!defined(q0) || !defined(q1) || !defined(s0) || !defined(s1)) {
throw new DeveloperError('q0, q1, s0, and s1 are required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var slerp0 = Quaternion.slerp(q0, q1, t, squadScratchQuaternion0);
var slerp1 = Quaternion.slerp(s0, s1, t, squadScratchQuaternion1);
return Quaternion.slerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
};
var fastSlerpScratchQuaternion = new Quaternion();
var opmu = 1.90110745351730037;
var u = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var v = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var bT = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var bD = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
for (var i = 0; i < 7; ++i) {
var s = i + 1.0;
var t = 2.0 * s + 1.0;
u[i] = 1.0 / (s * t);
v[i] = s / t;
}
u[7] = opmu / (8.0 * 17.0);
v[7] = opmu * 8.0 / 17.0;
/**
* Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
* This implementation is faster than {@link Quaternion#slerp}, but is only accurate up to 10-6.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#slerp
*/
Quaternion.fastSlerp = function(start, end, t, result) {
if (!defined(start)) {
throw new DeveloperError('start is required.');
}
if (!defined(end)) {
throw new DeveloperError('end is required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var x = Quaternion.dot(start, end);
var sign;
if (x >= 0) {
sign = 1.0;
} else {
sign = -1.0;
x = -x;
}
var xm1 = x - 1.0;
var d = 1.0 - t;
var sqrT = t * t;
var sqrD = d * d;
for (var i = 7; i >= 0; --i) {
bT[i] = (u[i] * sqrT - v[i]) * xm1;
bD[i] = (u[i] * sqrD - v[i]) * xm1;
}
var cT = sign * t * (
1.0 + bT[0] * (1.0 + bT[1] * (1.0 + bT[2] * (1.0 + bT[3] * (
1.0 + bT[4] * (1.0 + bT[5] * (1.0 + bT[6] * (1.0 + bT[7]))))))));
var cD = d * (
1.0 + bD[0] * (1.0 + bD[1] * (1.0 + bD[2] * (1.0 + bD[3] * (
1.0 + bD[4] * (1.0 + bD[5] * (1.0 + bD[6] * (1.0 + bD[7]))))))));
var temp = Quaternion.multiplyByScalar(start, cD, fastSlerpScratchQuaternion);
Quaternion.multiplyByScalar(end, cT, result);
return Quaternion.add(temp, result, result);
};
/**
* Computes the spherical quadrangle interpolation between quaternions.
* An implementation that is faster than {@link Quaternion#squad}, but less accurate.
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} s0 The first inner quadrangle.
* @param {Quaternion} s1 The second inner quadrangle.
* @param {Number} t The time in [0,1] used to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new instance if none was provided.
*
* @see Quaternion#squad
*/
Quaternion.fastSquad = function(q0, q1, s0, s1, t, result) {
if (!defined(q0) || !defined(q1) || !defined(s0) || !defined(s1)) {
throw new DeveloperError('q0, q1, s0, and s1 are required.');
}
if (typeof t !== 'number') {
throw new DeveloperError('t is required and must be a number.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
var slerp0 = Quaternion.fastSlerp(q0, q1, t, squadScratchQuaternion0);
var slerp1 = Quaternion.fastSlerp(s0, s1, t, squadScratchQuaternion1);
return Quaternion.fastSlerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
};
/**
* Compares the provided quaternions componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Quaternion} [left] The first quaternion.
* @param {Quaternion} [right] The second quaternion.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Quaternion.equals = function(left, right) {
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(left.x === right.x) &&
(left.y === right.y) &&
(left.z === right.z) &&
(left.w === right.w));
};
/**
* Compares the provided quaternions componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Quaternion} [left] The first quaternion.
* @param {Quaternion} [right] The second quaternion.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Quaternion.equalsEpsilon = function(left, right, epsilon) {
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon is required and must be a number.');
}
return (left === right) ||
((defined(left)) &&
(defined(right)) &&
(Math.abs(left.x - right.x) <= epsilon) &&
(Math.abs(left.y - right.y) <= epsilon) &&
(Math.abs(left.z - right.z) <= epsilon) &&
(Math.abs(left.w - right.w) <= epsilon));
};
/**
* An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 0.0).
*
* @type {Quaternion}
* @constant
*/
Quaternion.ZERO = freezeObject(new Quaternion(0.0, 0.0, 0.0, 0.0));
/**
* An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 1.0).
*
* @type {Quaternion}
* @constant
*/
Quaternion.IDENTITY = freezeObject(new Quaternion(0.0, 0.0, 0.0, 1.0));
/**
* Duplicates this Quaternion instance.
*
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.prototype.clone = function(result) {
return Quaternion.clone(this, result);
};
/**
* Compares this and the provided quaternion componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Quaternion} [right] The right hand side quaternion.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Quaternion.prototype.equals = function(right) {
return Quaternion.equals(this, right);
};
/**
* Compares this and the provided quaternion componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Quaternion} [right] The right hand side quaternion.
* @param {Number} epsilon The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Quaternion.prototype.equalsEpsilon = function(right, epsilon) {
return Quaternion.equalsEpsilon(this, right, epsilon);
};
/**
* Returns a string representing this quaternion in the format (x, y, z, w).
*
* @returns {String} A string representing this Quaternion.
