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@@ -0,0 +1,4292 @@
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+/**
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+ * @fileoverview gl-matrix - High performance matrix and vector operations
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+ * @author Brandon Jones
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+ * @author Colin MacKenzie IV
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+ * @version 2.2.2
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+ */
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+
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+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
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+
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+Redistribution and use in source and binary forms, with or without modification,
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+are permitted provided that the following conditions are met:
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+
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+ * Redistributions of source code must retain the above copyright notice, this
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+ list of conditions and the following disclaimer.
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+ * Redistributions in binary form must reproduce the above copyright notice,
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+ this list of conditions and the following disclaimer in the documentation
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+ and/or other materials provided with the distribution.
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+
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+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
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+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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+
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+
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+(function(_global) {
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+ "use strict";
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+
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+ var shim = {};
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+ if (typeof(exports) === 'undefined') {
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+ if(typeof define == 'function' && typeof define.amd == 'object' && define.amd) {
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+ shim.exports = {};
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+ define(function() {
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+ return shim.exports;
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+ });
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+ } else {
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+ // gl-matrix lives in a browser, define its namespaces in global
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+ shim.exports = typeof(window) !== 'undefined' ? window : _global;
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+ }
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+ }
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+ else {
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+ // gl-matrix lives in commonjs, define its namespaces in exports
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+ shim.exports = exports;
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+ }
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+
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+ (function(exports) {
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+ /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
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+
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+Redistribution and use in source and binary forms, with or without modification,
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+are permitted provided that the following conditions are met:
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+
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+ * Redistributions of source code must retain the above copyright notice, this
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+ list of conditions and the following disclaimer.
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+ * Redistributions in binary form must reproduce the above copyright notice,
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+ this list of conditions and the following disclaimer in the documentation
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+ and/or other materials provided with the distribution.
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+
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+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
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+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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+
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+
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+if(!GLMAT_EPSILON) {
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+ var GLMAT_EPSILON = 0.000001;
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+}
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+
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+if(!GLMAT_ARRAY_TYPE) {
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+ var GLMAT_ARRAY_TYPE = (typeof Float32Array !== 'undefined') ? Float32Array : Array;
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+}
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+
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+if(!GLMAT_RANDOM) {
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+ var GLMAT_RANDOM = Math.random;
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+}
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+
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+/**
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+ * @class Common utilities
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+ * @name glMatrix
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+ */
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+var glMatrix = {};
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+
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+/**
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+ * Sets the type of array used when creating new vectors and matrices
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+ *
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+ * @param {Type} type Array type, such as Float32Array or Array
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+ */
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+glMatrix.setMatrixArrayType = function(type) {
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+ GLMAT_ARRAY_TYPE = type;
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+}
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+
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+if(typeof(exports) !== 'undefined') {
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+ exports.glMatrix = glMatrix;
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+}
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+
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+var degree = Math.PI / 180;
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+
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+/**
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+* Convert Degree To Radian
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+*
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+* @param {Number} Angle in Degrees
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+*/
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+glMatrix.toRadian = function(a){
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+ return a * degree;
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+}
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+;
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+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
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+
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+Redistribution and use in source and binary forms, with or without modification,
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+are permitted provided that the following conditions are met:
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+
|
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+ * Redistributions of source code must retain the above copyright notice, this
|
|
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+ list of conditions and the following disclaimer.
|
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+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
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|
+ and/or other materials provided with the distribution.
|
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+
|
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+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
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+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
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+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
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+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
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+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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+
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+/**
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+ * @class 2 Dimensional Vector
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+ * @name vec2
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+ */
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+
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+var vec2 = {};
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+
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+/**
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+ * Creates a new, empty vec2
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+ *
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+ * @returns {vec2} a new 2D vector
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+ */
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+vec2.create = function() {
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+ var out = new GLMAT_ARRAY_TYPE(2);
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+ out[0] = 0;
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+ out[1] = 0;
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+ return out;
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+};
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+
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+/**
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+ * Creates a new vec2 initialized with values from an existing vector
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+ *
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+ * @param {vec2} a vector to clone
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+ * @returns {vec2} a new 2D vector
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+ */
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+vec2.clone = function(a) {
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+ var out = new GLMAT_ARRAY_TYPE(2);
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+ out[0] = a[0];
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+ out[1] = a[1];
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+ return out;
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+};
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+
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+/**
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+ * Creates a new vec2 initialized with the given values
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+ *
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+ * @param {Number} x X component
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+ * @param {Number} y Y component
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+ * @returns {vec2} a new 2D vector
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+ */
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+vec2.fromValues = function(x, y) {
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+ var out = new GLMAT_ARRAY_TYPE(2);
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+ out[0] = x;
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+ out[1] = y;
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+ return out;
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+};
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+
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+/**
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+ * Copy the values from one vec2 to another
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the source vector
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+ * @returns {vec2} out
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+ */
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+vec2.copy = function(out, a) {
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+ out[0] = a[0];
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+ out[1] = a[1];
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+ return out;
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+};
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+
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+/**
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+ * Set the components of a vec2 to the given values
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {Number} x X component
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+ * @param {Number} y Y component
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+ * @returns {vec2} out
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+ */
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+vec2.set = function(out, x, y) {
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+ out[0] = x;
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+ out[1] = y;
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+ return out;
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+};
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+
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+/**
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+ * Adds two vec2's
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.add = function(out, a, b) {
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+ out[0] = a[0] + b[0];
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+ out[1] = a[1] + b[1];
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+ return out;
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+};
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+
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+/**
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+ * Subtracts vector b from vector a
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.subtract = function(out, a, b) {
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+ out[0] = a[0] - b[0];
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+ out[1] = a[1] - b[1];
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+ return out;
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+};
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+
