Matrix3

Members

<static> COLUMN0ROW0

The index into Matrix3 for column 0, row 0.

<static> COLUMN0ROW1

The index into Matrix3 for column 0, row 1.

<static> COLUMN0ROW2

The index into Matrix3 for column 0, row 2.

<static> COLUMN1ROW0

The index into Matrix3 for column 1, row 0.

<static> COLUMN1ROW1

The index into Matrix3 for column 1, row 1.

<static> COLUMN1ROW2

The index into Matrix3 for column 1, row 2.

<static> COLUMN2ROW0

The index into Matrix3 for column 2, row 0.

<static> COLUMN2ROW1

The index into Matrix3 for column 2, row 1.

<static> COLUMN2ROW2

The index into Matrix3 for column 2, row 2.

<static> IDENTITY

An immutable Matrix3 instance initialized to the identity matrix.

Methods

clone

Duplicates the provided Matrix3 instance.

Parameters:

Name	Type	Argument	Description
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

equals

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

Parameters:

Name	Type	Argument	Description
right	Matrix3	<optional>	The right hand side matrix.

Returns:

Boolean true if they are equal, false otherwise.

equalsEpsilon

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

Parameters:

Name	Type	Argument	Description
right	Matrix3	<optional>	The right hand side matrix.
epsilon	Number		The epsilon to use for equality testing.

Returns:

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

toString

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)'.

<static> abs

Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix with signed elements.
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

<static> clone

Duplicates a Matrix3 instance.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to duplicate.
result	Matrix3	<optional>	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)

<static> determinant

Computes the determinant of the provided matrix.

Parameters:

Name	Type	Description
matrix	Matrix3	The matrix to use.

Returns:

Number The value of the determinant of the matrix.

<static> equals

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

Parameters:

Name	Type	Argument	Description
left	Matrix3	<optional>	The first matrix.
right	Matrix3	<optional>	The second matrix.

Returns:

Boolean true if left and right are equal, false otherwise.

<static> equalsEpsilon

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

Parameters:

Name	Type	Argument	Description
left	Matrix3	<optional>	The first matrix.
right	Matrix3	<optional>	The second matrix.
epsilon	Number		The epsilon to use for equality testing.

Returns:

Boolean true if left and right are within the provided epsilon, false otherwise.

<static> fromArray

Creates a Matrix3 from 9 consecutive elements in an array.

Parameters:

Name	Type	Argument	Default	Description
array	Array			The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
startingIndex	Number	<optional>	0	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:

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);

<static> fromColumnMajorArray

Creates a Matrix3 instance from a column-major order array.

Parameters:

Name	Type	Argument	Description
values	Array		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.

<static> fromQuaternion

Computes a 3x3 rotation matrix from the provided quaternion.

Parameters:

Name	Type	Description
quaternion	Quaternion	the quaternion to use.

Returns:

Matrix3 The 3x3 rotation matrix from this quaternion.

<static> fromRotationX

Creates a rotation matrix around the x-axis.

Parameters:

Name	Type	Argument	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);

<static> fromRotationY

Creates a rotation matrix around the y-axis.

Parameters:

Name	Type	Argument	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);

<static> fromRotationZ

Creates a rotation matrix around the z-axis.

Parameters:

Name	Type	Argument	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);

<static> fromRowMajorArray

Creates a Matrix3 instance from a row-major order array. The resulting matrix will be in column-major order.

Parameters:

Name	Type	Argument	Description
values	Array		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.

<static> fromScale

Computes a Matrix3 instance representing a non-uniform scale.

Parameters:

Name	Type	Argument	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));

<static> fromUniformScale

Computes a Matrix3 instance representing a uniform scale.

Parameters:

Name	Type	Argument	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);

<static> getColumn

Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to use.
index	Number		The zero-based index of the column to retrieve.
result	Cartesian3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : index must be 0, 1, or 2.

Returns:

Cartesian3 The modified result parameter or a new Cartesian3 instance if one was not provided.

See:

• Cartesian3

<static> getEigenDecomposition

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.

Parameters:

Name	Type	Argument	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:

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.getEigenDecomposition(a, result);

var unitaryTranspose = Cesium.Matrix3.transpose(result.unitary);
var b = Cesium.Matrix3.multiply(result.unitary, result.diagonal);
Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a

var lambda = Cesium.Matrix3.getColumn(result.diagonal, 0).x;  // first eigenvalue
var v = Cesium.Matrix3.getColumn(result.unitary, 0);          // first eigenvector
var c = Cesium.Cartesian3.multiplyByScalar(v, lambda);        // equal to Cesium.Matrix3.multiplyByVector(a, v)

<static> getElementIndex

Computes the array index of the element at the provided row and column.

Parameters:

Name	Type	Description
row	Number	The zero-based index of the row.
column	Number	The zero-based index of the column.

Throws:

• DeveloperError : row must be 0, 1, or 2.
• DeveloperError : column must be 0, 1, or 2.

Returns:

Number The index of the element at the provided row and column.

Example

var myMatrix = new Cesium.Matrix3();
var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
var column1Row0 = myMatrix[column1Row0Index]
myMatrix[column1Row0Index] = 10.0;

<static> getMaximumScale

Computes the maximum scale assuming the matrix is an affine transformation. The maximum scale is the maximum length of the column vectors.

Parameters:

Name	Type	Description
matrix	Matrix3	The matrix.

Returns:

Number The maximum scale.

<static> getRow

Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to use.
index	Number		The zero-based index of the row to retrieve.
result	Cartesian3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : index must be 0, 1, or 2.

Returns:

Cartesian3 The modified result parameter or a new Cartesian3 instance if one was not provided.

See:

• Cartesian3

<static> getScale

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

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix.
result	Cartesian3	<optional>	The object onto which to store the result.

Returns:

Cartesian3 The modified result parameter or a new Cartesian3 instance if one was not provided.

<static> inverse

Computes the inverse of the provided matrix.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to invert.
result	Matrix3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : matrix is not invertible.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

<static> multiply

Computes the product of two matrices.

Parameters:

Name	Type	Argument	Description
left	Matrix3		The first matrix.
right	Matrix3		The second matrix.
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

<static> multiplyByScalar

Computes the product of a matrix and a scalar.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix.
scalar	Number		The number to multiply by.
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Cartesian3 instance if one was not provided.

<static> multiplyByVector

Computes the product of a matrix and a column vector.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix.
cartesian	Cartesian3		The column.
result	Cartesian3	<optional>	The object onto which to store the result.

Returns:

Cartesian3 The modified result parameter or a new Cartesian3 instance if one was not provided.

<static> negate

Creates a negated copy of the provided matrix.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to negate.
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

<static> setColumn

Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.

Parameters:

Name	Type	Argument	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	Cartesian3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : index must be 0, 1, or 2.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

See:

• Cartesian3

<static> setRow

Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.

Parameters:

Name	Type	Argument	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	Cartesian3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : index must be 0, 1, or 2.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.

See:

• Cartesian3

<static> toArray

Creates an Array from the provided Matrix3 instance. The array will be in column-major order.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to use..
result	Array	<optional>	The Array onto which to store the result.

Returns:

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

<static> transpose

Computes the transpose of the provided matrix.

Parameters:

Name	Type	Argument	Description
matrix	Matrix3		The matrix to transpose.
result	Matrix3	<optional>	The object onto which to store the result.

Returns:

Matrix3 The modified result parameter or a new Matrix3 instance if one was not provided.