Matrix3

new Cesium.Matrix3(column0Row0, column1Row0, column2Row0, column0Row1, column1Row1, column2Row1, column0Row2, column1Row2, column2Row2)
Core/Matrix3.js 44

A 3x3 matrix, indexable as a column-major order array. Constructor parameters are in row-major order for code readability.
Name Type Default Description
column0Row0 Number 0.0 optional The value for column 0, row 0.
column1Row0 Number 0.0 optional The value for column 1, row 0.
column2Row0 Number 0.0 optional The value for column 2, row 0.
column0Row1 Number 0.0 optional The value for column 0, row 1.
column1Row1 Number 0.0 optional The value for column 1, row 1.
column2Row1 Number 0.0 optional The value for column 2, row 1.
column0Row2 Number 0.0 optional The value for column 0, row 2.
column1Row2 Number 0.0 optional The value for column 1, row 2.
column2Row2 Number 0.0 optional The value for column 2, row 2.
See:

Members

length : Number
Core/Matrix3.js 1546

Gets the number of items in the collection.

staticconstantCesium.Matrix3.COLUMN0ROW0 : Number
Core/Matrix3.js 1473

The index into Matrix3 for column 0, row 0.

staticconstantCesium.Matrix3.COLUMN0ROW1 : Number
Core/Matrix3.js 1481

The index into Matrix3 for column 0, row 1.

staticconstantCesium.Matrix3.COLUMN0ROW2 : Number
Core/Matrix3.js 1489

The index into Matrix3 for column 0, row 2.

staticconstantCesium.Matrix3.COLUMN1ROW0 : Number
Core/Matrix3.js 1497

The index into Matrix3 for column 1, row 0.

staticconstantCesium.Matrix3.COLUMN1ROW1 : Number
Core/Matrix3.js 1505

The index into Matrix3 for column 1, row 1.

staticconstantCesium.Matrix3.COLUMN1ROW2 : Number
Core/Matrix3.js 1513

The index into Matrix3 for column 1, row 2.

staticconstantCesium.Matrix3.COLUMN2ROW0 : Number
Core/Matrix3.js 1521

The index into Matrix3 for column 2, row 0.

staticconstantCesium.Matrix3.COLUMN2ROW1 : Number
Core/Matrix3.js 1529

The index into Matrix3 for column 2, row 1.

staticconstantCesium.Matrix3.COLUMN2ROW2 : Number
Core/Matrix3.js 1537

The index into Matrix3 for column 2, row 2.

staticconstantCesium.Matrix3.IDENTITY : Matrix3
Core/Matrix3.js 1453

An immutable Matrix3 instance initialized to the identity matrix.

staticCesium.Matrix3.packedLength : Number
Core/Matrix3.js 62

The number of elements used to pack the object into an array.

staticconstantCesium.Matrix3.ZERO : Matrix3
Core/Matrix3.js 1463

An immutable Matrix3 instance initialized to the zero matrix.

Methods

clone(result) → Matrix3
Core/Matrix3.js 1559

Duplicates the provided Matrix3 instance.
Name Type Description
result Matrix3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Matrix3 instance if one was not provided.

equals(right) → Boolean
Core/Matrix3.js 1570

Compares this matrix to the provided matrix componentwise and returns true if they are equal, false otherwise.
Name Type Description
right Matrix3 optional The right hand side matrix.
Returns:
true if they are equal, false otherwise.

equalsEpsilon(right, epsilon) → Boolean
Core/Matrix3.js 1598

Compares this matrix to the provided matrix componentwise and returns true if they are within the provided epsilon, false otherwise.
Name Type Description
right Matrix3 optional The right hand side matrix.
epsilon Number The epsilon to use for equality testing.
Returns:
true if they are within the provided epsilon, false otherwise.

toString() → String
Core/Matrix3.js 1608

Creates a string representing this Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
Returns:
A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.

staticCesium.Matrix3.abs(matrix, result) → Matrix3
Core/Matrix3.js 1293

Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
Name Type Description
matrix Matrix3 The matrix with signed elements.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.add(left, right, result) → Matrix3
Core/Matrix3.js 895

Computes the sum of two matrices.
Name Type Description
left Matrix3 The first matrix.
right Matrix3 The second matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.clone(matrix, result) → Matrix3
Core/Matrix3.js 139

Duplicates a Matrix3 instance.
Name Type Description
matrix Matrix3 The matrix to duplicate.
result Matrix3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)

staticCesium.Matrix3.computeEigenDecomposition(matrix, result) → Object
Core/Matrix3.js 1245

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.