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+/**
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+ * Alias for {@link vec2.subtract}
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+ * @function
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+ */
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+vec2.sub = vec2.subtract;
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+
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+/**
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+ * Multiplies two vec2's
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.multiply = function(out, a, b) {
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+ out[0] = a[0] * b[0];
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+ out[1] = a[1] * b[1];
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+ return out;
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+};
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+
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+/**
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+ * Alias for {@link vec2.multiply}
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+ * @function
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+ */
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+vec2.mul = vec2.multiply;
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+
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+/**
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+ * Divides two vec2's
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.divide = function(out, a, b) {
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+ out[0] = a[0] / b[0];
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+ out[1] = a[1] / b[1];
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+ return out;
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+};
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+
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+/**
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+ * Alias for {@link vec2.divide}
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+ * @function
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+ */
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+vec2.div = vec2.divide;
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+
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+/**
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+ * Returns the minimum of two vec2's
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.min = function(out, a, b) {
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+ out[0] = Math.min(a[0], b[0]);
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+ out[1] = Math.min(a[1], b[1]);
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+ return out;
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+};
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+
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+/**
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+ * Returns the maximum of two vec2's
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {vec2} out
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+ */
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+vec2.max = function(out, a, b) {
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+ out[0] = Math.max(a[0], b[0]);
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+ out[1] = Math.max(a[1], b[1]);
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+ return out;
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+};
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+
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+/**
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+ * Scales a vec2 by a scalar number
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the vector to scale
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+ * @param {Number} b amount to scale the vector by
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+ * @returns {vec2} out
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+ */
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+vec2.scale = function(out, a, b) {
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+ out[0] = a[0] * b;
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+ out[1] = a[1] * b;
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+ return out;
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+};
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+
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+/**
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+ * Adds two vec2's after scaling the second operand by a scalar value
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @param {Number} scale the amount to scale b by before adding
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+ * @returns {vec2} out
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+ */
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+vec2.scaleAndAdd = function(out, a, b, scale) {
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+ out[0] = a[0] + (b[0] * scale);
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+ out[1] = a[1] + (b[1] * scale);
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+ return out;
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+};
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+
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+/**
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+ * Calculates the euclidian distance between two vec2's
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+ *
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {Number} distance between a and b
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+ */
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+vec2.distance = function(a, b) {
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+ var x = b[0] - a[0],
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+ y = b[1] - a[1];
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+ return Math.sqrt(x*x + y*y);
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+};
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+
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+/**
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+ * Alias for {@link vec2.distance}
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+ * @function
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+ */
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+vec2.dist = vec2.distance;
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+
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+/**
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+ * Calculates the squared euclidian distance between two vec2's
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+ *
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+ * @param {vec2} a the first operand
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+ * @param {vec2} b the second operand
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+ * @returns {Number} squared distance between a and b
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+ */
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+vec2.squaredDistance = function(a, b) {
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+ var x = b[0] - a[0],
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+ y = b[1] - a[1];
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+ return x*x + y*y;
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+};
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+
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+/**
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+ * Alias for {@link vec2.squaredDistance}
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+ * @function
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+ */
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+vec2.sqrDist = vec2.squaredDistance;
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+
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+/**
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+ * Calculates the length of a vec2
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+ *
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+ * @param {vec2} a vector to calculate length of
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+ * @returns {Number} length of a
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+ */
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+vec2.length = function (a) {
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+ var x = a[0],
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+ y = a[1];
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+ return Math.sqrt(x*x + y*y);
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+};
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+
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+/**
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+ * Alias for {@link vec2.length}
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+ * @function
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+ */
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+vec2.len = vec2.length;
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+
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+/**
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+ * Calculates the squared length of a vec2
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+ *
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+ * @param {vec2} a vector to calculate squared length of
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+ * @returns {Number} squared length of a
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+ */
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+vec2.squaredLength = function (a) {
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+ var x = a[0],
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+ y = a[1];
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+ return x*x + y*y;
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+};
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+
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+/**
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+ * Alias for {@link vec2.squaredLength}
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+ * @function
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+ */
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+vec2.sqrLen = vec2.squaredLength;
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+
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+/**
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+ * Negates the components of a vec2
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+ *
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+ * @param {vec2} out the receiving vector
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+ * @param {vec2} a vector to negate
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+ * @returns {vec2} out
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+ */
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+vec2.negate = function(out, a) {
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+ out[0] = -a[0];
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+ out[1] = -a[1];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the inverse of the components of a vec2
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a vector to invert
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.inverse = function(out, a) {
|
|
|
+ out[0] = 1.0 / a[0];
|
|
|
+ out[1] = 1.0 / a[1];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Normalize a vec2
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a vector to normalize
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.normalize = function(out, a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1];
|
|
|
+ var len = x*x + y*y;
|
|
|
+ if (len > 0) {
|
|
|
+ //TODO: evaluate use of glm_invsqrt here?
|
|
|
+ len = 1 / Math.sqrt(len);
|
|
|
+ out[0] = a[0] * len;
|
|
|
+ out[1] = a[1] * len;
|
|
|
+ }
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the dot product of two vec2's
|
|
|
+ *
|
|
|
+ * @param {vec2} a the first operand
|
|
|
+ * @param {vec2} b the second operand
|
|
|
+ * @returns {Number} dot product of a and b
|
|
|
+ */
|
|
|
+vec2.dot = function (a, b) {
|
|
|
+ return a[0] * b[0] + a[1] * b[1];
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Computes the cross product of two vec2's
|
|
|
+ * Note that the cross product must by definition produce a 3D vector
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec2} a the first operand
|
|
|
+ * @param {vec2} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec2.cross = function(out, a, b) {
|
|
|
+ var z = a[0] * b[1] - a[1] * b[0];
|
|
|
+ out[0] = out[1] = 0;
|
|
|
+ out[2] = z;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Performs a linear interpolation between two vec2's
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a the first operand
|
|
|
+ * @param {vec2} b the second operand
|
|
|
+ * @param {Number} t interpolation amount between the two inputs
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.lerp = function (out, a, b, t) {
|
|
|
+ var ax = a[0],
|
|
|
+ ay = a[1];
|
|
|
+ out[0] = ax + t * (b[0] - ax);
|
|
|
+ out[1] = ay + t * (b[1] - ay);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a random vector with the given scale
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.random = function (out, scale) {
|
|
|
+ scale = scale || 1.0;
|
|
|
+ var r = GLMAT_RANDOM() * 2.0 * Math.PI;
|
|
|
+ out[0] = Math.cos(r) * scale;
|
|
|
+ out[1] = Math.sin(r) * scale;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec2 with a mat2
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a the vector to transform
|
|
|
+ * @param {mat2} m matrix to transform with
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.transformMat2 = function(out, a, m) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1];
|
|
|
+ out[0] = m[0] * x + m[2] * y;
|
|
|
+ out[1] = m[1] * x + m[3] * y;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec2 with a mat2d
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a the vector to transform
|
|
|
+ * @param {mat2d} m matrix to transform with
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.transformMat2d = function(out, a, m) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1];
|
|
|
+ out[0] = m[0] * x + m[2] * y + m[4];
|
|
|
+ out[1] = m[1] * x + m[3] * y + m[5];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec2 with a mat3
|
|
|
+ * 3rd vector component is implicitly '1'
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a the vector to transform
|
|
|
+ * @param {mat3} m matrix to transform with
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.transformMat3 = function(out, a, m) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1];
|
|
|
+ out[0] = m[0] * x + m[3] * y + m[6];
|
|
|
+ out[1] = m[1] * x + m[4] * y + m[7];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec2 with a mat4
|
|
|
+ * 3rd vector component is implicitly '0'
|
|
|
+ * 4th vector component is implicitly '1'
|
|
|
+ *
|
|
|
+ * @param {vec2} out the receiving vector
|
|
|
+ * @param {vec2} a the vector to transform
|
|
|
+ * @param {mat4} m matrix to transform with
|
|
|
+ * @returns {vec2} out
|
|
|
+ */
|
|
|
+vec2.transformMat4 = function(out, a, m) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1];
|
|
|
+ out[0] = m[0] * x + m[4] * y + m[12];
|
|
|
+ out[1] = m[1] * x + m[5] * y + m[13];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Perform some operation over an array of vec2s.