*/
Quaternion.prototype.toString = function() {
return '(' + this.x + ', ' + this.y + ', ' + this.z + ', ' + this.w + ')';
};
return Quaternion;
});
/*global define*/
define('Core/RectangleGeometryLibrary',[
'./Cartesian3',
'./Cartographic',
'./defined',
'./DeveloperError',
'./GeographicProjection',
'./Math',
'./Matrix2',
'./Rectangle'
], function(
Cartesian3,
Cartographic,
defined,
DeveloperError,
GeographicProjection,
CesiumMath,
Matrix2,
Rectangle) {
'use strict';
var cos = Math.cos;
var sin = Math.sin;
var sqrt = Math.sqrt;
/**
* @private
*/
var RectangleGeometryLibrary = {};
/**
* @private
*/
RectangleGeometryLibrary.computePosition = function(options, row, col, position, st) {
var radiiSquared = options.ellipsoid.radiiSquared;
var nwCorner = options.nwCorner;
var rectangle = options.rectangle;
var stLatitude = nwCorner.latitude - options.granYCos * row + col * options.granXSin;
var cosLatitude = cos(stLatitude);
var nZ = sin(stLatitude);
var kZ = radiiSquared.z * nZ;
var stLongitude = nwCorner.longitude + row * options.granYSin + col * options.granXCos;
var nX = cosLatitude * cos(stLongitude);
var nY = cosLatitude * sin(stLongitude);
var kX = radiiSquared.x * nX;
var kY = radiiSquared.y * nY;
var gamma = sqrt((kX * nX) + (kY * nY) + (kZ * nZ));
position.x = kX / gamma;
position.y = kY / gamma;
position.z = kZ / gamma;
if (defined(options.vertexFormat) && options.vertexFormat.st) {
var stNwCorner = options.stNwCorner;
if (defined(stNwCorner)) {
stLatitude = stNwCorner.latitude - options.stGranYCos * row + col * options.stGranXSin;
stLongitude = stNwCorner.longitude + row * options.stGranYSin + col * options.stGranXCos;
st.x = (stLongitude - options.stWest) * options.lonScalar;
st.y = (stLatitude - options.stSouth) * options.latScalar;
} else {
st.x = (stLongitude - rectangle.west) * options.lonScalar;
st.y = (stLatitude - rectangle.south) * options.latScalar;
}
}
};
var rotationMatrixScratch = new Matrix2();
var nwCartesian = new Cartesian3();
var centerScratch = new Cartographic();
var centerCartesian = new Cartesian3();
var proj = new GeographicProjection();
function getRotationOptions(nwCorner, rotation, granularityX, granularityY, center, width, height) {
var cosRotation = Math.cos(rotation);
var granYCos = granularityY * cosRotation;
var granXCos = granularityX * cosRotation;
var sinRotation = Math.sin(rotation);
var granYSin = granularityY * sinRotation;
var granXSin = granularityX * sinRotation;
nwCartesian = proj.project(nwCorner, nwCartesian);
nwCartesian = Cartesian3.subtract(nwCartesian, centerCartesian, nwCartesian);
var rotationMatrix = Matrix2.fromRotation(rotation, rotationMatrixScratch);
nwCartesian = Matrix2.multiplyByVector(rotationMatrix, nwCartesian, nwCartesian);
nwCartesian = Cartesian3.add(nwCartesian, centerCartesian, nwCartesian);
nwCorner = proj.unproject(nwCartesian, nwCorner);
width -= 1;
height -= 1;
var latitude = nwCorner.latitude;
var latitude0 = latitude + width * granXSin;
var latitude1 = latitude - granYCos * height;
var latitude2 = latitude - granYCos * height + width * granXSin;
var north = Math.max(latitude, latitude0, latitude1, latitude2);
var south = Math.min(latitude, latitude0, latitude1, latitude2);
var longitude = nwCorner.longitude;
var longitude0 = longitude + width * granXCos;
var longitude1 = longitude + height * granYSin;
var longitude2 = longitude + height * granYSin + width * granXCos;
var east = Math.max(longitude, longitude0, longitude1, longitude2);
var west = Math.min(longitude, longitude0, longitude1, longitude2);
return {
north: north,
south: south,
east: east,
west: west,
granYCos : granYCos,
granYSin : granYSin,
granXCos : granXCos,
granXSin : granXSin,
nwCorner : nwCorner
};
}
/**
* @private
*/
RectangleGeometryLibrary.computeOptions = function(geometry, rectangle, nwCorner, stNwCorner) {
var granularity = geometry._granularity;
var ellipsoid = geometry._ellipsoid;
var surfaceHeight = geometry._surfaceHeight;
var rotation = geometry._rotation;
var stRotation = geometry._stRotation;
var extrudedHeight = geometry._extrudedHeight;
var east = rectangle.east;
var west = rectangle.west;
var north = rectangle.north;
var south = rectangle.south;
var width;
var height;
var granularityX;
var granularityY;
var dx;
var dy = north - south;
if (west > east) {
dx = (CesiumMath.TWO_PI - west + east);
width = Math.ceil(dx / granularity) + 1;
height = Math.ceil(dy / granularity) + 1;
granularityX = dx / (width - 1);
granularityY = dy / (height - 1);
} else {
dx = east - west;
width = Math.ceil(dx / granularity) + 1;
height = Math.ceil(dy / granularity) + 1;
granularityX = dx / (width - 1);
granularityY = dy / (height - 1);
}
nwCorner = Rectangle.northwest(rectangle, nwCorner);
var center = Rectangle.center(rectangle, centerScratch);
if (rotation !== 0 || stRotation !== 0) {
if (center.longitude < nwCorner.longitude) {
center.longitude += CesiumMath.TWO_PI;
}
centerCartesian = proj.project(center, centerCartesian);
}
var granYCos = granularityY;
var granXCos = granularityX;
var granYSin = 0.0;
var granXSin = 0.0;
var options = {
granYCos : granYCos,
granYSin : granYSin,
granXCos : granXCos,
granXSin : granXSin,
ellipsoid : ellipsoid,
surfaceHeight : surfaceHeight,
extrudedHeight : extrudedHeight,
nwCorner : nwCorner,
rectangle : rectangle,
width: width,
height: height
};
if (rotation !== 0) {
var rotationOptions = getRotationOptions(nwCorner, rotation, granularityX, granularityY, center, width, height);
north = rotationOptions.north;
south = rotationOptions.south;
east = rotationOptions.east;
west = rotationOptions.west;
if (north < -CesiumMath.PI_OVER_TWO || north > CesiumMath.PI_OVER_TWO ||
south < -CesiumMath.PI_OVER_TWO || south > CesiumMath.PI_OVER_TWO) {
throw new DeveloperError('Rotated rectangle is invalid. It crosses over either the north or south pole.');
}
options.granYCos = rotationOptions.granYCos;
options.granYSin = rotationOptions.granYSin;
options.granXCos = rotationOptions.granXCos;
options.granXSin = rotationOptions.granXSin;
rectangle.north = north;
rectangle.south = south;
rectangle.east = east;
rectangle.west = west;
}
if (stRotation !== 0) {
rotation = rotation - stRotation;
stNwCorner = Rectangle.northwest(rectangle, stNwCorner);
var stRotationOptions = getRotationOptions(stNwCorner, rotation, granularityX, granularityY, center, width, height);
options.stGranYCos = stRotationOptions.granYCos;
options.stGranXCos = stRotationOptions.granXCos;
options.stGranYSin = stRotationOptions.granYSin;
options.stGranXSin = stRotationOptions.granXSin;
options.stNwCorner = stNwCorner;
options.stWest = stRotationOptions.west;
options.stSouth = stRotationOptions.south;
}
return options;
};
return RectangleGeometryLibrary;
});
/*global define*/
define('Core/VertexFormat',[
'./defaultValue',
'./defined',
'./DeveloperError',
'./freezeObject'
], function(
defaultValue,
defined,
DeveloperError,
freezeObject) {
'use strict';
/**
* A vertex format defines what attributes make up a vertex. A VertexFormat can be provided
* to a {@link Geometry} to request that certain properties be computed, e.g., just position,
* position and normal, etc.
