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1630 lines
47 KiB
JavaScript
1630 lines
47 KiB
JavaScript
import Cartesian3 from "./Cartesian3.js";
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import Check from "./Check.js";
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import defaultValue from "./defaultValue.js";
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import defined from "./defined.js";
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import DeveloperError from "./DeveloperError.js";
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import CesiumMath from "./Math.js";
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/**
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* A 3x3 matrix, indexable as a column-major order array.
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* Constructor parameters are in row-major order for code readability.
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* @alias Matrix3
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* @constructor
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* @implements {ArrayLike<number>}
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*
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* @param {Number} [column0Row0=0.0] The value for column 0, row 0.
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* @param {Number} [column1Row0=0.0] The value for column 1, row 0.
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* @param {Number} [column2Row0=0.0] The value for column 2, row 0.
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* @param {Number} [column0Row1=0.0] The value for column 0, row 1.
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* @param {Number} [column1Row1=0.0] The value for column 1, row 1.
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* @param {Number} [column2Row1=0.0] The value for column 2, row 1.
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* @param {Number} [column0Row2=0.0] The value for column 0, row 2.
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* @param {Number} [column1Row2=0.0] The value for column 1, row 2.
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* @param {Number} [column2Row2=0.0] The value for column 2, row 2.
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*
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* @see Matrix3.fromColumnMajorArray
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* @see Matrix3.fromRowMajorArray
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* @see Matrix3.fromQuaternion
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* @see Matrix3.fromScale
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* @see Matrix3.fromUniformScale
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* @see Matrix2
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* @see Matrix4
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*/
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function Matrix3(
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column0Row0,
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column1Row0,
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column2Row0,
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column0Row1,
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column1Row1,
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column2Row1,
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column0Row2,
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column1Row2,
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column2Row2
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) {
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this[0] = defaultValue(column0Row0, 0.0);
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this[1] = defaultValue(column0Row1, 0.0);
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this[2] = defaultValue(column0Row2, 0.0);
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this[3] = defaultValue(column1Row0, 0.0);
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this[4] = defaultValue(column1Row1, 0.0);
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this[5] = defaultValue(column1Row2, 0.0);
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this[6] = defaultValue(column2Row0, 0.0);
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this[7] = defaultValue(column2Row1, 0.0);
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this[8] = defaultValue(column2Row2, 0.0);
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}
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/**
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* The number of elements used to pack the object into an array.
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* @type {Number}
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*/
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Matrix3.packedLength = 9;
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/**
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* Stores the provided instance into the provided array.
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*
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* @param {Matrix3} value The value to pack.
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* @param {Number[]} array The array to pack into.
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* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
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*
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* @returns {Number[]} The array that was packed into
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*/
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Matrix3.pack = function (value, array, startingIndex) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("value", value);
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Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue(startingIndex, 0);
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array[startingIndex++] = value[0];
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array[startingIndex++] = value[1];
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array[startingIndex++] = value[2];
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array[startingIndex++] = value[3];
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array[startingIndex++] = value[4];
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array[startingIndex++] = value[5];
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array[startingIndex++] = value[6];
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array[startingIndex++] = value[7];
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array[startingIndex++] = value[8];
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return array;
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};
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/**
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* Retrieves an instance from a packed array.
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*
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* @param {Number[]} array The packed array.
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* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
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* @param {Matrix3} [result] The object into which to store the result.
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* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
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*/
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Matrix3.unpack = function (array, startingIndex, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue(startingIndex, 0);
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if (!defined(result)) {
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result = new Matrix3();
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}
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result[0] = array[startingIndex++];
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result[1] = array[startingIndex++];
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result[2] = array[startingIndex++];
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result[3] = array[startingIndex++];
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result[4] = array[startingIndex++];
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result[5] = array[startingIndex++];
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result[6] = array[startingIndex++];
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result[7] = array[startingIndex++];
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result[8] = array[startingIndex++];
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return result;
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};
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/**
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* Duplicates a Matrix3 instance.
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*
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* @param {Matrix3} matrix The matrix to duplicate.
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* @param {Matrix3} [result] The object onto which to store the result.