|
|
|
+ *
|
|
|
+ * @param {Array} a the array of vectors to iterate over
|
|
|
+ * @param {Number} stride Number of elements between the start of each vec2. If 0 assumes tightly packed
|
|
|
+ * @param {Number} offset Number of elements to skip at the beginning of the array
|
|
|
+ * @param {Number} count Number of vec2s to iterate over. If 0 iterates over entire array
|
|
|
+ * @param {Function} fn Function to call for each vector in the array
|
|
|
+ * @param {Object} [arg] additional argument to pass to fn
|
|
|
+ * @returns {Array} a
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec2.forEach = (function() {
|
|
|
+ var vec = vec2.create();
|
|
|
+
|
|
|
+ return function(a, stride, offset, count, fn, arg) {
|
|
|
+ var i, l;
|
|
|
+ if(!stride) {
|
|
|
+ stride = 2;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(!offset) {
|
|
|
+ offset = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(count) {
|
|
|
+ l = Math.min((count * stride) + offset, a.length);
|
|
|
+ } else {
|
|
|
+ l = a.length;
|
|
|
+ }
|
|
|
+
|
|
|
+ for(i = offset; i < l; i += stride) {
|
|
|
+ vec[0] = a[i]; vec[1] = a[i+1];
|
|
|
+ fn(vec, vec, arg);
|
|
|
+ a[i] = vec[0]; a[i+1] = vec[1];
|
|
|
+ }
|
|
|
+
|
|
|
+ return a;
|
|
|
+ };
|
|
|
+})();
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a vector
|
|
|
+ *
|
|
|
+ * @param {vec2} vec vector to represent as a string
|
|
|
+ * @returns {String} string representation of the vector
|
|
|
+ */
|
|
|
+vec2.str = function (a) {
|
|
|
+ return 'vec2(' + a[0] + ', ' + a[1] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.vec2 = vec2;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class 3 Dimensional Vector
|
|
|
+ * @name vec3
|
|
|
+ */
|
|
|
+
|
|
|
+var vec3 = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new, empty vec3
|
|
|
+ *
|
|
|
+ * @returns {vec3} a new 3D vector
|
|
|
+ */
|
|
|
+vec3.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(3);
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new vec3 initialized with values from an existing vector
|
|
|
+ *
|
|
|
+ * @param {vec3} a vector to clone
|
|
|
+ * @returns {vec3} a new 3D vector
|
|
|
+ */
|
|
|
+vec3.clone = function(a) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(3);
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new vec3 initialized with the given values
|
|
|
+ *
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @returns {vec3} a new 3D vector
|
|
|
+ */
|
|
|
+vec3.fromValues = function(x, y, z) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(3);
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one vec3 to another
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the source vector
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.copy = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set the components of a vec3 to the given values
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.set = function(out, x, y, z) {
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Adds two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.add = function(out, a, b) {
|
|
|
+ out[0] = a[0] + b[0];
|
|
|
+ out[1] = a[1] + b[1];
|
|
|
+ out[2] = a[2] + b[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Subtracts vector b from vector a
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.subtract = function(out, a, b) {
|
|
|
+ out[0] = a[0] - b[0];
|
|
|
+ out[1] = a[1] - b[1];
|
|
|
+ out[2] = a[2] - b[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.subtract}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.sub = vec3.subtract;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.multiply = function(out, a, b) {
|
|
|
+ out[0] = a[0] * b[0];
|
|
|
+ out[1] = a[1] * b[1];
|
|
|
+ out[2] = a[2] * b[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.mul = vec3.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Divides two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.divide = function(out, a, b) {
|
|
|
+ out[0] = a[0] / b[0];
|
|
|
+ out[1] = a[1] / b[1];
|
|
|
+ out[2] = a[2] / b[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.divide}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.div = vec3.divide;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the minimum of two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.min = function(out, a, b) {
|
|
|
+ out[0] = Math.min(a[0], b[0]);
|
|
|
+ out[1] = Math.min(a[1], b[1]);
|
|
|
+ out[2] = Math.min(a[2], b[2]);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the maximum of two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.max = function(out, a, b) {
|
|
|
+ out[0] = Math.max(a[0], b[0]);
|
|
|
+ out[1] = Math.max(a[1], b[1]);
|
|
|
+ out[2] = Math.max(a[2], b[2]);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales a vec3 by a scalar number
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the vector to scale
|
|
|
+ * @param {Number} b amount to scale the vector by
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.scale = function(out, a, b) {
|
|
|
+ out[0] = a[0] * b;
|
|
|
+ out[1] = a[1] * b;
|
|
|
+ out[2] = a[2] * b;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Adds two vec3's after scaling the second operand by a scalar value
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @param {Number} scale the amount to scale b by before adding
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.scaleAndAdd = function(out, a, b, scale) {
|
|
|
+ out[0] = a[0] + (b[0] * scale);
|
|
|
+ out[1] = a[1] + (b[1] * scale);
|
|
|
+ out[2] = a[2] + (b[2] * scale);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the euclidian distance between two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {Number} distance between a and b
|
|
|
+ */
|
|
|
+vec3.distance = function(a, b) {
|
|
|
+ var x = b[0] - a[0],
|
|
|
+ y = b[1] - a[1],
|
|
|
+ z = b[2] - a[2];
|
|
|
+ return Math.sqrt(x*x + y*y + z*z);
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.distance}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.dist = vec3.distance;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the squared euclidian distance between two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {Number} squared distance between a and b
|
|
|
+ */
|
|
|
+vec3.squaredDistance = function(a, b) {
|
|
|
+ var x = b[0] - a[0],
|
|
|
+ y = b[1] - a[1],
|
|
|
+ z = b[2] - a[2];
|
|
|
+ return x*x + y*y + z*z;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.squaredDistance}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.sqrDist = vec3.squaredDistance;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the length of a vec3
|
|
|
+ *
|
|
|
+ * @param {vec3} a vector to calculate length of
|
|
|
+ * @returns {Number} length of a
|
|
|
+ */
|
|
|
+vec3.length = function (a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2];
|
|
|
+ return Math.sqrt(x*x + y*y + z*z);
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.length}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.len = vec3.length;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the squared length of a vec3
|
|
|
+ *
|
|
|
+ * @param {vec3} a vector to calculate squared length of
|
|
|
+ * @returns {Number} squared length of a
|
|
|
+ */
|
|
|
+vec3.squaredLength = function (a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2];
|
|
|
+ return x*x + y*y + z*z;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec3.squaredLength}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.sqrLen = vec3.squaredLength;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Negates the components of a vec3
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a vector to negate
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.negate = function(out, a) {
|
|
|
+ out[0] = -a[0];
|
|
|
+ out[1] = -a[1];
|
|
|
+ out[2] = -a[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the inverse of the components of a vec3
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a vector to invert
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.inverse = function(out, a) {
|
|
|
+ out[0] = 1.0 / a[0];
|
|
|
+ out[1] = 1.0 / a[1];
|
|
|
+ out[2] = 1.0 / a[2];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Normalize a vec3
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a vector to normalize
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.normalize = function(out, a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2];
|
|
|
+ var len = x*x + y*y + z*z;
|
|
|
+ if (len > 0) {
|
|
|
+ //TODO: evaluate use of glm_invsqrt here?
