Matrix4

new Matrix4(column0Row0, column1Row0, column2Row0, column3Row0, column0Row1, column1Row1, column2Row1, column3Row1, column0Row2, column1Row2, column2Row2, column3Row2, column0Row3, column1Row3, column2Row3, column3Row3)
Math/Matrix4.js 47

A 4x4 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.
column3Row0 Number 0.0 optional

The value for column 3, 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.
column3Row1 Number 0.0 optional

The value for column 3, 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.
column3Row2 Number 0.0 optional

The value for column 3, row 2.
column0Row3 Number 0.0 optional

The value for column 0, row 3.
column1Row3 Number 0.0 optional

The value for column 1, row 3.
column2Row3 Number 0.0 optional

The value for column 2, row 3.
column3Row3 Number 0.0 optional

The value for column 3, row 3.
See:

Members

static constant Matrix4.IDENTITY : Matrix4
Math/Matrix4.js 1646

An immutable Matrix4 instance initialized to the identity matrix.

static constant Matrix4.ZERO : Matrix4
Math/Matrix4.js 1673

An immutable Matrix4 instance initialized to the zero matrix.

Methods

clone(result) → Matrix4
Math/Matrix4.js 1700

Duplicates the provided Matrix4 instance.

Name Type Description
result Matrix4 optional

The object onto which to store the result.
Returns:

The modified result parameter or a new Matrix4 instance if one was not provided.

equals(right) → Boolean
Math/Matrix4.js 1711

Compares this matrix to the provided matrix componentwise and returns true if they are equal, false otherwise.

Name Type Description
right Matrix4 optional

The right hand side matrix.
Returns:

true if they are equal, false otherwise.

equalsEpsilon(right, epsilon) → Boolean
Math/Matrix4.js 1724

Compares this matrix to the provided matrix componentwise and returns true if they are within the provided epsilon, false otherwise.

Name Type Default Description
right Matrix4 optional

The right hand side matrix.
epsilon Number 0 optional

The epsilon to use for equality testing.
Returns:

true if they are within the provided epsilon, false otherwise.

toString() → String
Math/Matrix4.js 1734

Computes a string representing this Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.

Returns:

A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.

static Matrix4.clone(matrix, result) → Matrix4
Math/Matrix4.js 98

Duplicates a Matrix4 instance.

Name Type Description
matrix Matrix4

The matrix to duplicate.
result Matrix4 optional

The object onto which to store the result.
Returns:

The modified result parameter or a new Matrix4 instance if one was not provided. (Returns undefined if matrix is undefined)

static Matrix4.computePerspectiveFieldOfView(fovY, aspectRatio, near, far, result) → Matrix4
Math/Matrix4.js 519

Computes a Matrix4 instance representing a perspective transformation matrix.

Name Type Description
fovY Number

The field of view along the Y axis in radians.
aspectRatio Number

The aspect ratio.
near Number

The distance to the near plane in meters.
far Number

The distance to the far plane in meters.
result Matrix4

The object in which the result will be stored.
Returns:

The modified result parameter.

Throws:
  • DeveloperError :

    fovY must be in (0, PI].

  • DeveloperError :

    aspectRatio must be greater than zero.

  • DeveloperError :

    near must be greater than zero.

  • DeveloperError :

    far must be greater than zero.

static Matrix4.computeView(position, direction, up, right, result) → Matrix4
Math/Matrix4.js 563

Computes a Matrix4 instance that transforms from world space to view space.

Name Type Description
position Cartesian3

The position of the camera.
direction Cartesian3

The forward direction.
up Cartesian3

The up direction.
right Cartesian3

The right direction.
result Matrix4

The object in which the result will be stored.
Returns:

The modified result parameter.

static Matrix4.equals(left, right) → Boolean
Math/Matrix4.js 1275

Compares the provided matrices componentwise and returns true if they are equal, false otherwise.