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* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
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*/
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Matrix3.clone = function (matrix, result) {
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if (!defined(matrix)) {
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return undefined;
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}
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if (!defined(result)) {
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return new Matrix3(
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matrix[0],
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matrix[3],
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matrix[6],
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matrix[1],
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matrix[4],
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matrix[7],
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matrix[2],
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matrix[5],
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matrix[8]
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);
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}
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result[0] = matrix[0];
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result[1] = matrix[1];
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result[2] = matrix[2];
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result[3] = matrix[3];
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result[4] = matrix[4];
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result[5] = matrix[5];
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result[6] = matrix[6];
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result[7] = matrix[7];
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result[8] = matrix[8];
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return result;
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};
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/**
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* Creates a Matrix3 from 9 consecutive elements in an array.
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*
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* @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
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* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
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* @param {Matrix3} [result] The object onto which to store the result.
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* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
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*
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* @example
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* // Create the Matrix3:
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* // [1.0, 2.0, 3.0]
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* // [1.0, 2.0, 3.0]
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* // [1.0, 2.0, 3.0]
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*
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* var v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
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* var m = Cesium.Matrix3.fromArray(v);
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*
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* // Create same Matrix3 with using an offset into an array
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* var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
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* var m2 = Cesium.Matrix3.fromArray(v2, 2);
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*/
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Matrix3.fromArray = function (array, startingIndex, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.defined("array", array);
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//>>includeEnd('debug');
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startingIndex = defaultValue(startingIndex, 0);
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if (!defined(result)) {
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result = new Matrix3();
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}
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result[0] = array[startingIndex];
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result[1] = array[startingIndex + 1];
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result[2] = array[startingIndex + 2];
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result[3] = array[startingIndex + 3];
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result[4] = array[startingIndex + 4];
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result[5] = array[startingIndex + 5];
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result[6] = array[startingIndex + 6];
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result[7] = array[startingIndex + 7];
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result[8] = array[startingIndex + 8];
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return result;
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};
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/**
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* Creates a Matrix3 instance from a column-major order array.
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*
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* @param {Number[]} values The column-major order array.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
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*/
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Matrix3.fromColumnMajorArray = function (values, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.defined("values", values);
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//>>includeEnd('debug');
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return Matrix3.clone(values, result);
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};
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/**
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* Creates a Matrix3 instance from a row-major order array.
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* The resulting matrix will be in column-major order.
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*
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* @param {Number[]} values The row-major order array.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
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*/
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Matrix3.fromRowMajorArray = function (values, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.defined("values", values);
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//>>includeEnd('debug');
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if (!defined(result)) {
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return new Matrix3(
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values[0],
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values[1],
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values[2],
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values[3],
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values[4],
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values[5],
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values[6],
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values[7],
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values[8]
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);
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}
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result[0] = values[0];
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result[1] = values[3];
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result[2] = values[6];
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result[3] = values[1];
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result[4] = values[4];
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result[5] = values[7];
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result[6] = values[2];
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result[7] = values[5];
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result[8] = values[8];
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return result;
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};
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/**
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* Computes a 3x3 rotation matrix from the provided quaternion.