*
* @param {Object} [options] An object with boolean properties corresponding to VertexFormat properties as shown in the code example.
*
* @alias VertexFormat
* @constructor
*
* @example
* // Create a vertex format with position and 2D texture coordinate attributes.
* var format = new Cesium.VertexFormat({
* position : true,
* st : true
* });
*
* @see Geometry#attributes
* @see Packable
*/
function VertexFormat(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
/**
* When true, the vertex has a 3D position attribute.
*
* 64-bit floating-point (for precision). 3 components per attribute.
*
*
* @type Boolean
*
* @default false
*/
this.position = defaultValue(options.position, false);
/**
* When true, the vertex has a normal attribute (normalized), which is commonly used for lighting.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type Boolean
*
* @default false
*/
this.normal = defaultValue(options.normal, false);
/**
* When true, the vertex has a 2D texture coordinate attribute.
*
* 32-bit floating-point. 2 components per attribute
*
*
* @type Boolean
*
* @default false
*/
this.st = defaultValue(options.st, false);
/**
* When true, the vertex has a binormal attribute (normalized), which is used for tangent-space effects like bump mapping.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type Boolean
*
* @default false
*/
this.binormal = defaultValue(options.binormal, false);
/**
* When true, the vertex has a tangent attribute (normalized), which is used for tangent-space effects like bump mapping.
*
* 32-bit floating-point. 3 components per attribute.
*
*
* @type Boolean
*
* @default false
*/
this.tangent = defaultValue(options.tangent, false);
/**
* When true, the vertex has an RGB color attribute.
*
* 8-bit unsigned byte. 3 components per attribute.
*
*
* @type Boolean
*
* @default false
*/
this.color = defaultValue(options.color, false);
}
/**
* An immutable vertex format with only a position attribute.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
*/
VertexFormat.POSITION_ONLY = freezeObject(new VertexFormat({
position : true
}));
/**
* An immutable vertex format with position and normal attributes.
* This is compatible with per-instance color appearances like {@link PerInstanceColorAppearance}.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#normal
*/
VertexFormat.POSITION_AND_NORMAL = freezeObject(new VertexFormat({
position : true,
normal : true
}));
/**
* An immutable vertex format with position, normal, and st attributes.
* This is compatible with {@link MaterialAppearance} when {@link MaterialAppearance#materialSupport}
* is TEXTURED/code>.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#normal
* @see VertexFormat#st
*/
VertexFormat.POSITION_NORMAL_AND_ST = freezeObject(new VertexFormat({
position : true,
normal : true,
st : true
}));
/**
* An immutable vertex format with position and st attributes.
* This is compatible with {@link EllipsoidSurfaceAppearance}.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#st
*/
VertexFormat.POSITION_AND_ST = freezeObject(new VertexFormat({
position : true,
st : true
}));
/**
* An immutable vertex format with position and color attributes.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#color
*/
VertexFormat.POSITION_AND_COLOR = freezeObject(new VertexFormat({
position : true,
color : true
}));
/**
* An immutable vertex format with well-known attributes: position, normal, st, binormal, and tangent.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#normal
* @see VertexFormat#st
* @see VertexFormat#binormal
* @see VertexFormat#tangent
*/
VertexFormat.ALL = freezeObject(new VertexFormat({
position : true,
normal : true,
st : true,
binormal : true,
tangent : true
}));
/**
* An immutable vertex format with position, normal, and st attributes.
* This is compatible with most appearances and materials; however
* normal and st attributes are not always required. When this is
* known in advance, another VertexFormat should be used.
*
* @type {VertexFormat}
* @constant
*
* @see VertexFormat#position
* @see VertexFormat#normal
*/
VertexFormat.DEFAULT = VertexFormat.POSITION_NORMAL_AND_ST;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
VertexFormat.packedLength = 6;
/**
* Stores the provided instance into the provided array.
*
* @param {VertexFormat} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
VertexFormat.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.position ? 1.0 : 0.0;
array[startingIndex++] = value.normal ? 1.0 : 0.0;
array[startingIndex++] = value.st ? 1.0 : 0.0;
array[startingIndex++] = value.binormal ? 1.0 : 0.0;
array[startingIndex++] = value.tangent ? 1.0 : 0.0;
array[startingIndex++] = value.color ? 1.0 : 0.0;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {VertexFormat} [result] The object into which to store the result.
* @returns {VertexFormat} The modified result parameter or a new VertexFormat instance if one was not provided.
*/
VertexFormat.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new VertexFormat();
}
result.position = array[startingIndex++] === 1.0;
result.normal = array[startingIndex++] === 1.0;
result.st = array[startingIndex++] === 1.0;
result.binormal = array[startingIndex++] === 1.0;
result.tangent = array[startingIndex++] === 1.0;
result.color = array[startingIndex++] === 1.0;
return result;
};
/**
* Duplicates a VertexFormat instance.
*
* @param {VertexFormat} cartesian The vertex format to duplicate.
* @param {VertexFormat} [result] The object onto which to store the result.