Name Type Description
left Matrix4 optional

The first matrix.
right Matrix4 optional

The second matrix.
Returns:

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(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

static Matrix4.equalsEpsilon(left, right, epsilon) → Boolean
Math/Matrix4.js 1337

Compares the provided matrices componentwise and returns true if they are within the provided epsilon, false otherwise.

Name Type Default Description
left Matrix4 optional

The first matrix.
right Matrix4 optional

The second matrix.
epsilon Number 0 optional

The epsilon to use for equality testing.
Returns:

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(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

static Matrix4.fromColumnMajorArray(values, result) → Matrix4
Math/Matrix4.js 148

Computes a Matrix4 instance from a column-major order array.

Name Type Description
values Array.<Number>

The column-major order array.
result Matrix4 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 Matrix4 instance if one was not provided.

static Matrix4.fromRotation(rotation, result) → Matrix4
Math/Matrix4.js 477

Creates a rotation matrix.

Name Type Description
rotation Matrix3

The rotation matrix.
result Matrix4 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 Matrix4 instance if one was not provided.

static Matrix4.fromRotationTranslation(rotation, translation, result) → Matrix4
Math/Matrix4.js 209

Computes a Matrix4 instance from a Matrix3 representing the rotation and a Cartesian3 representing the translation.

Name Type Default Description
rotation Matrix3

The upper left portion of the matrix representing the rotation.
translation Cartesian3 Cartesian3.ZERO optional

The upper right portion of the matrix representing the translation.
result Matrix4 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 Matrix4 instance if one was not provided.

static Matrix4.fromRowMajorArray(values, result) → Matrix4
Math/Matrix4.js 160

Computes a Matrix4 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 Matrix4 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 Matrix4 instance if one was not provided.

static Matrix4.fromScale(scale, result) → Matrix4
Math/Matrix4.js 373

Computes a Matrix4 instance representing a non-uniform scale.

Name Type Description
scale Cartesian3

The x, y, and z scale factors.
result Matrix4 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 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]
const m = Matrix4.fromScale(new Cartesian3(7.0, 8.0, 9.0));

static Matrix4.fromTranslation(translation, result) → Matrix4
Math/Matrix4.js 354

Creates a Matrix4 instance from a Cartesian3 representing the translation.

Name Type Description
translation Cartesian3

The upper right portion of the matrix representing the translation.
result Matrix4 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 Matrix4 instance if one was not provided.

See:
  • Matrix4.multiplyByTranslation

static Matrix4.fromTranslationQuaternionRotationScale(translation, rotation, scale, result) → Matrix4
Math/Matrix4.js 269

Computes a Matrix4 instance from a translation, rotation, and scale (TRS) representation with the rotation represented as a quaternion.

Name Type Description
translation Cartesian3

The translation transformation.
rotation Quaternion

The rotation transformation.
scale Cartesian3

The non-uniform scale transformation.
result Matrix4 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 Matrix4 instance if one was not provided.

Example:
const result = Matrix4.fromTranslationQuaternionRotationScale(
  new Cartesian3(1.0, 2.0, 3.0), // translation
  Quaternion.IDENTITY,           // rotation
  new Cartesian3(7.0, 8.0, 9.0), // scale
  result);

static Matrix4.fromTranslationRotationScale(translationRotationScale, result) → Matrix4
Math/Matrix4.js 333

Creates a Matrix4 instance from a TranslationRotationScale instance.

Name Type Description
translationRotationScale TranslationRotationScale

The instance.
result Matrix4 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 Matrix4 instance if one was not provided.

static Matrix4.fromUniformScale(scale, result) → Matrix4
Math/Matrix4.js 429

Computes a Matrix4 instance representing a uniform scale.

Name Type Description
scale Number

The uniform scale factor.
result Matrix4 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 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]
const m = Matrix4.fromUniformScale(2.0);

static Matrix4.getColumn(matrix, index, result) → Cartesian4
Math/Matrix4.js 611

Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.

