@cesium/engine
Version:
CesiumJS is a JavaScript library for creating 3D globes and 2D maps in a web browser without a plugin.
1,537 lines (1,388 loc) • 60 kB
JavaScript
// @ts-check
import Cartesian3 from "./Cartesian3.js";
import Check from "./Check.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import CesiumMath from "./Math.js";
/** @import Quaternion from "./Quaternion.js"; */
/** @import HeadingPitchRoll from "./HeadingPitchRoll.js"; */
/**
* @typedef {object} EigenDecompositionResult
* @property {Matrix3} [unitary]
* @property {Matrix3} [diagonal]
*/
/**
* A 3x3 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
*
* @implements {ArrayLike<number>}
*
* @see Matrix3.fromArray
* @see Matrix3.fromColumnMajorArray
* @see Matrix3.fromRowMajorArray
* @see Matrix3.fromQuaternion
* @see Matrix3.fromHeadingPitchRoll
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.fromCrossProduct
* @see Matrix3.fromRotationX
* @see Matrix3.fromRotationY
* @see Matrix3.fromRotationZ
* @see Matrix2
* @see Matrix4
*/
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
class Matrix3 {
/**
* @param {number} [column0Row0=0.0] The value for column 0, row 0.
* @param {number} [column1Row0=0.0] The value for column 1, row 0.
* @param {number} [column2Row0=0.0] The value for column 2, row 0.
* @param {number} [column0Row1=0.0] The value for column 0, row 1.
* @param {number} [column1Row1=0.0] The value for column 1, row 1.
* @param {number} [column2Row1=0.0] The value for column 2, row 1.
* @param {number} [column0Row2=0.0] The value for column 0, row 2.
* @param {number} [column1Row2=0.0] The value for column 1, row 2.
* @param {number} [column2Row2=0.0] The value for column 2, row 2.
*/
constructor(
column0Row0,
column1Row0,
column2Row0,
column0Row1,
column1Row1,
column2Row1,
column0Row2,
column1Row2,
column2Row2,
) {
this[0] = column0Row0 ?? 0.0;
this[1] = column0Row1 ?? 0.0;
this[2] = column0Row2 ?? 0.0;
this[3] = column1Row0 ?? 0.0;
this[4] = column1Row1 ?? 0.0;
this[5] = column1Row2 ?? 0.0;
this[6] = column2Row0 ?? 0.0;
this[7] = column2Row1 ?? 0.0;
this[8] = column2Row2 ?? 0.0;
}
/**
* Stores the provided instance into the provided array.
*
* @param {Matrix3} value The value to pack.
* @param {number[]} array The array to pack into.
* @param {number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {number[]} The array that was packed into
*/
static pack(value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("value", value);
Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = startingIndex ?? 0;
array[startingIndex++] = value[0];
array[startingIndex++] = value[1];
array[startingIndex++] = value[2];
array[startingIndex++] = value[3];
array[startingIndex++] = value[4];
array[startingIndex++] = value[5];
array[startingIndex++] = value[6];
array[startingIndex++] = value[7];
array[startingIndex++] = value[8];
return array;
}
/**
* Retrieves an instance from a packed array.
*
* @param {number[]} array The packed array.
* @param {number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Matrix3} [result] The object into which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
static unpack(array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = startingIndex ?? 0;
if (!defined(result)) {
result = new Matrix3();
}
result[0] = array[startingIndex++];
result[1] = array[startingIndex++];
result[2] = array[startingIndex++];
result[3] = array[startingIndex++];
result[4] = array[startingIndex++];
result[5] = array[startingIndex++];
result[6] = array[startingIndex++];
result[7] = array[startingIndex++];
result[8] = array[startingIndex++];
return result;
}
/**
* Flattens an array of Matrix3s into an array of components. The components
* are stored in column-major order.
*
* @param {Matrix3[]} array The array of matrices to pack.
* @param {number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 9 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 9) elements.
* @returns {number[]} The packed array.
*/
static packArray(array, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
//>>includeEnd('debug');
const length = array.length;
const resultLength = length * 9;
if (!defined(result)) {
result = new Array(resultLength);
// @ts-expect-error TODO(tsd-jsdoc): Requires conditional TypedArray types.