* @returns {VertexFormat} The modified result parameter or a new VertexFormat instance if one was not provided. (Returns undefined if vertexFormat is undefined)
*/
VertexFormat.clone = function(vertexFormat, result) {
if (!defined(vertexFormat)) {
return undefined;
}
if (!defined(result)) {
result = new VertexFormat();
}
result.position = vertexFormat.position;
result.normal = vertexFormat.normal;
result.st = vertexFormat.st;
result.binormal = vertexFormat.binormal;
result.tangent = vertexFormat.tangent;
result.color = vertexFormat.color;
return result;
};
return VertexFormat;
});
/*global define*/
define('Core/RectangleGeometry',[
'./BoundingSphere',
'./Cartesian2',
'./Cartesian3',
'./Cartographic',
'./ComponentDatatype',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./Ellipsoid',
'./Geometry',
'./GeometryAttribute',
'./GeometryAttributes',
'./GeometryInstance',
'./GeometryPipeline',
'./IndexDatatype',
'./Math',
'./Matrix2',
'./Matrix3',
'./PolygonPipeline',
'./PrimitiveType',
'./Quaternion',
'./Rectangle',
'./RectangleGeometryLibrary',
'./VertexFormat'
], function(
BoundingSphere,
Cartesian2,
Cartesian3,
Cartographic,
ComponentDatatype,
defaultValue,
defined,
defineProperties,
DeveloperError,
Ellipsoid,
Geometry,
GeometryAttribute,
GeometryAttributes,
GeometryInstance,
GeometryPipeline,
IndexDatatype,
CesiumMath,
Matrix2,
Matrix3,
PolygonPipeline,
PrimitiveType,
Quaternion,
Rectangle,
RectangleGeometryLibrary,
VertexFormat) {
'use strict';
var positionScratch = new Cartesian3();
var normalScratch = new Cartesian3();
var tangentScratch = new Cartesian3();
var binormalScratch = new Cartesian3();
var rectangleScratch = new Rectangle();
var stScratch = new Cartesian2();
var bottomBoundingSphere = new BoundingSphere();
var topBoundingSphere = new BoundingSphere();
function createAttributes(vertexFormat, attributes) {
var geo = new Geometry({
attributes : new GeometryAttributes(),
primitiveType : PrimitiveType.TRIANGLES
});
geo.attributes.position = new GeometryAttribute({
componentDatatype : ComponentDatatype.DOUBLE,
componentsPerAttribute : 3,
values : attributes.positions
});
if (vertexFormat.normal) {
geo.attributes.normal = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : attributes.normals
});
}
if (vertexFormat.tangent) {
geo.attributes.tangent = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : attributes.tangents
});
}
if (vertexFormat.binormal) {
geo.attributes.binormal = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 3,
values : attributes.binormals
});
}
return geo;
}
function calculateAttributes(positions, vertexFormat, ellipsoid, tangentRotationMatrix) {
var length = positions.length;
var normals = (vertexFormat.normal) ? new Float32Array(length) : undefined;
var tangents = (vertexFormat.tangent) ? new Float32Array(length) : undefined;
var binormals = (vertexFormat.binormal) ? new Float32Array(length) : undefined;
var attrIndex = 0;
var binormal = binormalScratch;
var tangent = tangentScratch;
var normal = normalScratch;
for (var i = 0; i < length; i += 3) {
var p = Cartesian3.fromArray(positions, i, positionScratch);
var attrIndex1 = attrIndex + 1;
var attrIndex2 = attrIndex + 2;
if (vertexFormat.normal || vertexFormat.tangent || vertexFormat.binormal) {
normal = ellipsoid.geodeticSurfaceNormal(p, normal);
if (vertexFormat.tangent || vertexFormat.binormal) {
Cartesian3.cross(Cartesian3.UNIT_Z, normal, tangent);
Matrix3.multiplyByVector(tangentRotationMatrix, tangent, tangent);
Cartesian3.normalize(tangent, tangent);
if (vertexFormat.binormal) {
Cartesian3.normalize(Cartesian3.cross(normal, tangent, binormal), binormal);
}
}
if (vertexFormat.normal) {
normals[attrIndex] = normal.x;
normals[attrIndex1] = normal.y;
normals[attrIndex2] = normal.z;
}
if (vertexFormat.tangent) {
tangents[attrIndex] = tangent.x;
tangents[attrIndex1] = tangent.y;
tangents[attrIndex2] = tangent.z;
}
if (vertexFormat.binormal) {
binormals[attrIndex] = binormal.x;
binormals[attrIndex1] = binormal.y;
binormals[attrIndex2] = binormal.z;
}
}
attrIndex += 3;
}
return createAttributes(vertexFormat, {
positions : positions,
normals : normals,
tangents : tangents,
binormals : binormals
});
}
var v1Scratch = new Cartesian3();
var v2Scratch = new Cartesian3();
function calculateAttributesWall(positions, vertexFormat, ellipsoid) {
var length = positions.length;
var normals = (vertexFormat.normal) ? new Float32Array(length) : undefined;
var tangents = (vertexFormat.tangent) ? new Float32Array(length) : undefined;
var binormals = (vertexFormat.binormal) ? new Float32Array(length) : undefined;
var normalIndex = 0;
var tangentIndex = 0;
var binormalIndex = 0;
var recomputeNormal = true;
var binormal = binormalScratch;
var tangent = tangentScratch;
var normal = normalScratch;
for (var i = 0; i < length; i += 6) {
var p = Cartesian3.fromArray(positions, i, positionScratch);
if (vertexFormat.normal || vertexFormat.tangent || vertexFormat.binormal) {
var p1 = Cartesian3.fromArray(positions, (i + 6) % length, v1Scratch);
if (recomputeNormal) {
var p2 = Cartesian3.fromArray(positions, (i + 3) % length, v2Scratch);
Cartesian3.subtract(p1, p, p1);
Cartesian3.subtract(p2, p, p2);
normal = Cartesian3.normalize(Cartesian3.cross(p2, p1, normal), normal);
recomputeNormal = false;
}
if (Cartesian3.equalsEpsilon(p1, p, CesiumMath.EPSILON10)) { // if we've reached a corner
recomputeNormal = true;
}
if (vertexFormat.tangent || vertexFormat.binormal) {
binormal = ellipsoid.geodeticSurfaceNormal(p, binormal);
if (vertexFormat.tangent) {
tangent = Cartesian3.normalize(Cartesian3.cross(binormal, normal, tangent), tangent);
}
}
if (vertexFormat.normal) {
normals[normalIndex++] = normal.x;
normals[normalIndex++] = normal.y;
normals[normalIndex++] = normal.z;