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*
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* @param {Quaternion} quaternion the quaternion to use.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
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*/
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Matrix3.fromQuaternion = function (quaternion, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("quaternion", quaternion);
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//>>includeEnd('debug');
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var x2 = quaternion.x * quaternion.x;
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var xy = quaternion.x * quaternion.y;
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var xz = quaternion.x * quaternion.z;
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var xw = quaternion.x * quaternion.w;
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var y2 = quaternion.y * quaternion.y;
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var yz = quaternion.y * quaternion.z;
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var yw = quaternion.y * quaternion.w;
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var z2 = quaternion.z * quaternion.z;
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var zw = quaternion.z * quaternion.w;
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var w2 = quaternion.w * quaternion.w;
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var m00 = x2 - y2 - z2 + w2;
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var m01 = 2.0 * (xy - zw);
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var m02 = 2.0 * (xz + yw);
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var m10 = 2.0 * (xy + zw);
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var m11 = -x2 + y2 - z2 + w2;
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var m12 = 2.0 * (yz - xw);
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var m20 = 2.0 * (xz - yw);
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var m21 = 2.0 * (yz + xw);
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var m22 = -x2 - y2 + z2 + w2;
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if (!defined(result)) {
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return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
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}
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result[0] = m00;
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result[1] = m10;
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result[2] = m20;
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result[3] = m01;
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result[4] = m11;
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result[5] = m21;
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result[6] = m02;
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result[7] = m12;
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result[8] = m22;
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return result;
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};
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/**
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* Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
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*
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* @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
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*/
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Matrix3.fromHeadingPitchRoll = function (headingPitchRoll, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("headingPitchRoll", headingPitchRoll);
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//>>includeEnd('debug');
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var cosTheta = Math.cos(-headingPitchRoll.pitch);
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var cosPsi = Math.cos(-headingPitchRoll.heading);
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var cosPhi = Math.cos(headingPitchRoll.roll);
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var sinTheta = Math.sin(-headingPitchRoll.pitch);
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var sinPsi = Math.sin(-headingPitchRoll.heading);
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var sinPhi = Math.sin(headingPitchRoll.roll);
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var m00 = cosTheta * cosPsi;
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var m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
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var m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
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var m10 = cosTheta * sinPsi;
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var m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
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var m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
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var m20 = -sinTheta;
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var m21 = sinPhi * cosTheta;
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var m22 = cosPhi * cosTheta;
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if (!defined(result)) {
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return new Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
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}
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result[0] = m00;
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result[1] = m10;
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result[2] = m20;
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result[3] = m01;
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result[4] = m11;
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result[5] = m21;
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result[6] = m02;
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result[7] = m12;
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result[8] = m22;
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return result;
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};
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/**
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* Computes a Matrix3 instance representing a non-uniform scale.
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*
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* @param {Cartesian3} scale The x, y, and z scale factors.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
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*
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* @example
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* // Creates
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* // [7.0, 0.0, 0.0]
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* // [0.0, 8.0, 0.0]
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* // [0.0, 0.0, 9.0]
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* var m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
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*/
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Matrix3.fromScale = function (scale, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.object("scale", scale);
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//>>includeEnd('debug');
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if (!defined(result)) {
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return new Matrix3(scale.x, 0.0, 0.0, 0.0, scale.y, 0.0, 0.0, 0.0, scale.z);
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}
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result[0] = scale.x;
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result[1] = 0.0;
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result[2] = 0.0;
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result[3] = 0.0;
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result[4] = scale.y;
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result[5] = 0.0;
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result[6] = 0.0;
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result[7] = 0.0;
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result[8] = scale.z;
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return result;
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};
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/**
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* Computes a Matrix3 instance representing a uniform scale.
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*
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* @param {Number} scale The uniform scale factor.
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
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* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
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*
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* @example
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* // Creates
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* // [2.0, 0.0, 0.0]
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* // [0.0, 2.0, 0.0]
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* // [0.0, 0.0, 2.0]
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* var m = Cesium.Matrix3.fromUniformScale(2.0);
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*/
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Matrix3.fromUniformScale = function (scale, result) {
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//>>includeStart('debug', pragmas.debug);
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Check.typeOf.number("scale", scale);
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//>>includeEnd('debug');
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|
|
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if (!defined(result)) {
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return new Matrix3(scale, 0.0, 0.0, 0.0, scale, 0.0, 0.0, 0.0, scale);
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}
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result[0] = scale;
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result[1] = 0.0;
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result[2] = 0.0;
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result[3] = 0.0;
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result[4] = scale;
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result[5] = 0.0;
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result[6] = 0.0;
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result[7] = 0.0;
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result[8] = scale;
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return result;
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};
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|
|
|
/**
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* Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
|
|
*
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* @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
|
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* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
|
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* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
|
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*
|
|
* @example
|
|
* // Creates
|
|
* // [0.0, -9.0, 8.0]
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* // [9.0, 0.0, -7.0]
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* // [-8.0, 7.0, 0.0]
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* var m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
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*/
|
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Matrix3.fromCrossProduct = function (vector, result) {
|
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//>>includeStart('debug', pragmas.debug);
|
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Check.typeOf.object("vector", vector);
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//>>includeEnd('debug');
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|
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if (!defined(result)) {
|
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return new Matrix3(
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0.0,
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-vector.z,
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vector.y,
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vector.z,
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0.0,
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-vector.x,
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-vector.y,
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vector.x,
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0.0
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);
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}
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result[0] = 0.0;
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result[1] = vector.z;
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result[2] = -vector.y;
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result[3] = -vector.z;
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result[4] = 0.0;
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result[5] = vector.x;
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result[6] = vector.y;
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result[7] = -vector.x;
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result[8] = 0.0;
|
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return result;
|
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};
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|
|
|
/**
|
|
* 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.