} else if (!Array.isArray(result) && result.length !== resultLength) {
//>>includeStart('debug', pragmas.debug);
throw new DeveloperError(
"If result is a typed array, it must have exactly array.length * 9 elements",
);
//>>includeEnd('debug');
} else if (result.length !== resultLength) {
/** @type {number[]} */ (result).length = resultLength;
}
for (let i = 0; i < length; ++i) {
Matrix3.pack(array[i], result, i * 9);
}
return result;
}
/**
* Unpacks an array of column-major matrix components into an array of Matrix3s.
*
* @param {number[]} array The array of components to unpack.
* @param {Matrix3[]} [result] The array onto which to store the result.
* @returns {Matrix3[]} The unpacked array.
*/
static unpackArray(array, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 9);
if (array.length % 9 !== 0) {
throw new DeveloperError("array length must be a multiple of 9.");
}
//>>includeEnd('debug');
const length = array.length;
if (!defined(result)) {
result = new Array(length / 9);
} else {
result.length = length / 9;
}
for (let i = 0; i < length; i += 9) {
const index = i / 9;
result[index] = Matrix3.unpack(array, i, result[index]);
}
return result;
}
/**
* Duplicates a Matrix3 instance.
*
* @param {Matrix3} matrix The matrix to duplicate.
* @param {Matrix3} [result] 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 clone(matrix, result) {
if (!defined(matrix)) {
return undefined;
}
if (!defined(result)) {
return new Matrix3(
matrix[0],
matrix[3],
matrix[6],
matrix[1],
matrix[4],
matrix[7],
matrix[2],
matrix[5],
matrix[8],
);
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
return result;
}
/**
* Creates a Matrix3 instance from a column-major order array.
*
* @param {number[]} values The column-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
static fromColumnMajorArray(values, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("values", values);
//>>includeEnd('debug');
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
return Matrix3.clone(values, result);
}
/**
* Creates a Matrix3 instance from a row-major order array.
* The resulting matrix will be in column-major order.
*
* @param {number[]} values The row-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
static fromRowMajorArray(values, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("values", values);
//>>includeEnd('debug');
if (!defined(result)) {
return new Matrix3(
values[0],
values[1],
values[2],
values[3],
values[4],
values[5],
values[6],
values[7],
values[8],
);
}
result[0] = values[0];
result[1] = values[3];
result[2] = values[6];
result[3] = values[1];
result[4] = values[4];
result[5] = values[7];
result[6] = values[2];
result[7] = values[5];
result[8] = values[8];
return result;
}
/**
* Computes a 3x3 rotation matrix from the provided quaternion.
*
* @param {Quaternion} quaternion the quaternion to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
*/
static fromQuaternion(quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
//>>includeEnd('debug');
const x2 = quaternion.x * quaternion.x;
const xy = quaternion.x * quaternion.y;
const xz = quaternion.x * quaternion.z;
const xw = quaternion.x * quaternion.w;
const y2 = quaternion.y * quaternion.y;
const yz = quaternion.y * quaternion.z;
const yw = quaternion.y * quaternion.w;
const z2 = quaternion.z * quaternion.z;
const zw = quaternion.z * quaternion.w;
const w2 = quaternion.w * quaternion.w;
const m00 = x2 - y2 - z2 + w2;
const m01 = 2.0 * (xy - zw);
const m02 = 2.0 * (xz + yw);
const m10 = 2.0 * (xy + zw);
const m11 = -x2 + y2 - z2 + w2;
const m12 = 2.0 * (yz - xw);
const m20 = 2.0 * (xz - yw);
const m21 = 2.0 * (yz + xw);
const m22 = -x2 - y2 + z2 + w2;
if (!defined(result)) {
return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
}
/**
* Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
*
* @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
*/
static fromHeadingPitchRoll(headingPitchRoll, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("headingPitchRoll", headingPitchRoll);
//>>includeEnd('debug');
const cosTheta = Math.cos(-headingPitchRoll.pitch);
const cosPsi = Math.cos(-headingPitchRoll.heading);
const cosPhi = Math.cos(headingPitchRoll.roll);
const sinTheta = Math.sin(-headingPitchRoll.pitch);
const sinPsi = Math.sin(-headingPitchRoll.heading);
const sinPhi = Math.sin(headingPitchRoll.roll);
const m00 = cosTheta * cosPsi;
const m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
const m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
const m10 = cosTheta * sinPsi;
const m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
const m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
const m20 = -sinTheta;
const m21 = sinPhi * cosTheta;
const m22 = cosPhi * cosTheta;
if (!defined(result)) {
return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
}
/**
* Computes a Matrix3 instance representing a non-uniform scale.