|
|
|
+ len = 1 / Math.sqrt(len);
|
|
|
+ out[0] = a[0] * len;
|
|
|
+ out[1] = a[1] * len;
|
|
|
+ out[2] = a[2] * len;
|
|
|
+ }
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the dot product of two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {Number} dot product of a and b
|
|
|
+ */
|
|
|
+vec3.dot = function (a, b) {
|
|
|
+ return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Computes the cross product of two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.cross = function(out, a, b) {
|
|
|
+ var ax = a[0], ay = a[1], az = a[2],
|
|
|
+ bx = b[0], by = b[1], bz = b[2];
|
|
|
+
|
|
|
+ out[0] = ay * bz - az * by;
|
|
|
+ out[1] = az * bx - ax * bz;
|
|
|
+ out[2] = ax * by - ay * bx;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Performs a linear interpolation between two vec3's
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the first operand
|
|
|
+ * @param {vec3} b the second operand
|
|
|
+ * @param {Number} t interpolation amount between the two inputs
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.lerp = function (out, a, b, t) {
|
|
|
+ var ax = a[0],
|
|
|
+ ay = a[1],
|
|
|
+ az = a[2];
|
|
|
+ out[0] = ax + t * (b[0] - ax);
|
|
|
+ out[1] = ay + t * (b[1] - ay);
|
|
|
+ out[2] = az + t * (b[2] - az);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a random vector with the given scale
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.random = function (out, scale) {
|
|
|
+ scale = scale || 1.0;
|
|
|
+
|
|
|
+ var r = GLMAT_RANDOM() * 2.0 * Math.PI;
|
|
|
+ var z = (GLMAT_RANDOM() * 2.0) - 1.0;
|
|
|
+ var zScale = Math.sqrt(1.0-z*z) * scale;
|
|
|
+
|
|
|
+ out[0] = Math.cos(r) * zScale;
|
|
|
+ out[1] = Math.sin(r) * zScale;
|
|
|
+ out[2] = z * scale;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec3 with a mat4.
|
|
|
+ * 4th vector component is implicitly '1'
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the vector to transform
|
|
|
+ * @param {mat4} m matrix to transform with
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.transformMat4 = function(out, a, m) {
|
|
|
+ var x = a[0], y = a[1], z = a[2],
|
|
|
+ w = m[3] * x + m[7] * y + m[11] * z + m[15];
|
|
|
+ w = w || 1.0;
|
|
|
+ out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
|
|
|
+ out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
|
|
|
+ out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec3 with a mat3.
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the vector to transform
|
|
|
+ * @param {mat4} m the 3x3 matrix to transform with
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.transformMat3 = function(out, a, m) {
|
|
|
+ var x = a[0], y = a[1], z = a[2];
|
|
|
+ out[0] = x * m[0] + y * m[3] + z * m[6];
|
|
|
+ out[1] = x * m[1] + y * m[4] + z * m[7];
|
|
|
+ out[2] = x * m[2] + y * m[5] + z * m[8];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec3 with a quat
|
|
|
+ *
|
|
|
+ * @param {vec3} out the receiving vector
|
|
|
+ * @param {vec3} a the vector to transform
|
|
|
+ * @param {quat} q quaternion to transform with
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.transformQuat = function(out, a, q) {
|
|
|
+ // benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations
|
|
|
+
|
|
|
+ var x = a[0], y = a[1], z = a[2],
|
|
|
+ qx = q[0], qy = q[1], qz = q[2], qw = q[3],
|
|
|
+
|
|
|
+ // calculate quat * vec
|
|
|
+ ix = qw * x + qy * z - qz * y,
|
|
|
+ iy = qw * y + qz * x - qx * z,
|
|
|
+ iz = qw * z + qx * y - qy * x,
|
|
|
+ iw = -qx * x - qy * y - qz * z;
|
|
|
+
|
|
|
+ // calculate result * inverse quat
|
|
|
+ out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
|
|
|
+ out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
|
|
|
+ out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotate a 3D vector around the x-axis
|
|
|
+ * @param {vec3} out The receiving vec3
|
|
|
+ * @param {vec3} a The vec3 point to rotate
|
|
|
+ * @param {vec3} b The origin of the rotation
|
|
|
+ * @param {Number} c The angle of rotation
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.rotateX = function(out, a, b, c){
|
|
|
+ var p = [], r=[];
|
|
|
+ //Translate point to the origin
|
|
|
+ p[0] = a[0] - b[0];
|
|
|
+ p[1] = a[1] - b[1];
|
|
|
+ p[2] = a[2] - b[2];
|
|
|
+
|
|
|
+ //perform rotation
|
|
|
+ r[0] = p[0];
|
|
|
+ r[1] = p[1]*Math.cos(c) - p[2]*Math.sin(c);
|
|
|
+ r[2] = p[1]*Math.sin(c) + p[2]*Math.cos(c);
|
|
|
+
|
|
|
+ //translate to correct position
|
|
|
+ out[0] = r[0] + b[0];
|
|
|
+ out[1] = r[1] + b[1];
|
|
|
+ out[2] = r[2] + b[2];
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotate a 3D vector around the y-axis
|
|
|
+ * @param {vec3} out The receiving vec3
|
|
|
+ * @param {vec3} a The vec3 point to rotate
|
|
|
+ * @param {vec3} b The origin of the rotation
|
|
|
+ * @param {Number} c The angle of rotation
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.rotateY = function(out, a, b, c){
|
|
|
+ var p = [], r=[];
|
|
|
+ //Translate point to the origin
|
|
|
+ p[0] = a[0] - b[0];
|
|
|
+ p[1] = a[1] - b[1];
|
|
|
+ p[2] = a[2] - b[2];
|
|
|
+
|
|
|
+ //perform rotation
|
|
|
+ r[0] = p[2]*Math.sin(c) + p[0]*Math.cos(c);
|
|
|
+ r[1] = p[1];
|
|
|
+ r[2] = p[2]*Math.cos(c) - p[0]*Math.sin(c);
|
|
|
+
|
|
|
+ //translate to correct position
|
|
|
+ out[0] = r[0] + b[0];
|
|
|
+ out[1] = r[1] + b[1];
|
|
|
+ out[2] = r[2] + b[2];
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotate a 3D vector around the z-axis
|
|
|
+ * @param {vec3} out The receiving vec3
|
|
|
+ * @param {vec3} a The vec3 point to rotate
|
|
|
+ * @param {vec3} b The origin of the rotation
