Matrix3

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

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

Gets the number of items in the collection.

static constant Cesium.Matrix3.COLUMN0ROW0 : Number

The index into Matrix3 for column 0, row 0.

static constant Cesium.Matrix3.COLUMN0ROW1 : Number

The index into Matrix3 for column 0, row 1.

static constant Cesium.Matrix3.COLUMN0ROW2 : Number

The index into Matrix3 for column 0, row 2.

static constant Cesium.Matrix3.COLUMN1ROW0 : Number

The index into Matrix3 for column 1, row 0.

static constant Cesium.Matrix3.COLUMN1ROW1 : Number

The index into Matrix3 for column 1, row 1.

static constant Cesium.Matrix3.COLUMN1ROW2 : Number

The index into Matrix3 for column 1, row 2.

static constant Cesium.Matrix3.COLUMN2ROW0 : Number

The index into Matrix3 for column 2, row 0.

static constant Cesium.Matrix3.COLUMN2ROW1 : Number

The index into Matrix3 for column 2, row 1.

static constant Cesium.Matrix3.COLUMN2ROW2 : Number

The index into Matrix3 for column 2, row 2.

static constant Cesium.Matrix3.IDENTITY : Matrix3

An immutable Matrix3 instance initialized to the identity matrix.

static Cesium.Matrix3.packedLength : Number

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

static constant Cesium.Matrix3.ZERO : Matrix3

An immutable Matrix3 instance initialized to the zero matrix.

Methods

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

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

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 Matrix3 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

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)'.

static Cesium.Matrix3.abs(matrix, result)Matrix3

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.

static Cesium.Matrix3.add(left, right, result)Matrix3

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.

static Cesium.Matrix3.clone(matrix, result)Matrix3

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)

static Cesium.Matrix3.computeEigenDecomposition(matrix, result)Object

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:
const a = //... symetric matrix
const result = {
    unitary : new Cesium.Matrix3(),
    diagonal : new Cesium.Matrix3()
};
Cesium.Matrix3.computeEigenDecomposition(a, result);

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

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

static Cesium.Matrix3.determinant(matrix)Number

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.

static Cesium.Matrix3.equals(left, right)Boolean

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.

static Cesium.Matrix3.equalsEpsilon(left, right, epsilon)Boolean

Compares the provided matrices componentwise and returns true if they are within the provided epsilon, false otherwise.
Name Type Default Description
left Matrix3 optional The first matrix.
right Matrix3 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.

static Cesium.Matrix3.fromArray(array, startingIndex, result)Matrix3

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]

const v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
const m = Cesium.Matrix3.fromArray(v);

// Create same Matrix3 with using an offset into an array
const v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
const m2 = Cesium.Matrix3.fromArray(v2, 2);

static Cesium.Matrix3.fromColumnMajorArray(values, result)Matrix3

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.

static Cesium.Matrix3.fromCrossProduct(vector, result)Matrix3

Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
Name Type Description
vector Cartesian3 the 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]
const m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));

static Cesium.Matrix3.fromHeadingPitchRoll(headingPitchRoll, result)Matrix3

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.

static Cesium.Matrix3.fromQuaternion(quaternion, result)Matrix3

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.

static Cesium.Matrix3.fromRotationX(angle, result)Matrix3

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.
const p = new Cesium.Cartesian3(5, 6, 7);
const m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());

static Cesium.Matrix3.fromRotationY(angle, result)Matrix3

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.
const p = new Cesium.Cartesian3(5, 6, 7);
const m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());

static Cesium.Matrix3.fromRotationZ(angle, result)Matrix3

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.
const p = new Cesium.Cartesian3(5, 6, 7);
const m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());

static Cesium.Matrix3.fromRowMajorArray(values, result)Matrix3

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.