*
* @param {Cartesian3} scale The x, y, and z scale factors.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromScale(scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("scale", scale);
//>>includeEnd('debug');
if (!defined(result)) {
return new Matrix3(
scale.x,
0.0,
0.0,
0.0,
scale.y,
0.0,
0.0,
0.0,
scale.z,
);
}
result[0] = scale.x;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = scale.y;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = scale.z;
return result;
}
/**
* Computes a Matrix3 instance representing a uniform scale.
*
* @param {number} scale The uniform scale factor.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromUniformScale(scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("scale", scale);
//>>includeEnd('debug');
if (!defined(result)) {
return new Matrix3(scale, 0.0, 0.0, 0.0, scale, 0.0, 0.0, 0.0, scale);
}
result[0] = scale;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = scale;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = scale;
return result;
}
/**
* Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
*
* @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromCrossProduct(vector, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("vector", vector);
//>>includeEnd('debug');
if (!defined(result)) {
return new Matrix3(
0.0,
-vector.z,
vector.y,
vector.z,
0.0,
-vector.x,
-vector.y,
vector.x,
0.0,
);
}
result[0] = 0.0;
result[1] = vector.z;
result[2] = -vector.y;
result[3] = -vector.z;
result[4] = 0.0;
result[5] = vector.x;
result[6] = vector.y;
result[7] = -vector.x;
result[8] = 0.0;
return result;
}
/**
* Creates a rotation matrix around the x-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromRotationX(angle, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("angle", angle);
//>>includeEnd('debug');
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
1.0,
0.0,
0.0,
0.0,
cosAngle,
-sinAngle,
0.0,
sinAngle,
cosAngle,
);
}
result[0] = 1.0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = cosAngle;
result[5] = sinAngle;
result[6] = 0.0;
result[7] = -sinAngle;
result[8] = cosAngle;
return result;
}
/**
* Creates a rotation matrix around the y-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromRotationY(angle, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("angle", angle);
//>>includeEnd('debug');
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
cosAngle,
0.0,
sinAngle,
0.0,
1.0,
0.0,
-sinAngle,
0.0,
cosAngle,
);
}
result[0] = cosAngle;
result[1] = 0.0;
result[2] = -sinAngle;
result[3] = 0.0;
result[4] = 1.0;
result[5] = 0.0;
result[6] = sinAngle;
result[7] = 0.0;
result[8] = cosAngle;
return result;
}
/**
* Creates a rotation matrix around the z-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} 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 fromRotationZ(angle, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("angle", angle);
//>>includeEnd('debug');
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined(result)) {
return new Matrix3(
cosAngle,
-sinAngle,
0.0,
sinAngle,
cosAngle,
0.0,
0.0,
0.0,
1.0,
);
}
result[0] = cosAngle;
result[1] = sinAngle;
result[2] = 0.0;
result[3] = -sinAngle;
result[4] = cosAngle;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 1.0;
return result;
}
/**
* Creates an Array from the provided Matrix3 instance.
* The array will be in column-major order.
*
* @param {Matrix3} matrix The matrix to use..
* @param {number[]} [result] The Array onto which to store the result.
* @returns {number[]} The modified Array parameter or a new Array instance if one was not provided.
*/
static toArray(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
//>>includeEnd('debug');
if (!defined(result)) {
return [
matrix[0],
matrix[1],
matrix[2],
matrix[3],
matrix[4],
matrix[5],
matrix[6],
matrix[7],
matrix[8],
];
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
return result;
}
/**
* Computes the array index of the element at the provided row and column.
*
* @param {number} column The zero-based index of the column.
* @param {number} row The zero-based index of the row.
* @returns {number} The index of the element at the provided row and column.
*
* @exception {DeveloperError} row must be 0, 1, or 2.