normals[normalIndex++] = normal.x;
normals[normalIndex++] = normal.y;
normals[normalIndex++] = normal.z;
}
if (vertexFormat.tangent) {
tangents[tangentIndex++] = tangent.x;
tangents[tangentIndex++] = tangent.y;
tangents[tangentIndex++] = tangent.z;
tangents[tangentIndex++] = tangent.x;
tangents[tangentIndex++] = tangent.y;
tangents[tangentIndex++] = tangent.z;
}
if (vertexFormat.binormal) {
binormals[binormalIndex++] = binormal.x;
binormals[binormalIndex++] = binormal.y;
binormals[binormalIndex++] = binormal.z;
binormals[binormalIndex++] = binormal.x;
binormals[binormalIndex++] = binormal.y;
binormals[binormalIndex++] = binormal.z;
}
}
}
return createAttributes(vertexFormat, {
positions : positions,
normals : normals,
tangents : tangents,
binormals : binormals
});
}
function constructRectangle(options) {
var vertexFormat = options.vertexFormat;
var ellipsoid = options.ellipsoid;
var size = options.size;
var height = options.height;
var width = options.width;
var positions = (vertexFormat.position) ? new Float64Array(size * 3) : undefined;
var textureCoordinates = (vertexFormat.st) ? new Float32Array(size * 2) : undefined;
var posIndex = 0;
var stIndex = 0;
var position = positionScratch;
var st = stScratch;
var minX = Number.MAX_VALUE;
var minY = Number.MAX_VALUE;
var maxX = -Number.MAX_VALUE;
var maxY = -Number.MAX_VALUE;
for (var row = 0; row < height; ++row) {
for (var col = 0; col < width; ++col) {
RectangleGeometryLibrary.computePosition(options, row, col, position, st);
positions[posIndex++] = position.x;
positions[posIndex++] = position.y;
positions[posIndex++] = position.z;
if (vertexFormat.st) {
textureCoordinates[stIndex++] = st.x;
textureCoordinates[stIndex++] = st.y;
minX = Math.min(minX, st.x);
minY = Math.min(minY, st.y);
maxX = Math.max(maxX, st.x);
maxY = Math.max(maxY, st.y);
}
}
}
if (vertexFormat.st && (minX < 0.0 || minY < 0.0 || maxX > 1.0 || maxY > 1.0)) {
for (var k = 0; k < textureCoordinates.length; k += 2) {
textureCoordinates[k] = (textureCoordinates[k] - minX) / (maxX - minX);
textureCoordinates[k + 1] = (textureCoordinates[k + 1] - minY) / (maxY - minY);
}
}
var geo = calculateAttributes(positions, vertexFormat, ellipsoid, options.tangentRotationMatrix);
var indicesSize = 6 * (width - 1) * (height - 1);
var indices = IndexDatatype.createTypedArray(size, indicesSize);
var index = 0;
var indicesIndex = 0;
for (var i = 0; i < height - 1; ++i) {
for (var j = 0; j < width - 1; ++j) {
var upperLeft = index;
var lowerLeft = upperLeft + width;
var lowerRight = lowerLeft + 1;
var upperRight = upperLeft + 1;
indices[indicesIndex++] = upperLeft;
indices[indicesIndex++] = lowerLeft;
indices[indicesIndex++] = upperRight;
indices[indicesIndex++] = upperRight;
indices[indicesIndex++] = lowerLeft;
indices[indicesIndex++] = lowerRight;
++index;
}
++index;
}
geo.indices = indices;
if (vertexFormat.st) {
geo.attributes.st = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 2,
values : textureCoordinates
});
}
return geo;
}
function addWallPositions(wallPositions, posIndex, i, topPositions, bottomPositions) {
wallPositions[posIndex++] = topPositions[i];
wallPositions[posIndex++] = topPositions[i + 1];
wallPositions[posIndex++] = topPositions[i + 2];
wallPositions[posIndex++] = bottomPositions[i];
wallPositions[posIndex++] = bottomPositions[i + 1];
wallPositions[posIndex++] = bottomPositions[i + 2];
return wallPositions;
}
function addWallTextureCoordinates(wallTextures, stIndex, i, st) {
wallTextures[stIndex++] = st[i];
wallTextures[stIndex++] = st[i + 1];
wallTextures[stIndex++] = st[i];
wallTextures[stIndex++] = st[i + 1];
return wallTextures;
}
function constructExtrudedRectangle(options) {
var vertexFormat = options.vertexFormat;
var surfaceHeight = options.surfaceHeight;
var extrudedHeight = options.extrudedHeight;
var minHeight = Math.min(extrudedHeight, surfaceHeight);
var maxHeight = Math.max(extrudedHeight, surfaceHeight);
var height = options.height;
var width = options.width;
var ellipsoid = options.ellipsoid;
var i;
var topBottomGeo = constructRectangle(options);
if (CesiumMath.equalsEpsilon(minHeight, maxHeight, CesiumMath.EPSILON10)) {
return topBottomGeo;
}
var topPositions = PolygonPipeline.scaleToGeodeticHeight(topBottomGeo.attributes.position.values, maxHeight, ellipsoid, false);
topPositions = new Float64Array(topPositions);
var length = topPositions.length;
var newLength = length*2;
var positions = new Float64Array(newLength);
positions.set(topPositions);
var bottomPositions = PolygonPipeline.scaleToGeodeticHeight(topBottomGeo.attributes.position.values, minHeight, ellipsoid);
positions.set(bottomPositions, length);
topBottomGeo.attributes.position.values = positions;
var normals = (vertexFormat.normal) ? new Float32Array(newLength) : undefined;
var tangents = (vertexFormat.tangent) ? new Float32Array(newLength) : undefined;
var binormals = (vertexFormat.binormal) ? new Float32Array(newLength) : undefined;
var textures = (vertexFormat.st) ? new Float32Array(newLength/3*2) : undefined;
var topSt;
if (vertexFormat.normal) {
var topNormals = topBottomGeo.attributes.normal.values;
normals.set(topNormals);
for (i = 0; i < length; i ++) {
topNormals[i] = -topNormals[i];
}
normals.set(topNormals, length);
topBottomGeo.attributes.normal.values = normals;
}
if (vertexFormat.tangent) {
var topTangents = topBottomGeo.attributes.tangent.values;
tangents.set(topTangents);
for (i = 0; i < length; i ++) {
topTangents[i] = -topTangents[i];
}
tangents.set(topTangents, length);
topBottomGeo.attributes.tangent.values = tangents;
}
if (vertexFormat.binormal) {
var topBinormals = topBottomGeo.attributes.binormal.values;
binormals.set(topBinormals);
binormals.set(topBinormals, length);
topBottomGeo.attributes.binormal.values = binormals;
}
