Class: Matrix3

Matrix3

new Matrix3(column0Row0opt, column1Row0opt, column2Row0opt, column0Row1opt, column1Row1opt, column2Row1opt, column0Row2opt, column1Row2opt, column2Row2opt)

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

Members

length :Number

Gets the number of items in the collection.
Type:
  • Number
Source:

(static, constant) COLUMN0ROW0 :Number

The index into Matrix3 for column 0, row 0.
Type:
  • Number
Source:

(static, constant) COLUMN0ROW1 :Number

The index into Matrix3 for column 0, row 1.
Type:
  • Number
Source:

(static, constant) COLUMN0ROW2 :Number

The index into Matrix3 for column 0, row 2.
Type:
  • Number
Source:

(static, constant) COLUMN1ROW0 :Number

The index into Matrix3 for column 1, row 0.
Type:
  • Number
Source:

(static, constant) COLUMN1ROW1 :Number

The index into Matrix3 for column 1, row 1.
Type:
  • Number
Source:

(static, constant) COLUMN1ROW2 :Number

The index into Matrix3 for column 1, row 2.
Type:
  • Number
Source:

(static, constant) COLUMN2ROW0 :Number

The index into Matrix3 for column 2, row 0.
Type:
  • Number
Source:

(static, constant) COLUMN2ROW1 :Number

The index into Matrix3 for column 2, row 1.
Type:
  • Number
Source:

(static, constant) COLUMN2ROW2 :Number

The index into Matrix3 for column 2, row 2.
Type:
  • Number
Source:

(static, constant) IDENTITY :Matrix3

An immutable Matrix3 instance initialized to the identity matrix.
Type:
Source:

(static) packedLength :Number

The number of elements used to pack the object into an array.
Type:
  • Number
Source:

(static, constant) ZERO :Matrix3

An immutable Matrix3 instance initialized to the zero matrix.
Type:
Source:

Methods

clone(resultopt) → {Matrix3}

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

equals(rightopt) → {Boolean}

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

equalsEpsilon(rightopt, epsilon) → {Boolean}

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

toString() → {String}

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

(static) abs(matrix, result) → {Matrix3}

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

(static) add(left, right, result) → {Matrix3}

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

(static) clone(matrix, resultopt) → {Matrix3}

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

(static) computeEigenDecomposition(matrix, resultopt) → {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.

Parameters:
Name Type Attributes 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.
Source:
Returns:
An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
Type
Object
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)

(static) determinant(matrix) → {Number}

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

(static) equals(leftopt, rightopt) → {Boolean}

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

(static) equalsEpsilon(leftopt, rightopt, epsilon) → {Boolean}

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

(static) fromArray(array, startingIndexopt, resultopt) → {Matrix3}

Creates a Matrix3 from 9 consecutive elements in an array.
Parameters:
Name Type Attributes Default Description
array Array.<Number> 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.
Source:
Returns:
The modified result parameter or a new Matrix3 instance if one was not provided.
Type
Matrix3
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(values, resultopt) → {Matrix3}

Creates a Matrix3 instance from a column-major order array.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3

(static) fromCrossProduct(the, resultopt) → {Matrix3}

Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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));

(static) fromHeadingPitchRoll(headingPitchRoll, resultopt) → {Matrix3}

Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
Parameters:
Name Type Attributes 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.
Source:
Returns:
The 3x3 rotation matrix from this headingPitchRoll.
Type
Matrix3

(static) fromQuaternion(quaternion, resultopt) → {Matrix3}

Computes a 3x3 rotation matrix from the provided quaternion.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The 3x3 rotation matrix from this quaternion.
Type
Matrix3

(static) fromRotationX(angle, resultopt) → {Matrix3}

Creates a rotation matrix around the x-axis.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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());

(static) fromRotationY(angle, resultopt) → {Matrix3}

Creates a rotation matrix around the y-axis.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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());

(static) fromRotationZ(angle, resultopt) → {Matrix3}

Creates a rotation matrix around the z-axis.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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());

(static) fromRowMajorArray(values, resultopt) → {Matrix3}

Creates a Matrix3 instance from a row-major order array. The resulting matrix will be in column-major order.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3

(static) fromScale(scale, resultopt) → {Matrix3}

Computes a Matrix3 instance representing a non-uniform scale.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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(scale, resultopt) → {Matrix3}

Computes a Matrix3 instance representing a uniform scale.
Parameters:
Name Type Attributes 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.
Source:
Returns:
The modified result parameter, or a new Matrix3 instance if one was not provided.
Type
Matrix3
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(matrix, index, result) → {Cartesian3}

Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
Parameters:
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.
Source:
Throws:
index must be 0, 1, or 2.
Type
DeveloperError
Returns:
The modified result parameter.
Type
Cartesian3

(static) getElementIndex(row, column) → {Number}

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

(static) 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.
Parameters:
Name Type Description
matrix Matrix3 The matrix.
Source:
Returns:
The maximum scale.
Type
Number

(static) getRow(matrix, index, result) → {Cartesian3}

Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
Parameters:
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.
Source:
Throws:
index must be 0, 1, or 2.
Type
DeveloperError
Returns:
The modified result parameter.
Type
Cartesian3

(static) getScale(matrix, result) → {Cartesian3}

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

(static) inverse(matrix, result) → {Matrix3}

Computes the inverse of the provided matrix.
Parameters:
Name Type Description
matrix Matrix3 The matrix to invert.
result Matrix3 The object onto which to store the result.
Source:
Throws:
matrix is not invertible.
Type
DeveloperError
Returns:
The modified result parameter.
Type
Matrix3

(static) multiply(left, right, result) → {Matrix3}

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

(static) multiplyByScalar(matrix, scalar, result) → {Matrix3}

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

(static) multiplyByScale(matrix, scale, result) → {Matrix3}

Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
Parameters:
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.
Source:
See:
Returns:
The modified result parameter.
Type
Matrix3
Example
// Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
Cesium.Matrix3.multiplyByScale(m, scale, m);

(static) multiplyByVector(matrix, cartesian, result) → {Cartesian3}

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

(static) negate(matrix, result) → {Matrix3}

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

(static) pack(value, array, startingIndexopt) → {Array.<Number>}

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

(static) setColumn(matrix, index, cartesian, result) → {Matrix3}

Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
Parameters:
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.
Source:
Throws:
index must be 0, 1, or 2.
Type
DeveloperError
Returns:
The modified result parameter.
Type
Matrix3

(static) setRow(matrix, index, cartesian, result) → {Matrix3}

Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
Parameters:
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.
Source:
Throws:
index must be 0, 1, or 2.
Type
DeveloperError
Returns:
The modified result parameter.
Type
Matrix3

(static) subtract(left, right, result) → {Matrix3}

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

(static) toArray(matrix, resultopt) → {Array.<Number>}

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

(static) transpose(matrix, result) → {Matrix3}

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

(static) unpack(array, startingIndexopt, resultopt) → {Matrix3}

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