* @exception {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;
*/
static getElementIndex(column, row) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number.greaterThanOrEquals("row", row, 0);
Check.typeOf.number.lessThanOrEquals("row", row, 2);
Check.typeOf.number.greaterThanOrEquals("column", column, 0);
Check.typeOf.number.lessThanOrEquals("column", column, 2);
//>>includeEnd('debug');
return column * 3 + row;
}
/**
* Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the column to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static getColumn(matrix, index, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
Check.typeOf.number.lessThanOrEquals("index", index, 2);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const startIndex = index * 3;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const x = matrix[startIndex];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const y = matrix[startIndex + 1];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const z = matrix[startIndex + 2];
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the column to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static setColumn(matrix, index, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
Check.typeOf.number.lessThanOrEquals("index", index, 2);
Check.typeOf.object("cartesian", cartesian);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result = Matrix3.clone(matrix, result);
const startIndex = index * 3;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex] = cartesian.x;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex + 1] = cartesian.y;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex + 2] = cartesian.z;
return result;
}
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the row to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static getRow(matrix, index, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
Check.typeOf.number.lessThanOrEquals("index", index, 2);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const x = matrix[index];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const y = matrix[index + 3];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const z = matrix[index + 6];
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the row to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static setRow(matrix, index, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
Check.typeOf.number.lessThanOrEquals("index", index, 2);
Check.typeOf.object("cartesian", cartesian);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result = Matrix3.clone(matrix, result);
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index] = cartesian.x;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index + 3] = cartesian.y;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index + 6] = cartesian.z;
return result;
}
/**
* Computes a new matrix that replaces the scale with the provided scale.
* This assumes the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.getScale
*/
static setScale(matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("scale", scale);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const existingScale = Matrix3.getScale(matrix, scaleScratch1);
const scaleRatioX = scale.x / existingScale.x;
const scaleRatioY = scale.y / existingScale.y;
const scaleRatioZ = scale.z / existingScale.z;
result[0] = matrix[0] * scaleRatioX;
result[1] = matrix[1] * scaleRatioX;
result[2] = matrix[2] * scaleRatioX;
result[3] = matrix[3] * scaleRatioY;
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioZ;
result[7] = matrix[7] * scaleRatioZ;
result[8] = matrix[8] * scaleRatioZ;
return result;
}
/**
* Computes a new matrix that replaces the scale with the provided uniform scale.
* This assumes the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} scale The uniform scale that replaces the scale of the provided matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.getScale
*/
static setUniformScale(matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number("scale", scale);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const existingScale = Matrix3.getScale(matrix, scaleScratch2);
const scaleRatioX = scale / existingScale.x;
const scaleRatioY = scale / existingScale.y;
const scaleRatioZ = scale / existingScale.z;
result[0] = matrix[0] * scaleRatioX;
result[1] = matrix[1] * scaleRatioX;
result[2] = matrix[2] * scaleRatioX;
result[3] = matrix[3] * scaleRatioY;
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioZ;
result[7] = matrix[7] * scaleRatioZ;
result[8] = matrix[8] * scaleRatioZ;
return result;
}
/**
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
*/
static getScale(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Cartesian3.magnitude(
Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn),
);
result.y = Cartesian3.magnitude(
Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn),
);
result.z = Cartesian3.magnitude(
Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn),
);
return result;
}
/**
* Computes the maximum scale assuming the matrix is an affine transformation.
* The maximum scale is the maximum length of the column vectors.
*
* @param {Matrix3} matrix The matrix.
* @returns {number} The maximum scale.