if (vertexFormat.st) {
topSt = topBottomGeo.attributes.st.values;
textures.set(topSt);
textures.set(topSt, length/3*2);
topBottomGeo.attributes.st.values = textures;
}
var indices = topBottomGeo.indices;
var indicesLength = indices.length;
var posLength = length / 3;
var newIndices = IndexDatatype.createTypedArray(newLength/3, indicesLength*2);
newIndices.set(indices);
for (i = 0; i < indicesLength; i += 3) {
newIndices[i + indicesLength] = indices[i + 2] + posLength;
newIndices[i + 1 + indicesLength] = indices[i + 1] + posLength;
newIndices[i + 2 + indicesLength] = indices[i] + posLength;
}
topBottomGeo.indices = newIndices;
var perimeterPositions = 2 * width + 2 * height - 4;
var wallCount = (perimeterPositions + 4) * 2;
var wallPositions = new Float64Array(wallCount * 3);
var wallTextures = (vertexFormat.st) ? new Float32Array(wallCount * 2) : undefined;
var posIndex = 0;
var stIndex = 0;
var area = width * height;
for (i = 0; i < area; i+=width) {
wallPositions = addWallPositions(wallPositions, posIndex, i*3, topPositions, bottomPositions);
posIndex += 6;
if (vertexFormat.st) {
wallTextures = addWallTextureCoordinates(wallTextures, stIndex, i*2, topSt);
stIndex += 4;
}
}
for (i = area-width; i < area; i++) {
wallPositions = addWallPositions(wallPositions, posIndex, i*3, topPositions, bottomPositions);
posIndex += 6;
if (vertexFormat.st) {
wallTextures = addWallTextureCoordinates(wallTextures, stIndex, i*2, topSt);
stIndex += 4;
}
}
for (i = area-1; i > 0; i-=width) {
wallPositions = addWallPositions(wallPositions, posIndex, i*3, topPositions, bottomPositions);
posIndex += 6;
if (vertexFormat.st) {
wallTextures = addWallTextureCoordinates(wallTextures, stIndex, i*2, topSt);
stIndex += 4;
}
}
for (i = width-1; i >= 0; i--) {
wallPositions = addWallPositions(wallPositions, posIndex, i*3, topPositions, bottomPositions);
posIndex += 6;
if (vertexFormat.st) {
wallTextures = addWallTextureCoordinates(wallTextures, stIndex, i*2, topSt);
stIndex += 4;
}
}
var geo = calculateAttributesWall(wallPositions, vertexFormat, ellipsoid);
if (vertexFormat.st) {
geo.attributes.st = new GeometryAttribute({
componentDatatype : ComponentDatatype.FLOAT,
componentsPerAttribute : 2,
values : wallTextures
});
}
var wallIndices = IndexDatatype.createTypedArray(wallCount, perimeterPositions * 6);
var upperLeft;
var lowerLeft;
var lowerRight;
var upperRight;
length = wallPositions.length / 3;
var index = 0;
for (i = 0; i < length - 1; i+=2) {
upperLeft = i;
upperRight = (upperLeft + 2) % length;
var p1 = Cartesian3.fromArray(wallPositions, upperLeft * 3, v1Scratch);
var p2 = Cartesian3.fromArray(wallPositions, upperRight * 3, v2Scratch);
if (Cartesian3.equalsEpsilon(p1, p2, CesiumMath.EPSILON10)) {
continue;
}
lowerLeft = (upperLeft + 1) % length;
lowerRight = (lowerLeft + 2) % length;
wallIndices[index++] = upperLeft;
wallIndices[index++] = lowerLeft;
wallIndices[index++] = upperRight;
wallIndices[index++] = upperRight;
wallIndices[index++] = lowerLeft;
wallIndices[index++] = lowerRight;
}
geo.indices = wallIndices;
geo = GeometryPipeline.combineInstances([
new GeometryInstance({
geometry : topBottomGeo
}),
new GeometryInstance({
geometry : geo
})
]);
return geo[0];
}
var scratchRotationMatrix = new Matrix3();
var scratchCartesian3 = new Cartesian3();
var scratchQuaternion = new Quaternion();
var scratchRectanglePoints = [new Cartesian3(), new Cartesian3(), new Cartesian3(), new Cartesian3()];
var scratchCartographicPoints = [new Cartographic(), new Cartographic(), new Cartographic(), new Cartographic()];
function computeRectangle(rectangle, ellipsoid, rotation) {
if (rotation === 0.0) {
return Rectangle.clone(rectangle);
}
Rectangle.northeast(rectangle, scratchCartographicPoints[0]);
Rectangle.northwest(rectangle, scratchCartographicPoints[1]);
Rectangle.southeast(rectangle, scratchCartographicPoints[2]);
Rectangle.southwest(rectangle, scratchCartographicPoints[3]);
ellipsoid.cartographicArrayToCartesianArray(scratchCartographicPoints, scratchRectanglePoints);
var surfaceNormal = ellipsoid.geodeticSurfaceNormalCartographic(Rectangle.center(rectangle, scratchCartesian3));
Quaternion.fromAxisAngle(surfaceNormal, rotation, scratchQuaternion);
Matrix3.fromQuaternion(scratchQuaternion, scratchRotationMatrix);
for (var i = 0; i < 4; ++i) {
// Apply the rotation
Matrix3.multiplyByVector(scratchRotationMatrix, scratchRectanglePoints[i], scratchRectanglePoints[i]);
}
ellipsoid.cartesianArrayToCartographicArray(scratchRectanglePoints, scratchCartographicPoints);
return Rectangle.fromCartographicArray(scratchCartographicPoints);
}
/**
* A description of a cartographic rectangle on an ellipsoid centered at the origin. Rectangle geometry can be rendered with both {@link Primitive} and {@link GroundPrimitive}.
*
* @alias RectangleGeometry
* @constructor
*
* @param {Object} options Object with the following properties:
* @param {Rectangle} options.rectangle A cartographic rectangle with north, south, east and west properties in radians.
* @param {VertexFormat} [options.vertexFormat=VertexFormat.DEFAULT] The vertex attributes to be computed.
* @param {Ellipsoid} [options.ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the rectangle lies.
* @param {Number} [options.granularity=CesiumMath.RADIANS_PER_DEGREE] The distance, in radians, between each latitude and longitude. Determines the number of positions in the buffer.
* @param {Number} [options.height=0.0] The distance in meters between the rectangle and the ellipsoid surface.
* @param {Number} [options.rotation=0.0] The rotation of the rectangle, in radians. A positive rotation is counter-clockwise.
* @param {Number} [options.stRotation=0.0] The rotation of the texture coordinates, in radians. A positive rotation is counter-clockwise.