|
|
* 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());
|
|
*/
|
|
Matrix3.fromRotationX = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
var cosAngle = Math.cos(angle);
|
|
var 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.
|
|
* 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());
|
|
*/
|
|
Matrix3.fromRotationY = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
var cosAngle = Math.cos(angle);
|
|
var 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.
|
|
* 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());
|
|
*/
|
|
Matrix3.fromRotationZ = function (angle, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.number("angle", angle);
|
|
//>>includeEnd('debug');
|
|
|
|
var cosAngle = Math.cos(angle);
|
|
var 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.
|
|
*/
|
|
Matrix3.toArray = function (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} row The zero-based index of the row.
|
|
* @param {Number} column The zero-based index of the column.
|
|
* @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
|
|
* var myMatrix = new Cesium.Matrix3();
|
|
* var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
|
|
* var column1Row0 = myMatrix[column1Row0Index]
|
|
* myMatrix[column1Row0Index] = 10.0;
|
|
*/
|
|
Matrix3.getElementIndex = function (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.
|
|
*/
|
|
Matrix3.getColumn = function (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');
|
|
|
|
var startIndex = index * 3;
|
|
var x = matrix[startIndex];
|
|
var y = matrix[startIndex + 1];
|
|
var 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.
|
|
*/
|
|
Matrix3.setColumn = function (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);
|
|
var startIndex = index * 3;
|
|
result[startIndex] = cartesian.x;
|
|
result[startIndex + 1] = cartesian.y;
|
|
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.
|
|
*/
|
|
Matrix3.getRow = function (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');
|
|
|
|
var x = matrix[index];
|
|
var y = matrix[index + 3];
|
|
var 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.
|
|
*/
|
|
Matrix3.setRow = function (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);
|
|
result[index] = cartesian.x;
|
|
result[index + 3] = cartesian.y;
|
|
result[index + 6] = cartesian.z;
|
|
return result;
|
|
};
|
|
|
|
var scratchColumn = new Cartesian3();
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
Matrix3.getScale = function (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;
|
|
};
|
|
|
|
var scratchScale = new Cartesian3();
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
Matrix3.getMaximumScale = function (matrix) {
|
|
Matrix3.getScale(matrix, scratchScale);
|
|
return Cartesian3.maximumComponent(scratchScale);
|
|
};
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
Matrix3.multiply = function (left, right, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("left", left);
|
|
Check.typeOf.object("right", right);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var column0Row0 =
|
|
left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
|
|
var column0Row1 =
|
|
left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
|
|
var column0Row2 =
|
|
left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
|
|
|
|
var column1Row0 =
|
|
left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
|
|
var column1Row1 =
|
|
left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
|
|
var column1Row2 =
|
|
left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
|
|
|
|
var column2Row0 =
|
|
left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
|
|
var column2Row1 =
|
|
left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
|
|
var 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.
|
|
*/
|
|
Matrix3.add = function (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.
|
|
*/
|
|
Matrix3.subtract = function (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.
|
|
*/
|
|
Matrix3.multiplyByVector = function (matrix, cartesian, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var vX = cartesian.x;
|
|
var vY = cartesian.y;
|
|
var vZ = cartesian.z;
|
|
|
|
var x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
|
|
var y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
|
|
var 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.
|
|
*/
|
|
Matrix3.multiplyByScalar = function (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.fromScale
|
|
* @see Matrix3.multiplyByUniformScale
|
|
*/
|
|
Matrix3.multiplyByScale = function (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;
|
|
};
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
Matrix3.negate = function (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.
