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/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/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/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/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/PointGeometry',[
'./BoundingSphere',
'./ComponentDatatype',
'./defaultValue',
'./defined',
'./DeveloperError',
'./Geometry',
'./GeometryAttribute',
'./GeometryAttributes',
'./PrimitiveType'
], function(
BoundingSphere,
ComponentDatatype,
defaultValue,
defined,
DeveloperError,
Geometry,
GeometryAttribute,
GeometryAttributes,
PrimitiveType) {
'use strict';
/**
* Describes a collection of points made up of positions and colors.
*
* @alias PointGeometry
* @constructor
*
* @param {Object} options Object with the following properties:
* @param {TypedArray} options.positionsTypedArray The position values of the points stored in a typed array. Positions are stored as packed (x, y, z) floats.
* @param {TypedArray} options.colorsTypedArray The color values of the points stored in a typed array. Colors are stored as packed (r, g, b) unsigned bytes.
* @param {BoundingSphere} [options.boundingSphere] Optional precomputed bounding sphere to save computation time.
*
* @example
* // Create a PointGeometry with two points
* var points = new Cesium.PointGeometry({
* positionsTypedArray : new Float32Array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]),
* colorsTypedArray : new Uint8Array([255, 0, 0, 127, 127, 127]),
* boundingSphere : boundingSphere
* });
* var geometry = Cesium.PointGeometry.createGeometry(points);
*
* @private
*/
function PointGeometry(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
if (!defined(options.positionsTypedArray)) {
throw new DeveloperError('options.positionsTypedArray is required.');
}
if (!defined(options.colorsTypedArray)) {
throw new DeveloperError('options.colorsTypedArray is required');
}
this._positionsTypedArray = options.positionsTypedArray;
this._colorsTypedArray = options.colorsTypedArray;
this._boundingSphere = BoundingSphere.clone(options.boundingSphere);
this._workerName = 'createPointGeometry';
}
/**
* Computes the geometric representation a point collection, including its vertices and a bounding sphere.
*
* @param {PointGeometry} pointGeometry A description of the points.
* @returns {Geometry} The computed vertices.
*/
PointGeometry.createGeometry = function(pointGeometry) {
var positions = pointGeometry._positionsTypedArray;
var componentByteLength = positions.byteLength / positions.length;
var componentDatatype = componentByteLength === 4 ? ComponentDatatype.FLOAT : ComponentDatatype.DOUBLE;
var attributes = new GeometryAttributes();
attributes.position = new GeometryAttribute({
componentDatatype : componentDatatype,
componentsPerAttribute : 3,
values : positions
});
attributes.color = new GeometryAttribute({
componentDatatype : ComponentDatatype.UNSIGNED_BYTE,
componentsPerAttribute : 3,
values : pointGeometry._colorsTypedArray,
normalize : true
});
// User provided bounding sphere to save computation time.
var boundingSphere = pointGeometry._boundingSphere;
if (!defined(boundingSphere)) {
boundingSphere = BoundingSphere.fromVertices(positions);
}
return new Geometry({
attributes : attributes,
primitiveType : PrimitiveType.POINTS,
boundingSphere : boundingSphere
});
};
return PointGeometry;
});
/*global define*/
define('Workers/createPointGeometry',[
'../Core/PointGeometry'
], function(
PointGeometry) {
'use strict';
return PointGeometry.createGeometry;
});
}());