* @param {Number} [options.extrudedHeight] The distance in meters between the rectangle's extruded face and the ellipsoid surface.
* @param {Boolean} [options.closeTop=true] Specifies whether the rectangle has a top cover when extruded.
* @param {Boolean} [options.closeBottom=true] Specifies whether the rectangle has a bottom cover when extruded.
*
* @exception {DeveloperError} options.rectangle.north must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} options.rectangle.south must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} options.rectangle.east must be in the interval [-Pi, Pi].
* @exception {DeveloperError} options.rectangle.west must be in the interval [-Pi, Pi].
* @exception {DeveloperError} options.rectangle.north must be greater than options.rectangle.south.
*
* @see RectangleGeometry#createGeometry
*
* @demo {@link http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Rectangle.html|Cesium Sandcastle Rectangle Demo}
*
* @example
* // 1. create an rectangle
* var rectangle = new Cesium.RectangleGeometry({
* ellipsoid : Cesium.Ellipsoid.WGS84,
* rectangle : Cesium.Rectangle.fromDegrees(-80.0, 39.0, -74.0, 42.0),
* height : 10000.0
* });
* var geometry = Cesium.RectangleGeometry.createGeometry(rectangle);
*
* // 2. create an extruded rectangle without a top
* var rectangle = new Cesium.RectangleGeometry({
* ellipsoid : Cesium.Ellipsoid.WGS84,
* rectangle : Cesium.Rectangle.fromDegrees(-80.0, 39.0, -74.0, 42.0),
* height : 10000.0,
* extrudedHeight: 300000,
* closeTop: false
* });
* var geometry = Cesium.RectangleGeometry.createGeometry(rectangle);
*/
function RectangleGeometry(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var rectangle = options.rectangle;
var granularity = defaultValue(options.granularity, CesiumMath.RADIANS_PER_DEGREE);
var ellipsoid = defaultValue(options.ellipsoid, Ellipsoid.WGS84);
var surfaceHeight = defaultValue(options.height, 0.0);
var rotation = defaultValue(options.rotation, 0.0);
var stRotation = defaultValue(options.stRotation, 0.0);
var vertexFormat = defaultValue(options.vertexFormat, VertexFormat.DEFAULT);
var extrudedHeight = options.extrudedHeight;
var extrude = defined(extrudedHeight);
var closeTop = defaultValue(options.closeTop, true);
var closeBottom = defaultValue(options.closeBottom, true);
if (!defined(rectangle)) {
throw new DeveloperError('rectangle is required.');
}
Rectangle.validate(rectangle);
if (rectangle.north < rectangle.south) {
throw new DeveloperError('options.rectangle.north must be greater than options.rectangle.south');
}
this._rectangle = rectangle;
this._granularity = granularity;
this._ellipsoid = Ellipsoid.clone(ellipsoid);
this._surfaceHeight = surfaceHeight;
this._rotation = rotation;
this._stRotation = stRotation;
this._vertexFormat = VertexFormat.clone(vertexFormat);
this._extrudedHeight = defaultValue(extrudedHeight, 0.0);
this._extrude = extrude;
this._closeTop = closeTop;
this._closeBottom = closeBottom;
this._workerName = 'createRectangleGeometry';
this._rotatedRectangle = computeRectangle(this._rectangle, this._ellipsoid, rotation);
}
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
RectangleGeometry.packedLength = Rectangle.packedLength + Ellipsoid.packedLength + VertexFormat.packedLength + Rectangle.packedLength + 8;
/**
* Stores the provided instance into the provided array.
*
* @param {RectangleGeometry} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
RectangleGeometry.pack = function(value, array, startingIndex) {
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
Rectangle.pack(value._rectangle, array, startingIndex);
startingIndex += Rectangle.packedLength;
Ellipsoid.pack(value._ellipsoid, array, startingIndex);
startingIndex += Ellipsoid.packedLength;
VertexFormat.pack(value._vertexFormat, array, startingIndex);
startingIndex += VertexFormat.packedLength;
Rectangle.pack(value._rotatedRectangle, array, startingIndex);
startingIndex += Rectangle.packedLength;
array[startingIndex++] = value._granularity;
array[startingIndex++] = value._surfaceHeight;
array[startingIndex++] = value._rotation;
array[startingIndex++] = value._stRotation;
array[startingIndex++] = value._extrudedHeight;
array[startingIndex++] = value._extrude ? 1.0 : 0.0;
array[startingIndex++] = value._closeTop ? 1.0 : 0.0;
array[startingIndex] = value._closeBottom ? 1.0 : 0.0;
return array;
};
var scratchRectangle = new Rectangle();
var scratchRotatedRectangle = new Rectangle();
var scratchEllipsoid = Ellipsoid.clone(Ellipsoid.UNIT_SPHERE);
var scratchVertexFormat = new VertexFormat();
var scratchOptions = {
rectangle : scratchRectangle,
ellipsoid : scratchEllipsoid,
vertexFormat : scratchVertexFormat,
granularity : undefined,
height : undefined,
rotation : undefined,
stRotation : undefined,
extrudedHeight : undefined,
closeTop : undefined,
closeBottom : undefined
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {RectangleGeometry} [result] The object into which to store the result.
* @returns {RectangleGeometry} The modified result parameter or a new RectangleGeometry instance if one was not provided.