|
|
|
+ * @param {Number} c The angle of rotation
|
|
|
+ * @returns {vec3} out
|
|
|
+ */
|
|
|
+vec3.rotateZ = function(out, a, b, c){
|
|
|
+ var p = [], r=[];
|
|
|
+ //Translate point to the origin
|
|
|
+ p[0] = a[0] - b[0];
|
|
|
+ p[1] = a[1] - b[1];
|
|
|
+ p[2] = a[2] - b[2];
|
|
|
+
|
|
|
+ //perform rotation
|
|
|
+ r[0] = p[0]*Math.cos(c) - p[1]*Math.sin(c);
|
|
|
+ r[1] = p[0]*Math.sin(c) + p[1]*Math.cos(c);
|
|
|
+ r[2] = p[2];
|
|
|
+
|
|
|
+ //translate to correct position
|
|
|
+ out[0] = r[0] + b[0];
|
|
|
+ out[1] = r[1] + b[1];
|
|
|
+ out[2] = r[2] + b[2];
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Perform some operation over an array of vec3s.
|
|
|
+ *
|
|
|
+ * @param {Array} a the array of vectors to iterate over
|
|
|
+ * @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed
|
|
|
+ * @param {Number} offset Number of elements to skip at the beginning of the array
|
|
|
+ * @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array
|
|
|
+ * @param {Function} fn Function to call for each vector in the array
|
|
|
+ * @param {Object} [arg] additional argument to pass to fn
|
|
|
+ * @returns {Array} a
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec3.forEach = (function() {
|
|
|
+ var vec = vec3.create();
|
|
|
+
|
|
|
+ return function(a, stride, offset, count, fn, arg) {
|
|
|
+ var i, l;
|
|
|
+ if(!stride) {
|
|
|
+ stride = 3;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(!offset) {
|
|
|
+ offset = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(count) {
|
|
|
+ l = Math.min((count * stride) + offset, a.length);
|
|
|
+ } else {
|
|
|
+ l = a.length;
|
|
|
+ }
|
|
|
+
|
|
|
+ for(i = offset; i < l; i += stride) {
|
|
|
+ vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2];
|
|
|
+ fn(vec, vec, arg);
|
|
|
+ a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2];
|
|
|
+ }
|
|
|
+
|
|
|
+ return a;
|
|
|
+ };
|
|
|
+})();
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a vector
|
|
|
+ *
|
|
|
+ * @param {vec3} vec vector to represent as a string
|
|
|
+ * @returns {String} string representation of the vector
|
|
|
+ */
|
|
|
+vec3.str = function (a) {
|
|
|
+ return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.vec3 = vec3;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class 4 Dimensional Vector
|
|
|
+ * @name vec4
|
|
|
+ */
|
|
|
+
|
|
|
+var vec4 = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new, empty vec4
|
|
|
+ *
|
|
|
+ * @returns {vec4} a new 4D vector
|
|
|
+ */
|
|
|
+vec4.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new vec4 initialized with values from an existing vector
|
|
|
+ *
|
|
|
+ * @param {vec4} a vector to clone
|
|
|
+ * @returns {vec4} a new 4D vector
|
|
|
+ */
|
|
|
+vec4.clone = function(a) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new vec4 initialized with the given values
|
|
|
+ *
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @param {Number} w W component
|
|
|
+ * @returns {vec4} a new 4D vector
|
|
|
+ */
|
|
|
+vec4.fromValues = function(x, y, z, w) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = w;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one vec4 to another
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the source vector
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.copy = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set the components of a vec4 to the given values
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @param {Number} w W component
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.set = function(out, x, y, z, w) {
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = w;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Adds two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.add = function(out, a, b) {
|
|
|
+ out[0] = a[0] + b[0];
|
|
|
+ out[1] = a[1] + b[1];
|
|
|
+ out[2] = a[2] + b[2];
|
|
|
+ out[3] = a[3] + b[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Subtracts vector b from vector a
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.subtract = function(out, a, b) {
|
|
|
+ out[0] = a[0] - b[0];
|
|
|
+ out[1] = a[1] - b[1];
|
|
|
+ out[2] = a[2] - b[2];
|
|
|
+ out[3] = a[3] - b[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.subtract}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.sub = vec4.subtract;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.multiply = function(out, a, b) {
|
|
|
+ out[0] = a[0] * b[0];
|
|
|
+ out[1] = a[1] * b[1];
|
|
|
+ out[2] = a[2] * b[2];
|
|
|
+ out[3] = a[3] * b[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.mul = vec4.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Divides two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.divide = function(out, a, b) {
|
|
|
+ out[0] = a[0] / b[0];
|
|
|
+ out[1] = a[1] / b[1];
|
|
|
+ out[2] = a[2] / b[2];
|
|
|
+ out[3] = a[3] / b[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.divide}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.div = vec4.divide;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the minimum of two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.min = function(out, a, b) {
|
|
|
+ out[0] = Math.min(a[0], b[0]);
|
|
|
+ out[1] = Math.min(a[1], b[1]);
|
|
|
+ out[2] = Math.min(a[2], b[2]);
|
|
|
+ out[3] = Math.min(a[3], b[3]);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the maximum of two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.max = function(out, a, b) {
|
|
|
+ out[0] = Math.max(a[0], b[0]);
|
|
|
+ out[1] = Math.max(a[1], b[1]);
|
|
|
+ out[2] = Math.max(a[2], b[2]);
|
|
|