|
|
*/
|
|
Matrix3.transpose = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var column0Row0 = matrix[0];
|
|
var column0Row1 = matrix[3];
|
|
var column0Row2 = matrix[6];
|
|
var column1Row0 = matrix[1];
|
|
var column1Row1 = matrix[4];
|
|
var column1Row2 = matrix[7];
|
|
var column2Row0 = matrix[2];
|
|
var column2Row1 = matrix[5];
|
|
var 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;
|
|
};
|
|
|
|
var UNIT = new Cartesian3(1, 1, 1);
|
|
|
|
/**
|
|
* Extracts the rotation 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
|
|
*/
|
|
Matrix3.getRotation = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var inverseScale = Cartesian3.divideComponents(
|
|
UNIT,
|
|
Matrix3.getScale(matrix, scratchScale),
|
|
scratchScale
|
|
);
|
|
result = Matrix3.multiplyByScale(matrix, inverseScale, result);
|
|
|
|
return result;
|
|
};
|
|
|
|
function computeFrobeniusNorm(matrix) {
|
|
var norm = 0.0;
|
|
for (var i = 0; i < 9; ++i) {
|
|
var temp = matrix[i];
|
|
norm += temp * temp;
|
|
}
|
|
|
|
return Math.sqrt(norm);
|
|
}
|
|
|
|
var rowVal = [1, 0, 0];
|
|
var colVal = [2, 2, 1];
|
|
|
|
function offDiagonalFrobeniusNorm(matrix) {
|
|
// Computes the "off-diagonal" Frobenius norm.
|
|
// Assumes matrix is symmetric.
|
|
|
|
var norm = 0.0;
|
|
for (var i = 0; i < 3; ++i) {
|
|
var temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
|
|
norm += 2.0 * temp * temp;
|
|
}
|
|
|
|
return Math.sqrt(norm);
|
|
}
|
|
|
|
function shurDecomposition(matrix, result) {
|
|
// This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
|
|
// section 8.4.2 The 2by2 Symmetric Schur Decomposition.
|
|
//
|
|
// The routine takes a matrix, which is assumed to be symmetric, and
|
|
// finds the largest off-diagonal term, and then creates
|
|
// a matrix (result) which can be used to help reduce it
|
|
|
|
var tolerance = CesiumMath.EPSILON15;
|
|
|
|
var maxDiagonal = 0.0;
|
|
var rotAxis = 1;
|
|
|
|
// find pivot (rotAxis) based on max diagonal of matrix
|
|
for (var i = 0; i < 3; ++i) {
|
|
var temp = Math.abs(matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]);
|
|
if (temp > maxDiagonal) {
|
|
rotAxis = i;
|
|
maxDiagonal = temp;
|
|
}
|
|
}
|
|
|
|
var c = 1.0;
|
|
var s = 0.0;
|
|
|
|
var p = rowVal[rotAxis];
|
|
var q = colVal[rotAxis];
|
|
|
|
if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
|
|
var qq = matrix[Matrix3.getElementIndex(q, q)];
|
|
var pp = matrix[Matrix3.getElementIndex(p, p)];
|
|
var qp = matrix[Matrix3.getElementIndex(q, p)];
|
|
|
|
var tau = (qq - pp) / 2.0 / qp;
|
|
var t;
|
|
|
|
if (tau < 0.0) {
|
|
t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));
|
|
} else {
|
|
t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));
|
|
}
|
|
|
|
c = 1.0 / Math.sqrt(1.0 + t * t);
|
|
s = t * c;
|
|
}
|
|
|
|
result = Matrix3.clone(Matrix3.IDENTITY, result);
|
|
|
|
result[Matrix3.getElementIndex(p, p)] = result[
|
|
Matrix3.getElementIndex(q, q)
|
|
] = c;
|
|
result[Matrix3.getElementIndex(q, p)] = s;
|
|
result[Matrix3.getElementIndex(p, q)] = -s;
|
|
|
|
return result;
|
|
}
|
|
|
|
var jMatrix = new Matrix3();
|
|
var jMatrixTranspose = new Matrix3();
|
|
|
|
/**
|
|
* 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 {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
|
|
* @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
|
|
*
|
|
* @example
|
|
* var a = //... symetric matrix
|
|
* var result = {
|
|
* unitary : new Cesium.Matrix3(),
|
|
* diagonal : new Cesium.Matrix3()
|
|
* };
|
|
* Cesium.Matrix3.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)
|
|
*/
|
|
Matrix3.computeEigenDecomposition = function (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
|
|
|
|
var tolerance = CesiumMath.EPSILON20;
|
|
var maxSweeps = 10;
|
|
|
|
var count = 0;
|
|
var sweep = 0;
|
|
|
|
if (!defined(result)) {
|
|
result = {};
|
|
}
|
|
|
|
var unitaryMatrix = (result.unitary = Matrix3.clone(
|
|
Matrix3.IDENTITY,
|
|
result.unitary
|
|
));
|
|
var diagMatrix = (result.diagonal = Matrix3.clone(matrix, result.diagonal));
|
|
|
|
var 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.