*/
static getMaximumScale(matrix) {
Matrix3.getScale(matrix, scaleScratch3);
return Cartesian3.maximumComponent(scaleScratch3);
}
/**
* Sets the rotation assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Matrix3} rotation The rotation matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.getRotation
*/
static setRotation(matrix, rotation, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const scale = Matrix3.getScale(matrix, scaleScratch4);
result[0] = rotation[0] * scale.x;
result[1] = rotation[1] * scale.x;
result[2] = rotation[2] * scale.x;
result[3] = rotation[3] * scale.y;
result[4] = rotation[4] * scale.y;
result[5] = rotation[5] * scale.y;
result[6] = rotation[6] * scale.z;
result[7] = rotation[7] * scale.z;
result[8] = rotation[8] * scale.z;
return result;
}
/**
* Extracts the rotation matrix assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setRotation
*/
static getRotation(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const scale = Matrix3.getScale(matrix, scaleScratch5);
result[0] = matrix[0] / scale.x;
result[1] = matrix[1] / scale.x;
result[2] = matrix[2] / scale.x;
result[3] = matrix[3] / scale.y;
result[4] = matrix[4] / scale.y;
result[5] = matrix[5] / scale.y;
result[6] = matrix[6] / scale.z;
result[7] = matrix[7] / scale.z;
result[8] = matrix[8] / scale.z;
return result;
}
/**
* Computes the product of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static multiply(left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const column0Row0 =
left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
const column0Row1 =
left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
const column0Row2 =
left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
const column1Row0 =
left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
const column1Row1 =
left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
const column1Row2 =
left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
const column2Row0 =
left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
const column2Row1 =
left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
const column2Row2 =
left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
}
/**
* Computes the sum of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static add(left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = left[0] + right[0];
result[1] = left[1] + right[1];
result[2] = left[2] + right[2];
result[3] = left[3] + right[3];
result[4] = left[4] + right[4];
result[5] = left[5] + right[5];
result[6] = left[6] + right[6];
result[7] = left[7] + right[7];
result[8] = left[8] + right[8];
return result;
}
/**
* Computes the difference of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static subtract(left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = left[0] - right[0];
result[1] = left[1] - right[1];
result[2] = left[2] - right[2];
result[3] = left[3] - right[3];
result[4] = left[4] - right[4];
result[5] = left[5] - right[5];
result[6] = left[6] - right[6];
result[7] = left[7] - right[7];
result[8] = left[8] - right[8];
return result;
}
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} cartesian The column.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
static multiplyByVector(matrix, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("cartesian", cartesian);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
const y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
const z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix3} matrix The matrix.
* @param {number} scalar The number to multiply by.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static multiplyByScalar(matrix, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number("scalar", scalar);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
result[4] = matrix[4] * scalar;
result[5] = matrix[5] * scalar;
result[6] = matrix[6] * scalar;
result[7] = matrix[7] * scalar;
result[8] = matrix[8] * scalar;
return result;
}
/**
* Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
*
* @param {Matrix3} matrix The matrix on the left-hand side.
* @param {Cartesian3} scale The non-uniform scale on the right-hand side.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
* Cesium.Matrix3.multiplyByScale(m, scale, m);
*
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
* @see Matrix3.getScale
*/
static multiplyByScale(matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("scale", scale);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0] * scale.x;
result[1] = matrix[1] * scale.x;
result[2] = matrix[2] * scale.x;
result[3] = matrix[3] * scale.y;
result[4] = matrix[4] * scale.y;
result[5] = matrix[5] * scale.y;
result[6] = matrix[6] * scale.z;
result[7] = matrix[7] * scale.z;
result[8] = matrix[8] * scale.z;
return result;
}
/**
* Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.
*
* @param {Matrix3} matrix The matrix on the left-hand side.
* @param {number} scale The uniform scale on the right-hand side.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromUniformScale(scale), m);
* Cesium.Matrix3.multiplyByUniformScale(m, scale, m);
*
* @see Matrix3.multiplyByScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
* @see Matrix3.getScale
*/
static multiplyByUniformScale(matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.number("scale", scale);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0] * scale;
result[1] = matrix[1] * scale;
result[2] = matrix[2] * scale;
result[3] = matrix[3] * scale;
result[4] = matrix[4] * scale;
result[5] = matrix[5] * scale;
result[6] = matrix[6] * scale;
result[7] = matrix[7] * scale;
result[8] = matrix[8] * scale;
return result;
}
/**
* Creates a negated copy of the provided matrix.
*
* @param {Matrix3} matrix The matrix to negate.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static negate(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
result[4] = -matrix[4];
result[5] = -matrix[5];
result[6] = -matrix[6];
result[7] = -matrix[7];
result[8] = -matrix[8];
return result;
}
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix3} matrix The matrix to transpose.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static transpose(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const column0Row0 = matrix[0];
const column0Row1 = matrix[3];
const column0Row2 = matrix[6];
const column1Row0 = matrix[1];
const column1Row1 = matrix[4];
const column1Row2 = matrix[7];
const column2Row0 = matrix[2];
const column2Row1 = matrix[5];
const column2Row2 = matrix[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
}
/**
* Computes the eigenvectors and eigenvalues of a symmetric matrix.