+ out[3] = Math.max(a[3], b[3]);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales a vec4 by a scalar number
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the vector to scale
|
|
|
+ * @param {Number} b amount to scale the vector by
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.scale = function(out, a, b) {
|
|
|
+ out[0] = a[0] * b;
|
|
|
+ out[1] = a[1] * b;
|
|
|
+ out[2] = a[2] * b;
|
|
|
+ out[3] = a[3] * b;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Adds two vec4's after scaling the second operand by a scalar value
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @param {Number} scale the amount to scale b by before adding
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.scaleAndAdd = function(out, a, b, scale) {
|
|
|
+ out[0] = a[0] + (b[0] * scale);
|
|
|
+ out[1] = a[1] + (b[1] * scale);
|
|
|
+ out[2] = a[2] + (b[2] * scale);
|
|
|
+ out[3] = a[3] + (b[3] * scale);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the euclidian distance between two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {Number} distance between a and b
|
|
|
+ */
|
|
|
+vec4.distance = function(a, b) {
|
|
|
+ var x = b[0] - a[0],
|
|
|
+ y = b[1] - a[1],
|
|
|
+ z = b[2] - a[2],
|
|
|
+ w = b[3] - a[3];
|
|
|
+ return Math.sqrt(x*x + y*y + z*z + w*w);
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.distance}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.dist = vec4.distance;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the squared euclidian distance between two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {Number} squared distance between a and b
|
|
|
+ */
|
|
|
+vec4.squaredDistance = function(a, b) {
|
|
|
+ var x = b[0] - a[0],
|
|
|
+ y = b[1] - a[1],
|
|
|
+ z = b[2] - a[2],
|
|
|
+ w = b[3] - a[3];
|
|
|
+ return x*x + y*y + z*z + w*w;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.squaredDistance}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.sqrDist = vec4.squaredDistance;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the length of a vec4
|
|
|
+ *
|
|
|
+ * @param {vec4} a vector to calculate length of
|
|
|
+ * @returns {Number} length of a
|
|
|
+ */
|
|
|
+vec4.length = function (a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2],
|
|
|
+ w = a[3];
|
|
|
+ return Math.sqrt(x*x + y*y + z*z + w*w);
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.length}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.len = vec4.length;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the squared length of a vec4
|
|
|
+ *
|
|
|
+ * @param {vec4} a vector to calculate squared length of
|
|
|
+ * @returns {Number} squared length of a
|
|
|
+ */
|
|
|
+vec4.squaredLength = function (a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2],
|
|
|
+ w = a[3];
|
|
|
+ return x*x + y*y + z*z + w*w;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link vec4.squaredLength}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.sqrLen = vec4.squaredLength;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Negates the components of a vec4
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a vector to negate
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.negate = function(out, a) {
|
|
|
+ out[0] = -a[0];
|
|
|
+ out[1] = -a[1];
|
|
|
+ out[2] = -a[2];
|
|
|
+ out[3] = -a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns the inverse of the components of a vec4
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a vector to invert
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.inverse = function(out, a) {
|
|
|
+ out[0] = 1.0 / a[0];
|
|
|
+ out[1] = 1.0 / a[1];
|
|
|
+ out[2] = 1.0 / a[2];
|
|
|
+ out[3] = 1.0 / a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Normalize a vec4
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a vector to normalize
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.normalize = function(out, a) {
|
|
|
+ var x = a[0],
|
|
|
+ y = a[1],
|
|
|
+ z = a[2],
|
|
|
+ w = a[3];
|
|
|
+ var len = x*x + y*y + z*z + w*w;
|
|
|
+ if (len > 0) {
|
|
|
+ len = 1 / Math.sqrt(len);
|
|
|
+ out[0] = a[0] * len;
|
|
|
+ out[1] = a[1] * len;
|
|
|
+ out[2] = a[2] * len;
|
|
|
+ out[3] = a[3] * len;
|
|
|
+ }
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the dot product of two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @returns {Number} dot product of a and b
|
|
|
+ */
|
|
|
+vec4.dot = function (a, b) {
|
|
|
+ return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Performs a linear interpolation between two vec4's
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the first operand
|
|
|
+ * @param {vec4} b the second operand
|
|
|
+ * @param {Number} t interpolation amount between the two inputs
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.lerp = function (out, a, b, t) {
|
|
|
+ var ax = a[0],
|
|
|
+ ay = a[1],
|
|
|
+ az = a[2],
|
|
|
+ aw = a[3];
|
|
|
+ out[0] = ax + t * (b[0] - ax);
|
|
|
+ out[1] = ay + t * (b[1] - ay);
|
|
|
+ out[2] = az + t * (b[2] - az);
|
|
|
+ out[3] = aw + t * (b[3] - aw);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a random vector with the given scale
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.random = function (out, scale) {
|
|
|
+ scale = scale || 1.0;
|
|
|
+
|
|
|
+ //TODO: This is a pretty awful way of doing this. Find something better.
|
|
|
+ out[0] = GLMAT_RANDOM();
|
|
|
+ out[1] = GLMAT_RANDOM();
|
|
|
+ out[2] = GLMAT_RANDOM();
|
|
|
+ out[3] = GLMAT_RANDOM();
|
|
|
+ vec4.normalize(out, out);
|
|
|
+ vec4.scale(out, out, scale);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec4 with a mat4.