|
|
*/
|
|
Matrix3.abs = function (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.
|
|
*/
|
|
Matrix3.determinant = function (matrix) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
//>>includeEnd('debug');
|
|
|
|
var m11 = matrix[0];
|
|
var m21 = matrix[3];
|
|
var m31 = matrix[6];
|
|
var m12 = matrix[1];
|
|
var m22 = matrix[4];
|
|
var m32 = matrix[7];
|
|
var m13 = matrix[2];
|
|
var m23 = matrix[5];
|
|
var 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.
|
|
*/
|
|
Matrix3.inverse = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var m11 = matrix[0];
|
|
var m21 = matrix[1];
|
|
var m31 = matrix[2];
|
|
var m12 = matrix[3];
|
|
var m22 = matrix[4];
|
|
var m32 = matrix[5];
|
|
var m13 = matrix[6];
|
|
var m23 = matrix[7];
|
|
var m33 = matrix[8];
|
|
|
|
var 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;
|
|
|
|
var scale = 1.0 / determinant;
|
|
return Matrix3.multiplyByScalar(result, scale, result);
|
|
};
|
|
|
|
var scratchTransposeMatrix = new Matrix3();
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
Matrix3.inverseTranspose = function (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> if left and right are equal, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.equals = function (left, right) {
|
|
return (
|
|
left === right ||
|
|
(defined(left) &&
|
|
defined(right) &&
|
|
left[0] === right[0] &&
|
|
left[1] === right[1] &&
|
|
left[2] === right[2] &&
|
|
left[3] === right[3] &&
|
|
left[4] === right[4] &&
|
|
left[5] === right[5] &&
|
|
left[6] === right[6] &&
|
|
left[7] === right[7] &&
|
|
left[8] === right[8])
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares the provided matrices componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [left] The first matrix.
|
|
* @param {Matrix3} [right] The second matrix.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.equalsEpsilon = function (left, right, epsilon) {
|
|
epsilon = defaultValue(epsilon, 0);
|
|
|
|
return (
|
|
left === right ||
|
|
(defined(left) &&
|
|
defined(right) &&
|
|
Math.abs(left[0] - right[0]) <= epsilon &&
|
|
Math.abs(left[1] - right[1]) <= epsilon &&
|
|
Math.abs(left[2] - right[2]) <= epsilon &&
|
|
Math.abs(left[3] - right[3]) <= epsilon &&
|
|
Math.abs(left[4] - right[4]) <= epsilon &&
|
|
Math.abs(left[5] - right[5]) <= epsilon &&
|
|
Math.abs(left[6] - right[6]) <= epsilon &&
|
|
Math.abs(left[7] - right[7]) <= epsilon &&
|
|
Math.abs(left[8] - right[8]) <= epsilon)
|
|
);
|
|
};
|
|
|
|
/**
|
|
* An immutable Matrix3 instance initialized to the identity matrix.
|
|
*
|
|
* @type {Matrix3}
|
|
* @constant
|
|
*/
|
|
Matrix3.IDENTITY = Object.freeze(
|
|
new Matrix3(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)
|
|
);
|
|
|
|
/**
|
|
* An immutable Matrix3 instance initialized to the zero matrix.
|
|
*
|
|
* @type {Matrix3}
|
|
* @constant
|
|
*/
|
|
Matrix3.ZERO = Object.freeze(
|
|
new Matrix3(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
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);
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/**
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* The index into Matrix3 for column 0, row 0.
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*
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* @type {Number}
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* @constant
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*/
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Matrix3.COLUMN0ROW0 = 0;
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|
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/**
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* The index into Matrix3 for column 0, row 1.