* <p>
* Returns a diagonal matrix and unitary matrix such that:
* <code>matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)</code>
* </p>
* <p>
* The values along the diagonal of the diagonal matrix are the eigenvalues. The columns
* of the unitary matrix are the corresponding eigenvectors.
* </p>
*
* @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
* @param {EigenDecompositionResult} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
* @returns {EigenDecompositionResult} 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 computeEigenDecomposition(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
//>>includeEnd('debug');
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
// section 8.4.3 The Classical Jacobi Algorithm
const tolerance = CesiumMath.EPSILON20;
const maxSweeps = 10;
let count = 0;
let sweep = 0;
if (!defined(result)) {
result = {};
}
const unitaryMatrix = (result.unitary = Matrix3.clone(
Matrix3.IDENTITY,
result.unitary,
));
const diagMatrix = (result.diagonal = Matrix3.clone(
matrix,
result.diagonal,
));
const epsilon = tolerance * computeFrobeniusNorm(diagMatrix);
while (
sweep < maxSweeps &&
offDiagonalFrobeniusNorm(diagMatrix) > epsilon
) {
shurDecomposition(diagMatrix, jMatrix);
Matrix3.transpose(jMatrix, jMatrixTranspose);
Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);
Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);
Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);
if (++count > 2) {
++sweep;
count = 0;
}
}
return result;
}
/**
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
*
* @param {Matrix3} matrix The matrix with signed elements.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static abs(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = Math.abs(matrix[0]);
result[1] = Math.abs(matrix[1]);
result[2] = Math.abs(matrix[2]);
result[3] = Math.abs(matrix[3]);
result[4] = Math.abs(matrix[4]);
result[5] = Math.abs(matrix[5]);
result[6] = Math.abs(matrix[6]);
result[7] = Math.abs(matrix[7]);
result[8] = Math.abs(matrix[8]);
return result;
}
/**
* Computes the determinant of the provided matrix.
*
* @param {Matrix3} matrix The matrix to use.
* @returns {number} The value of the determinant of the matrix.
*/
static determinant(matrix) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
//>>includeEnd('debug');
const m11 = matrix[0];
const m21 = matrix[3];
const m31 = matrix[6];
const m12 = matrix[1];
const m22 = matrix[4];
const m32 = matrix[7];
const m13 = matrix[2];
const m23 = matrix[5];
const m33 = matrix[8];
return (
m11 * (m22 * m33 - m23 * m32) +
m12 * (m23 * m31 - m21 * m33) +
m13 * (m21 * m32 - m22 * m31)
);
}
/**
* Computes the inverse of the provided matrix.
*
* @param {Matrix3} matrix The matrix to invert.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} matrix is not invertible.
*/
static inverse(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const m11 = matrix[0];
const m21 = matrix[1];
const m31 = matrix[2];
const m12 = matrix[3];
const m22 = matrix[4];
const m32 = matrix[5];
const m13 = matrix[6];
const m23 = matrix[7];
const m33 = matrix[8];
const determinant = Matrix3.determinant(matrix);
//>>includeStart('debug', pragmas.debug);
if (Math.abs(determinant) <= CesiumMath.EPSILON15) {
throw new DeveloperError("matrix is not invertible");
}
//>>includeEnd('debug');
result[0] = m22 * m33 - m23 * m32;
result[1] = m23 * m31 - m21 * m33;
result[2] = m21 * m32 - m22 * m31;
result[3] = m13 * m32 - m12 * m33;
result[4] = m11 * m33 - m13 * m31;
result[5] = m12 * m31 - m11 * m32;
result[6] = m12 * m23 - m13 * m22;
result[7] = m13 * m21 - m11 * m23;
result[8] = m11 * m22 - m12 * m21;
const scale = 1.0 / determinant;
return Matrix3.multiplyByScalar(result, scale, result);
}
/**
* Computes the inverse transpose of a matrix.
*
* @param {Matrix3} matrix The matrix to transpose and invert.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static inverseTranspose(matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
return Matrix3.inverse(
Matrix3.transpose(matrix, scratchTransposeMatrix),
result,
);
}
/**
* Compares the provided matrices componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @returns {boolean} <code>true</code