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the vector to transform
|
|
|
+ * @param {mat4} m matrix to transform with
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.transformMat4 = function(out, a, m) {
|
|
|
+ var x = a[0], y = a[1], z = a[2], w = a[3];
|
|
|
+ out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
|
|
|
+ out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
|
|
|
+ out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
|
|
|
+ out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transforms the vec4 with a quat
|
|
|
+ *
|
|
|
+ * @param {vec4} out the receiving vector
|
|
|
+ * @param {vec4} a the vector to transform
|
|
|
+ * @param {quat} q quaternion to transform with
|
|
|
+ * @returns {vec4} out
|
|
|
+ */
|
|
|
+vec4.transformQuat = function(out, a, q) {
|
|
|
+ var x = a[0], y = a[1], z = a[2],
|
|
|
+ qx = q[0], qy = q[1], qz = q[2], qw = q[3],
|
|
|
+
|
|
|
+ // calculate quat * vec
|
|
|
+ ix = qw * x + qy * z - qz * y,
|
|
|
+ iy = qw * y + qz * x - qx * z,
|
|
|
+ iz = qw * z + qx * y - qy * x,
|
|
|
+ iw = -qx * x - qy * y - qz * z;
|
|
|
+
|
|
|
+ // calculate result * inverse quat
|
|
|
+ out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
|
|
|
+ out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
|
|
|
+ out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Perform some operation over an array of vec4s.
|
|
|
+ *
|
|
|
+ * @param {Array} a the array of vectors to iterate over
|
|
|
+ * @param {Number} stride Number of elements between the start of each vec4. If 0 assumes tightly packed
|
|
|
+ * @param {Number} offset Number of elements to skip at the beginning of the array
|
|
|
+ * @param {Number} count Number of vec4s to iterate over. If 0 iterates over entire array
|
|
|
+ * @param {Function} fn Function to call for each vector in the array
|
|
|
+ * @param {Object} [arg] additional argument to pass to fn
|
|
|
+ * @returns {Array} a
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+vec4.forEach = (function() {
|
|
|
+ var vec = vec4.create();
|
|
|
+
|
|
|
+ return function(a, stride, offset, count, fn, arg) {
|
|
|
+ var i, l;
|
|
|
+ if(!stride) {
|
|
|
+ stride = 4;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(!offset) {
|
|
|
+ offset = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ if(count) {
|
|
|
+ l = Math.min((count * stride) + offset, a.length);
|
|
|
+ } else {
|
|
|
+ l = a.length;
|
|
|
+ }
|
|
|
+
|
|
|
+ for(i = offset; i < l; i += stride) {
|
|
|
+ vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2]; vec[3] = a[i+3];
|
|
|
+ fn(vec, vec, arg);
|
|
|
+ a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2]; a[i+3] = vec[3];
|
|
|
+ }
|
|
|
+
|
|
|
+ return a;
|
|
|
+ };
|
|
|
+})();
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a vector
|
|
|
+ *
|
|
|
+ * @param {vec4} vec vector to represent as a string
|
|
|
+ * @returns {String} string representation of the vector
|
|
|
+ */
|
|
|
+vec4.str = function (a) {
|
|
|
+ return 'vec4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.vec4 = vec4;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class 2x2 Matrix
|
|
|
+ * @name mat2
|
|
|
+ */
|
|
|
+
|
|
|
+var mat2 = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new identity mat2
|
|
|
+ *
|
|
|
+ * @returns {mat2} a new 2x2 matrix
|
|
|
+ */
|
|
|
+mat2.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new mat2 initialized with values from an existing matrix
|
|
|
+ *
|
|
|
+ * @param {mat2} a matrix to clone
|
|
|
+ * @returns {mat2} a new 2x2 matrix
|
|
|
+ */
|
|
|
+mat2.clone = function(a) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one mat2 to another
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the source matrix
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.copy = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set a mat2 to the identity matrix
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.identity = function(out) {
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transpose the values of a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the source matrix
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.transpose = function(out, a) {
|
|
|
+ // If we are transposing ourselves we can skip a few steps but have to cache some values
|
|
|
+ if (out === a) {
|
|
|
+ var a1 = a[1];
|
|
|
+ out[1] = a[2];
|
|
|
+ out[2] = a1;
|
|
|
+ } else {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[2];
|
|
|
+ out[2] = a[1];
|
|
|
+ out[3] = a[3];
|
|
|
+ }
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Inverts a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the source matrix
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.invert = function(out, a) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3],
|
|
|
+
|
|
|
+ // Calculate the determinant
|
|
|
+ det = a0 * a3 - a2 * a1;
|
|
|
+
|
|
|
+ if (!det) {
|
|
|
+ return null;
|
|
|
+ }
|
|
|
+ det = 1.0 / det;
|
|
|
+
|
|
|
+ out[0] = a3 * det;
|
|
|
+ out[1] = -a1 * det;
|
|
|
+ out[2] = -a2 * det;
|
|
|
+ out[3] = a0 * det;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the adjugate of a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the source matrix
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.adjoint = function(out, a) {
|
|
|
+ // Caching this value is nessecary if out == a
|
|
|
+ var a0 = a[0];
|
|
|
+ out[0] = a[3];
|
|
|
+ out[1] = -a[1];
|
|
|
+ out[2] = -a[2];
|
|
|
+ out[3] = a0;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the determinant of a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} a the source matrix
|
|
|
+ * @returns {Number} determinant of a
|
|
|
+ */
|
|
|
+mat2.determinant = function (a) {
|
|
|
+ return a[0] * a[3] - a[2] * a[1];
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two mat2's
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the first operand
|
|
|
+ * @param {mat2} b the second operand
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.multiply = function (out, a, b) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
|
|
|
+ var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
|
|
|
+ out[0] = a0 * b0 + a2 * b1;
|
|
|
+ out[1] = a1 * b0 + a3 * b1;
|
|
|
+ out[2] = a0 * b2 + a2 * b3;
|
|
|
+ out[3] = a1 * b2 + a3 * b3;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link mat2.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+mat2.mul = mat2.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a mat2 by the given angle
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat2} out
|
|
|
+ */
|
|
|
+mat2.rotate = function (out, a, rad) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3],
|
|
|
+ s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad);
|
|
|
+ out[0] = a0 * c + a2 * s;
|
|
|
+ out[1] = a1 * c + a3 * s;
|
|
|
+ out[2] = a0 * -s + a2 * c;
|
|
|
+ out[3] = a1 * -s + a3 * c;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales the mat2 by the dimensions in the given vec2
|
|
|
+ *
|
|
|
+ * @param {mat2} out the receiving matrix
|
|
|
+ * @param {mat2} a the matrix to rotate
|
|
|
+ * @param {vec2} v the vec2 to scale the matrix by
|
|
|
+ * @returns {mat2} out
|
|
|
+ **/
|
|
|
+mat2.scale = function(out, a, v) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3],
|
|
|
+ v0 = v[0], v1 = v[1];
|
|
|
+ out[0] = a0 * v0;
|
|
|
+ out[1] = a1 * v0;
|
|
|
+ out[2] = a2 * v1;
|
|
|
+ out[3] = a3 * v1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} mat matrix to represent as a string
|
|
|
+ * @returns {String} string representation of the matrix
|
|
|
+ */
|
|
|
+mat2.str = function (a) {
|
|
|
+ return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns Frobenius norm of a mat2
|
|
|
+ *
|
|
|
+ * @param {mat2} a the matrix to calculate Frobenius norm of
|
|
|
+ * @returns {Number} Frobenius norm
|
|
|
+ */
|
|
|
+mat2.frob = function (a) {
|
|
|
+ return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2)))
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix
|
|
|
+ * @param {mat2} L the lower triangular matrix
|
|
|
+ * @param {mat2} D the diagonal matrix
|
|
|
+ * @param {mat2} U the upper triangular matrix
|
|
|
+ * @param {mat2} a the input matrix to factorize
|
|
|
+ */
|
|
|
+
|
|
|
+mat2.LDU = function (L, D, U, a) {
|
|
|
+ L[2] = a[2]/a[0];
|
|
|
+ U[0] = a[0];
|
|
|
+ U[1] = a[1];
|
|
|
+ U[3] = a[3] - L[2] * U[1];
|
|
|
+ return [L, D, U];
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.mat2 = mat2;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class 2x3 Matrix
|
|
|
+ * @name mat2d
|
|
|
+ *
|
|
|
+ * @description
|
|
|
+ * A mat2d contains six elements defined as:
|
|
|
+ * <pre>
|
|
|
+ * [a, c, tx,
|
|
|
+ * b, d, ty]
|
|
|
+ * </pre>
|
|
|
+ * This is a short form for the 3x3 matrix:
|
|
|
+ * <pre>
|
|
|
+ * [a, c, tx,
|
|
|
+ * b, d, ty,
|
|
|
+ * 0, 0, 1]
|
|
|
+ * </pre>
|
|
|
+ * The last row is ignored so the array is shorter and operations are faster.