Name Type Description
matrix Matrix4

The matrix to use.
index Number

The zero-based index of the column to retrieve.
result Cartesian4

The object onto which to store the result.
Returns:

The modified result parameter.

Throws:
  • DeveloperError :

    index must be 0, 1, 2, or 3.

Examples:
//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
const a = Matrix4.getColumn(m, 2, new Cartesian4());
//Example 2: Sets values for Cartesian instance
const a = new Cartesian4();
Matrix4.getColumn(m, 2, a);

// a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;

static Matrix4.getMatrix3(matrix, result) → Matrix3
Math/Matrix4.js 1399

Gets the upper left 3x3 matrix of the provided matrix.

Name Type Description
matrix Matrix4

The matrix to use.
result Matrix3

The object onto which to store the result.
Returns:

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]

const b = new Matrix3();
Matrix4.getMatrix3(m,b);

// b = [10.0, 14.0, 18.0]
//     [11.0, 15.0, 19.0]
//     [12.0, 16.0, 20.0]

static Matrix4.getRotation(matrix, result) → Matrix4
Math/Matrix4.js 929

Extracts the rotation matrix assuming the matrix is an affine transformation.

Name Type Description
matrix Matrix4

The matrix.
result Matrix3

The object onto which to store the result.
Returns:

The modified result parameter.

See:

static Matrix4.getRow(matrix, index, result) → Cartesian4
Math/Matrix4.js 689

Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.

Name Type Description
matrix Matrix4

The matrix to use.
index Number

The zero-based index of the row to retrieve.
result Cartesian4

The object onto which to store the result.
Returns:

The modified result parameter.

Throws:
  • DeveloperError :

    index must be 0, 1, 2, or 3.

Examples:
//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
const a = Matrix4.getRow(m, 2, new Cartesian4());
//Example 2: Sets values for a Cartesian instance
const a = new Cartesian4();
Matrix4.getRow(m, 2, a);

// a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;

static Matrix4.getScale(matrix, result) → Cartesian3
Math/Matrix4.js 866

Extracts the non-uniform scale assuming the matrix is an affine transformation.

Name Type Description
matrix Matrix4

The matrix.
result Cartesian3

The object onto which to store the result.
Returns:

The modified result parameter

See:

static Matrix4.getTranslation(matrix, result) → Cartesian3
Math/Matrix4.js 1370

Gets the translation portion of the provided matrix, assuming the matrix is an affine transformation matrix.

Name Type Description
matrix Matrix4

The matrix to use.
result Cartesian3

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.inverse(matrix, result) → Matrix4
Math/Matrix4.js 1427

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.

Name Type Description
matrix Matrix4

The matrix to invert.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

Throws:
  • Error :

    matrix is not invertible because its determinate is zero.

static Matrix4.inverseTranspose(matrix, result) → Matrix4
Math/Matrix4.js 1633

Computes the inverse transpose of a matrix.

Name Type Description
matrix Matrix4

The matrix to transpose and invert.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.multiply(left, right, result) → Matrix4
Math/Matrix4.js 955

Computes the product of two matrices.

Name Type Description
left Matrix4

The first matrix.
right Matrix4

The second matrix.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.multiplyByMatrix3(matrix, rotation, result) → Matrix4
Math/Matrix4.js 1060

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.

Name Type Description
matrix Matrix4

The matrix on the left-hand side.
rotation Matrix3

The 3x3 rotation matrix on the right-hand side.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

Example:
// Instead of Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m);
Matrix4.multiplyByMatrix3(m, rotation, m);

static Matrix4.multiplyByPoint(matrix, cartesian, result) → Cartesian3
Math/Matrix4.js 1182

Computes the product of a matrix and a Cartesian3. This is equivalent to calling Matrix4.multiplyByVector with a Cartesian4 with a w component of 1, but returns a Cartesian3 instead of a Cartesian4.