*/
RectangleGeometry.unpack = function(array, startingIndex, result) {
if (!defined(array)) {
throw new DeveloperError('array is required');
}
startingIndex = defaultValue(startingIndex, 0);
var rectangle = Rectangle.unpack(array, startingIndex, scratchRectangle);
startingIndex += Rectangle.packedLength;
var ellipsoid = Ellipsoid.unpack(array, startingIndex, scratchEllipsoid);
startingIndex += Ellipsoid.packedLength;
var vertexFormat = VertexFormat.unpack(array, startingIndex, scratchVertexFormat);
startingIndex += VertexFormat.packedLength;
var rotatedRectangle = Rectangle.unpack(array, startingIndex, scratchRotatedRectangle);
startingIndex += Rectangle.packedLength;
var granularity = array[startingIndex++];
var surfaceHeight = array[startingIndex++];
var rotation = array[startingIndex++];
var stRotation = array[startingIndex++];
var extrudedHeight = array[startingIndex++];
var extrude = array[startingIndex++] === 1.0;
var closeTop = array[startingIndex++] === 1.0;
var closeBottom = array[startingIndex] === 1.0;
if (!defined(result)) {
scratchOptions.granularity = granularity;
scratchOptions.height = surfaceHeight;
scratchOptions.rotation = rotation;
scratchOptions.stRotation = stRotation;
scratchOptions.extrudedHeight = extrude ? extrudedHeight : undefined;
scratchOptions.closeTop = closeTop;
scratchOptions.closeBottom = closeBottom;
return new RectangleGeometry(scratchOptions);
}
result._rectangle = Rectangle.clone(rectangle, result._rectangle);
result._ellipsoid = Ellipsoid.clone(ellipsoid, result._ellipsoid);
result._vertexFormat = VertexFormat.clone(vertexFormat, result._vertexFormat);
result._granularity = granularity;
result._surfaceHeight = surfaceHeight;
result._rotation = rotation;
result._stRotation = stRotation;
result._extrudedHeight = extrude ? extrudedHeight : undefined;
result._extrude = extrude;
result._closeTop = closeTop;
result._closeBottom = closeBottom;
result._rotatedRectangle = rotatedRectangle;
return result;
};
var tangentRotationMatrixScratch = new Matrix3();
var nwScratch = new Cartographic();
var stNwScratch = new Cartographic();
var quaternionScratch = new Quaternion();
var centerScratch = new Cartographic();
/**
* Computes the geometric representation of an rectangle, including its vertices, indices, and a bounding sphere.
*
* @param {RectangleGeometry} rectangleGeometry A description of the rectangle.
* @returns {Geometry|undefined} The computed vertices and indices.
*
* @exception {DeveloperError} Rotated rectangle is invalid.
*/
RectangleGeometry.createGeometry = function(rectangleGeometry) {
if ((CesiumMath.equalsEpsilon(rectangleGeometry._rectangle.north, rectangleGeometry._rectangle.south, CesiumMath.EPSILON10) ||
(CesiumMath.equalsEpsilon(rectangleGeometry._rectangle.east, rectangleGeometry._rectangle.west, CesiumMath.EPSILON10)))) {
return undefined;
}
var rectangle = Rectangle.clone(rectangleGeometry._rectangle, rectangleScratch);
var ellipsoid = rectangleGeometry._ellipsoid;
var surfaceHeight = rectangleGeometry._surfaceHeight;
var extrude = rectangleGeometry._extrude;
var extrudedHeight = rectangleGeometry._extrudedHeight;
var rotation = rectangleGeometry._rotation;
var stRotation = rectangleGeometry._stRotation;
var vertexFormat = rectangleGeometry._vertexFormat;
var options = RectangleGeometryLibrary.computeOptions(rectangleGeometry, rectangle, nwScratch, stNwScratch);
var tangentRotationMatrix = tangentRotationMatrixScratch;
if (stRotation !== 0 || rotation !== 0) {
var center = Rectangle.center(rectangle, centerScratch);
var axis = ellipsoid.geodeticSurfaceNormalCartographic(center, v1Scratch);
Quaternion.fromAxisAngle(axis, -stRotation, quaternionScratch);
Matrix3.fromQuaternion(quaternionScratch, tangentRotationMatrix);
} else {
Matrix3.clone(Matrix3.IDENTITY, tangentRotationMatrix);
}
options.lonScalar = 1.0 / rectangleGeometry._rectangle.width;
options.latScalar = 1.0 / rectangleGeometry._rectangle.height;
options.vertexFormat = vertexFormat;
options.rotation = rotation;
options.stRotation = stRotation;
options.tangentRotationMatrix = tangentRotationMatrix;
options.size = options.width * options.height;
var geometry;
var boundingSphere;
rectangle = rectangleGeometry._rectangle;
if (extrude) {
geometry = constructExtrudedRectangle(options);
var topBS = BoundingSphere.fromRectangle3D(rectangle, ellipsoid, surfaceHeight, topBoundingSphere);
var bottomBS = BoundingSphere.fromRectangle3D(rectangle, ellipsoid, extrudedHeight, bottomBoundingSphere);
boundingSphere = BoundingSphere.union(topBS, bottomBS);
} else {
geometry = constructRectangle(options);
geometry.attributes.position.values = PolygonPipeline.scaleToGeodeticHeight(geometry.attributes.position.values, surfaceHeight, ellipsoid, false);
boundingSphere = BoundingSphere.fromRectangle3D(rectangle, ellipsoid, surfaceHeight);
}
if (!vertexFormat.position) {
delete geometry.attributes.position;
}
return new Geometry({
attributes : new GeometryAttributes(geometry.attributes),
indices : geometry.indices,
primitiveType : geometry.primitiveType,
boundingSphere : boundingSphere
});
};
/**
* @private
*/
RectangleGeometry.createShadowVolume = function(rectangleGeometry, minHeightFunc, maxHeightFunc) {
var granularity = rectangleGeometry._granularity;
var ellipsoid = rectangleGeometry._ellipsoid;
var minHeight = minHeightFunc(granularity, ellipsoid);
var maxHeight = maxHeightFunc(granularity, ellipsoid);
// TODO: stRotation
return new RectangleGeometry({
rectangle : rectangleGeometry._rectangle,
rotation : rectangleGeometry._rotation,
ellipsoid : ellipsoid,
stRotation : rectangleGeometry._stRotation,
granularity : granularity,
extrudedHeight : maxHeight,
height : minHeight,
closeTop : true,
closeBottom : true,
vertexFormat : VertexFormat.POSITION_ONLY
});
};
defineProperties(RectangleGeometry.prototype, {
/**
* @private
*/
rectangle : {
get : function() {
return this._rotatedRectangle;
}
}
});
return RectangleGeometry;
});
/*global define*/
define('Workers/createRectangleGeometry',[
'../Core/defined',
'../Core/Ellipsoid',
'../Core/Rectangle',
'../Core/RectangleGeometry'
], function(
defined,
Ellipsoid,
Rectangle,
RectangleGeometry) {
'use strict';
function createRectangleGeometry(rectangleGeometry, offset) {
if (defined(offset)) {
rectangleGeometry = RectangleGeometry.unpack(rectangleGeometry, offset);
}
rectangleGeometry._ellipsoid = Ellipsoid.clone(rectangleGeometry._ellipsoid);
rectangleGeometry._rectangle = Rectangle.clone(rectangleGeometry._rectangle);
return RectangleGeometry.createGeometry(rectangleGeometry);
}
return createRectangleGeometry;
});
}());