Name Type Description
matrix Matrix3 The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
result Object optional An object with unitary and diagonal properties which are matrices onto which to store the result.
Returns:
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)

staticCesium.Matrix3.determinant(matrix) → Number
Core/Matrix3.js 1322

Computes the determinant of the provided matrix.
Name Type Description
matrix Matrix3 The matrix to use.
Returns:
The value of the determinant of the matrix.

staticCesium.Matrix3.equals(left, right) → Boolean
Core/Matrix3.js 1401

Compares the provided matrices componentwise and returns true if they are equal, false otherwise.
Name Type Description
left Matrix3 optional The first matrix.
right Matrix3 optional The second matrix.
Returns:
true if left and right are equal, false otherwise.

staticCesium.Matrix3.equalsEpsilon(left, right, epsilon) → Boolean
Core/Matrix3.js 1426

Compares the provided matrices componentwise and returns true if they are within the provided epsilon, false otherwise.
Name Type Description
left Matrix3 optional The first matrix.
right Matrix3 optional The second matrix.
epsilon Number The epsilon to use for equality testing.
Returns:
true if left and right are within the provided epsilon, false otherwise.

staticCesium.Matrix3.fromArray(array, startingIndex, result) → Matrix3
Core/Matrix3.js 181

Creates a Matrix3 from 9 consecutive elements in an array.
Name Type Default Description
array Array.<Number> The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
startingIndex Number 0 optional The offset into the array of the first element, which corresponds to first column first row position in the matrix.
result Matrix3 optional The object onto which to store the result.
Returns:
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);

staticCesium.Matrix3.fromColumnMajorArray(values, result) → Matrix3
Core/Matrix3.js 213

Creates a Matrix3 instance from a column-major order array.
Name Type Description
values Array.<Number> The column-major order array.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.

staticCesium.Matrix3.fromCrossProduct(the, result) → Matrix3
Core/Matrix3.js 452

Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
Name Type Description
the Cartesian3 vector on the left hand side of the cross product operation.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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));

staticCesium.Matrix3.fromHeadingPitchRoll(headingPitchRoll, result) → Matrix3
Core/Matrix3.js 316

Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
Name Type Description
headingPitchRoll HeadingPitchRoll the headingPitchRoll to use.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
The 3x3 rotation matrix from this headingPitchRoll.

staticCesium.Matrix3.fromQuaternion(quaternion, result) → Matrix3
Core/Matrix3.js 262

Computes a 3x3 rotation matrix from the provided quaternion.
Name Type Description
quaternion Quaternion the quaternion to use.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
The 3x3 rotation matrix from this quaternion.

staticCesium.Matrix3.fromRotationX(angle, result) → Matrix3
Core/Matrix3.js 491

Creates a rotation matrix around the x-axis.
Name Type Description
angle Number The angle, in radians, of the rotation. Positive angles are counterclockwise.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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());

staticCesium.Matrix3.fromRotationY(angle, result) → Matrix3
Core/Matrix3.js 534

Creates a rotation matrix around the y-axis.
Name Type Description
angle Number The angle, in radians, of the rotation. Positive angles are counterclockwise.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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());

staticCesium.Matrix3.fromRotationZ(angle, result) → Matrix3
Core/Matrix3.js 577

Creates a rotation matrix around the z-axis.
Name Type Description
angle Number The angle, in radians, of the rotation. Positive angles are counterclockwise.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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());

staticCesium.Matrix3.fromRowMajorArray(values, result) → Matrix3
Core/Matrix3.js 231

Creates a Matrix3 instance from a row-major order array. The resulting matrix will be in column-major order.
Name Type Description
values Array.<Number> The row-major order array.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.

staticCesium.Matrix3.fromScale(scale, result) → Matrix3
Core/Matrix3.js 372

Computes a Matrix3 instance representing a non-uniform scale.
Name Type Description
scale Cartesian3 The x, y, and z scale factors.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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));

staticCesium.Matrix3.fromUniformScale(scale, result) → Matrix3
Core/Matrix3.js 412

Computes a Matrix3 instance representing a uniform scale.
Name Type Description
scale Number The uniform scale factor.
result Matrix3 optional The object in which the result will be stored, if undefined a new instance will be created.
Returns:
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);

staticCesium.Matrix3.getColumn(matrix, index, result) → Cartesian3
Core/Matrix3.js 676

Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
Name Type Description
matrix Matrix3 The matrix to use.
index Number The zero-based index of the column to retrieve.
result Cartesian3 The object onto which to store the result.
Returns:
The modified result parameter.
Throws:

staticCesium.Matrix3.getElementIndex(row, column) → Number
Core/Matrix3.js 653

Computes the array index of the element at the provided row and column.
Name Type Description
row Number The zero-based index of the row.
column Number The zero-based index of the column.
Returns:
The index of the element at the provided row and column.
Throws:
Example:
var myMatrix = new Cesium.Matrix3();
var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
var column1Row0 = myMatrix[column1Row0Index]
myMatrix[column1Row0Index] = 10.0;

staticCesium.Matrix3.getMaximumScale(matrix) → Number
Core/Matrix3.js 837

Computes the maximum scale assuming the matrix is an affine transformation. The maximum scale is the maximum length of the column vectors.
Name Type Description
matrix Matrix3 The matrix.
Returns:
The maximum scale.