Name Type Description
matrix Matrix4

The matrix.
cartesian Cartesian3

The point.
result Cartesian3

The object onto which to store the result.
Returns:

The modified result parameter.

Example:
const p = new Cartesian3(1.0, 2.0, 3.0);
const result = Matrix4.multiplyByPoint(matrix, p, new Cartesian3());

static Matrix4.multiplyByPointAsVector(matrix, cartesian, result) → Cartesian3
Math/Matrix4.js 1154

Computes the product of a matrix and a Cartesian3. This is equivalent to calling Matrix4.multiplyByVector with a Cartesian4 with a w component of zero.

Name Type Description
matrix Matrix4

The matrix.
cartesian Cartesian3

The point.
result Cartesian3

The object onto which to store the result.
Returns:

The modified result parameter.

Example:
const p = new Cartesian3(1.0, 2.0, 3.0);
const result = Matrix4.multiplyByPointAsVector(matrix, p, new Cartesian3());
// A shortcut for
//   Cartesian3 p = ...
//   Matrix4.multiplyByVector(matrix, new Cartesian4(p.x, p.y, p.z, 0.0), result);

static Matrix4.multiplyByVector(matrix, cartesian, result) → Cartesian4
Math/Matrix4.js 1120

Computes the product of a matrix and a column vector.

Name Type Description
matrix Matrix4

The matrix.
cartesian Cartesian4

The vector.
result Cartesian4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.setColumn(matrix, index, cartesian, result) → Matrix4
Math/Matrix4.js 651

Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.

Name Type Description
matrix Matrix4

The matrix to use.
index Number

The zero-based index of the column to set.
cartesian Cartesian4

The Cartesian whose values will be assigned to the specified column.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

Throws:
  • 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]

const a = Matrix4.setColumn(m, 2, new Cartesian4(99.0, 98.0, 97.0, 96.0), new 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]

static Matrix4.setRotation(matrix, rotation) → Matrix4
Math/Matrix4.js 891

Sets the rotation assuming the matrix is an affine transformation.

Name Type Description
matrix Matrix4

The matrix.
rotation Matrix3

The rotation matrix.
Returns:

The modified result parameter.

See:

static Matrix4.setRow(matrix, index, cartesian, result) → Matrix4
Math/Matrix4.js 728

Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.

Name Type Description
matrix Matrix4

The matrix to use.
index Number

The zero-based index of the row to set.
cartesian Cartesian4

The Cartesian whose values will be assigned to the specified row.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

Throws:
  • 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]

const a = Matrix4.setRow(m, 2, new Cartesian4(99.0, 98.0, 97.0, 96.0), new 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]

static Matrix4.setScale(matrix, scale, result) → Matrix4
Math/Matrix4.js 781

Computes a new matrix that replaces the scale with the provided scale. This assumes the matrix is an affine transformation.

Name Type Description
matrix Matrix4

The matrix to use.
scale Cartesian3

The scale that replaces the scale of the provided matrix.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.setTranslation(matrix, translation, result) → Matrix4
Math/Matrix4.js 746

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.

Name Type Description
matrix Matrix4

The matrix to use.
translation Cartesian3

The translation that replaces the translation of the provided matrix.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.setUniformScale(matrix, scale, result) → Matrix4
Math/Matrix4.js 821

Computes a new matrix that replaces the scale with the provided uniform scale. This assumes the matrix is an affine transformation.

Name Type Description
matrix Matrix4

The matrix to use.
scale Number

The uniform scale that replaces the scale of the provided matrix.
result Matrix4

The object onto which to store the result.
Returns:

The modified result parameter.

static Matrix4.transpose(matrix, result) → Matrix4
Math/Matrix4.js 1219

Computes the transpose of the provided matrix.

Name Type Description
matrix Matrix4

The matrix to transpose.
result Matrix4

The object onto which to store the result.
Returns:

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]

const a = Matrix4.transpose(m, new 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]