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*
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* @type {Number}
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* @constant
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*/
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Matrix3.COLUMN0ROW1 = 1;
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|
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|
/**
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|
* The index into Matrix3 for column 0, row 2.
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*
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* @type {Number}
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* @constant
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|
*/
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Matrix3.COLUMN0ROW2 = 2;
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|
|
|
/**
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|
* The index into Matrix3 for column 1, row 0.
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*
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|
* @type {Number}
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|
* @constant
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|
*/
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Matrix3.COLUMN1ROW0 = 3;
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|
|
|
/**
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|
* The index into Matrix3 for column 1, row 1.
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*
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|
* @type {Number}
|
|
* @constant
|
|
*/
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|
Matrix3.COLUMN1ROW1 = 4;
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|
|
|
/**
|
|
* The index into Matrix3 for column 1, row 2.
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|
*
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|
* @type {Number}
|
|
* @constant
|
|
*/
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|
Matrix3.COLUMN1ROW2 = 5;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 0.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW0 = 6;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 1.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW1 = 7;
|
|
|
|
/**
|
|
* The index into Matrix3 for column 2, row 2.
|
|
*
|
|
* @type {Number}
|
|
* @constant
|
|
*/
|
|
Matrix3.COLUMN2ROW2 = 8;
|
|
|
|
Object.defineProperties(Matrix3.prototype, {
|
|
/**
|
|
* Gets the number of items in the collection.
|
|
* @memberof Matrix3.prototype
|
|
*
|
|
* @type {Number}
|
|
*/
|
|
length: {
|
|
get: function () {
|
|
return Matrix3.packedLength;
|
|
},
|
|
},
|
|
});
|
|
|
|
/**
|
|
* Duplicates the provided Matrix3 instance.
|
|
*
|
|
* @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.
|
|
*/
|
|
Matrix3.prototype.clone = function (result) {
|
|
return Matrix3.clone(this, result);
|
|
};
|
|
|
|
/**
|
|
* Compares this matrix to the provided matrix componentwise and returns
|
|
* <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [right] The right hand side matrix.
|
|
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.prototype.equals = function (right) {
|
|
return Matrix3.equals(this, right);
|
|
};
|
|
|
|
/**
|
|
* @private
|
|
*/
|
|
Matrix3.equalsArray = function (matrix, array, offset) {
|
|
return (
|
|
matrix[0] === array[offset] &&
|
|
matrix[1] === array[offset + 1] &&
|
|
matrix[2] === array[offset + 2] &&
|
|
matrix[3] === array[offset + 3] &&
|
|
matrix[4] === array[offset + 4] &&
|
|
matrix[5] === array[offset + 5] &&
|
|
matrix[6] === array[offset + 6] &&
|
|
matrix[7] === array[offset + 7] &&
|
|
matrix[8] === array[offset + 8]
|
|
);
|
|
};
|
|
|
|
/**
|
|
* Compares this matrix to the provided matrix componentwise and returns
|
|
* <code>true</code> if they are within the provided epsilon,
|
|
* <code>false</code> otherwise.
|
|
*
|
|
* @param {Matrix3} [right] The right hand side matrix.
|
|
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
|
|
* @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
|
|
*/
|
|
Matrix3.prototype.equalsEpsilon = function (right, epsilon) {
|
|
return Matrix3.equalsEpsilon(this, right, epsilon);
|
|
};
|
|
|
|
/**
|
|
* Creates a string representing this Matrix with each row being
|
|
* on a separate line and in the format '(column0, column1, column2)'.
|
|
*
|
|
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
|
|
*/
|
|
Matrix3.prototype.toString = function () {
|
|
return (
|
|
"(" +
|
|
this[0] +
|
|
", " +
|
|
this[3] +
|
|
", " +
|
|
this[6] +
|
|
")\n" +
|
|
"(" +
|
|
this[1] +
|
|
", " +
|
|
this[4] +
|
|
", " +
|
|
this[7] +
|
|
")\n" +
|
|
"(" +
|
|
this[2] +
|
|
", " +
|
|
this[5] +
|
|
", " +
|
|
this[8] +
|
|
")"
|
|
);
|
|
};
|
|
export default Matrix3;
|