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. |
Members
Gets the number of items in the collection.
The index into Matrix3 for column 0, row 0.
The index into Matrix3 for column 0, row 1.
The index into Matrix3 for column 0, row 2.
The index into Matrix3 for column 1, row 0.
The index into Matrix3 for column 1, row 1.
The index into Matrix3 for column 1, row 2.
The index into Matrix3 for column 2, row 0.
The index into Matrix3 for column 2, row 1.
The index into Matrix3 for column 2, row 2.
static constant Cesium.Matrix3.IDENTITY : Matrix3
An immutable Matrix3 instance initialized to the identity matrix.
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
clone(result) → Matrix3
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.
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.
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.
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)
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)
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.
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.
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:
-
DeveloperError : index must be 0, 1, or 2.
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:
-
DeveloperError : row must be 0, 1, or 2.
-
DeveloperError : column must be 0, 1, or 2.
Example:
const myMatrix = new Cesium.Matrix3();
const column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
const column1Row0 = myMatrix[column1Row0Index]
myMatrix[column1Row0Index] = 10.0;
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:
-
DeveloperError : index must be 0, 1, or 2.
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:
-
DeveloperError : matrix is not invertible.
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.
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
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:
-
DeveloperError : index must be 0, 1, or 2.
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:
-
DeveloperError : index must be 0, 1, or 2.
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.
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.