staticCesium.Matrix3.getRow(matrix, index, result) → Cartesian3
Core/Matrix3.js 746

Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
Name Type Description
matrix Matrix3 The matrix to use.
index Number The zero-based index of the row to retrieve.
result Cartesian3 The object onto which to store the result.
Returns:
The modified result parameter.
Throws:

staticCesium.Matrix3.getScale(matrix, result) → Cartesian3
Core/Matrix3.js 812

Extracts the non-uniform scale assuming the matrix is an affine transformation.
Name Type Description
matrix Matrix3 The matrix.
result Cartesian3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.inverse(matrix, result) → Matrix3
Core/Matrix3.js 1351

Computes the inverse of the provided matrix.
Name Type Description
matrix Matrix3 The matrix to invert.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
Throws:

staticCesium.Matrix3.multiply(left, right, result) → Matrix3
Core/Matrix3.js 850

Computes the product of two matrices.
Name Type Description
left Matrix3 The first matrix.
right Matrix3 The second matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.multiplyByScalar(matrix, scalar, result) → Matrix3
Core/Matrix3.js 996

Computes the product of a matrix and a scalar.
Name Type Description
matrix Matrix3 The matrix.
scalar Number The number to multiply by.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.multiplyByScale(matrix, scale, result) → Matrix3
Core/Matrix3.js 1037

Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
Name Type Description
matrix Matrix3 The matrix on the left-hand side.
scale Cartesian3 The non-uniform scale on the right-hand side.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
Example:
// Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
Cesium.Matrix3.multiplyByScale(m, scale, m);
See:

staticCesium.Matrix3.multiplyByVector(matrix, cartesian, result) → Cartesian3
Core/Matrix3.js 961

Computes the product of a matrix and a column vector.
Name Type Description
matrix Matrix3 The matrix.
cartesian Cartesian3 The column.
result Cartesian3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.negate(matrix, result) → Matrix3
Core/Matrix3.js 1069

Creates a negated copy of the provided matrix.
Name Type Description
matrix Matrix3 The matrix to negate.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.pack(value, array, startingIndex) → Array.<Number>
Core/Matrix3.js 73

Stores the provided instance into the provided array.
Name Type Default Description
value Matrix3 The value to pack.
array Array.<Number> The array to pack into.
startingIndex Number 0 optional The index into the array at which to start packing the elements.
Returns:
The array that was packed into

staticCesium.Matrix3.setColumn(matrix, index, cartesian, result) → Matrix3
Core/Matrix3.js 712

Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
Name Type Description
matrix Matrix3 The matrix to use.
index Number The zero-based index of the column to set.
cartesian Cartesian3 The Cartesian whose values will be assigned to the specified column.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
Throws:

staticCesium.Matrix3.setRow(matrix, index, cartesian, result) → Matrix3
Core/Matrix3.js 780

Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
Name Type Description
matrix Matrix3 The matrix to use.
index Number The zero-based index of the row to set.
cartesian Cartesian3 The Cartesian whose values will be assigned to the specified row.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
Throws:

staticCesium.Matrix3.subtract(left, right, result) → Matrix3
Core/Matrix3.js 928

Computes the difference of two matrices.
Name Type Description
left Matrix3 The first matrix.
right Matrix3 The second matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.toArray(matrix, result) → Array.<Number>
Core/Matrix3.js 615

Creates an Array from the provided Matrix3 instance. The array will be in column-major order.
Name Type Description
matrix Matrix3 The matrix to use..
result Array.<Number> optional The Array onto which to store the result.
Returns:
The modified Array parameter or a new Array instance if one was not provided.

staticCesium.Matrix3.transpose(matrix, result) → Matrix3
Core/Matrix3.js 1098

Computes the transpose of the provided matrix.
Name Type Description
matrix Matrix3 The matrix to transpose.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.

staticCesium.Matrix3.unpack(array, startingIndex, result) → Matrix3
Core/Matrix3.js 107

Retrieves an instance from a packed array.
Name Type Default Description
array Array.<Number> The packed array.
startingIndex Number 0 optional The starting index of the element to be unpacked.
result Matrix3 optional The object into which to store the result.
Returns:
The modified result parameter or a new Matrix3 instance if one was not provided.