static Cesium.Matrix3.fromScale(scale, result)Matrix3

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]
const m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));

static Cesium.Matrix3.fromUniformScale(scale, result)Matrix3

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]
const m = Cesium.Matrix3.fromUniformScale(2.0);

static Cesium.Matrix3.getColumn(matrix, index, result)Cartesian3

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:

static Cesium.Matrix3.getElementIndex(column, row)Number

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

static Cesium.Matrix3.getMaximumScale(matrix)Number

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.

static Cesium.Matrix3.getRotation(matrix, result)Matrix3

Extracts the rotation matrix assuming the matrix is an affine transformation.
Name Type Description
matrix Matrix3 The matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
See:

static Cesium.Matrix3.getRow(matrix, index, result)Cartesian3

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:

static Cesium.Matrix3.getScale(matrix, result)Cartesian3

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.
See:

static Cesium.Matrix3.inverse(matrix, result)Matrix3

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:

static Cesium.Matrix3.inverseTranspose(matrix, result)Matrix3

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

static Cesium.Matrix3.multiply(left, right, result)Matrix3

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.

static Cesium.Matrix3.multiplyByScalar(matrix, scalar, result)Matrix3

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.

static Cesium.Matrix3.multiplyByScale(matrix, scale, result)Matrix3

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:

static Cesium.Matrix3.multiplyByUniformScale(matrix, scale, result)Matrix3

Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.
Name Type Description
matrix Matrix3 The matrix on the left-hand side.
scale Number The 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.fromUniformScale(scale), m);
Cesium.Matrix3.multiplyByUniformScale(m, scale, m);
See:

static Cesium.Matrix3.multiplyByVector(matrix, cartesian, result)Cartesian3

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.

static Cesium.Matrix3.negate(matrix, result)Matrix3

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.

static Cesium.Matrix3.pack(value, array, startingIndex)Array.<Number>

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

static Cesium.Matrix3.packArray(array, result)Array.<Number>

Flattens an array of Matrix3s into an array of components. The components are stored in column-major order.
Name Type Description
array Array.<Matrix3> The array of matrices to pack.
result Array.<Number> optional The array onto which to store the result. If this is a typed array, it must have array.length * 9 components, else a DeveloperError will be thrown. If it is a regular array, it will be resized to have (array.length * 9) elements.
Returns:
The packed array.

static Cesium.Matrix3.setColumn(matrix, index, cartesian, result)Matrix3

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:

static Cesium.Matrix3.setRotation(matrix, rotation, result)Matrix3

Sets the rotation assuming the matrix is an affine transformation.
Name Type Description
matrix Matrix3 The matrix.
rotation Matrix3 The rotation matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
See:

static Cesium.Matrix3.setRow(matrix, index, cartesian, result)Matrix3

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:

static Cesium.Matrix3.setScale(matrix, scale, result)Matrix3

Computes a new matrix that replaces the scale with the provided scale. This assumes the matrix is an affine transformation.
Name Type Description
matrix Matrix3 The matrix to use.
scale Cartesian3 The scale that replaces the scale of the provided matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
See:

static Cesium.Matrix3.setUniformScale(matrix, scale, result)Matrix3

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 Matrix3 The matrix to use.
scale Number The uniform scale that replaces the scale of the provided matrix.
result Matrix3 The object onto which to store the result.
Returns:
The modified result parameter.
See:

static Cesium.Matrix3.subtract(left, right, result)Matrix3

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.

static Cesium.Matrix3.toArray(matrix, result)Array.<Number>

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.

static Cesium.Matrix3.transpose(matrix, result)Matrix3

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.

static Cesium.Matrix3.unpack(array, startingIndex, result)Matrix3

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.

static Cesium.Matrix3.unpackArray(array, result)Array.<Matrix3>

Unpacks an array of column-major matrix components into an array of Matrix3s.
Name Type Description
array Array.<Number> The array of components to unpack.
result Array.<Matrix3> optional The array onto which to store the result.
Returns:
The unpacked array.
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