|
|
|
+ */
|
|
|
+
|
|
|
+var mat2d = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new identity mat2d
|
|
|
+ *
|
|
|
+ * @returns {mat2d} a new 2x3 matrix
|
|
|
+ */
|
|
|
+mat2d.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(6);
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ out[4] = 0;
|
|
|
+ out[5] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new mat2d initialized with values from an existing matrix
|
|
|
+ *
|
|
|
+ * @param {mat2d} a matrix to clone
|
|
|
+ * @returns {mat2d} a new 2x3 matrix
|
|
|
+ */
|
|
|
+mat2d.clone = function(a) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(6);
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[5];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one mat2d to another
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the source matrix
|
|
|
+ * @returns {mat2d} out
|
|
|
+ */
|
|
|
+mat2d.copy = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[5];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set a mat2d to the identity matrix
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @returns {mat2d} out
|
|
|
+ */
|
|
|
+mat2d.identity = function(out) {
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ out[4] = 0;
|
|
|
+ out[5] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Inverts a mat2d
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the source matrix
|
|
|
+ * @returns {mat2d} out
|
|
|
+ */
|
|
|
+mat2d.invert = function(out, a) {
|
|
|
+ var aa = a[0], ab = a[1], ac = a[2], ad = a[3],
|
|
|
+ atx = a[4], aty = a[5];
|
|
|
+
|
|
|
+ var det = aa * ad - ab * ac;
|
|
|
+ if(!det){
|
|
|
+ return null;
|
|
|
+ }
|
|
|
+ det = 1.0 / det;
|
|
|
+
|
|
|
+ out[0] = ad * det;
|
|
|
+ out[1] = -ab * det;
|
|
|
+ out[2] = -ac * det;
|
|
|
+ out[3] = aa * det;
|
|
|
+ out[4] = (ac * aty - ad * atx) * det;
|
|
|
+ out[5] = (ab * atx - aa * aty) * det;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the determinant of a mat2d
|
|
|
+ *
|
|
|
+ * @param {mat2d} a the source matrix
|
|
|
+ * @returns {Number} determinant of a
|
|
|
+ */
|
|
|
+mat2d.determinant = function (a) {
|
|
|
+ return a[0] * a[3] - a[1] * a[2];
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two mat2d's
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the first operand
|
|
|
+ * @param {mat2d} b the second operand
|
|
|
+ * @returns {mat2d} out
|
|
|
+ */
|
|
|
+mat2d.multiply = function (out, a, b) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5],
|
|
|
+ b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5];
|
|
|
+ out[0] = a0 * b0 + a2 * b1;
|
|
|
+ out[1] = a1 * b0 + a3 * b1;
|
|
|
+ out[2] = a0 * b2 + a2 * b3;
|
|
|
+ out[3] = a1 * b2 + a3 * b3;
|
|
|
+ out[4] = a0 * b4 + a2 * b5 + a4;
|
|
|
+ out[5] = a1 * b4 + a3 * b5 + a5;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link mat2d.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+mat2d.mul = mat2d.multiply;
|
|
|
+
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a mat2d by the given angle
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat2d} out
|
|
|
+ */
|
|
|
+mat2d.rotate = function (out, a, rad) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5],
|
|
|
+ s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad);
|
|
|
+ out[0] = a0 * c + a2 * s;
|
|
|
+ out[1] = a1 * c + a3 * s;
|
|
|
+ out[2] = a0 * -s + a2 * c;
|
|
|
+ out[3] = a1 * -s + a3 * c;
|
|
|
+ out[4] = a4;
|
|
|
+ out[5] = a5;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales the mat2d by the dimensions in the given vec2
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the matrix to translate
|
|
|
+ * @param {vec2} v the vec2 to scale the matrix by
|
|
|
+ * @returns {mat2d} out
|
|
|
+ **/
|
|
|
+mat2d.scale = function(out, a, v) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5],
|
|
|
+ v0 = v[0], v1 = v[1];
|
|
|
+ out[0] = a0 * v0;
|
|
|
+ out[1] = a1 * v0;
|
|
|
+ out[2] = a2 * v1;
|
|
|
+ out[3] = a3 * v1;
|
|
|
+ out[4] = a4;
|
|
|
+ out[5] = a5;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Translates the mat2d by the dimensions in the given vec2
|
|
|
+ *
|
|
|
+ * @param {mat2d} out the receiving matrix
|
|
|
+ * @param {mat2d} a the matrix to translate
|
|
|
+ * @param {vec2} v the vec2 to translate the matrix by
|
|
|
+ * @returns {mat2d} out
|
|
|
+ **/
|
|
|
+mat2d.translate = function(out, a, v) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5],
|
|
|
+ v0 = v[0], v1 = v[1];
|
|
|
+ out[0] = a0;
|
|
|
+ out[1] = a1;
|
|
|
+ out[2] = a2;
|
|
|
+ out[3] = a3;
|
|
|
+ out[4] = a0 * v0 + a2 * v1 + a4;
|
|
|
+ out[5] = a1 * v0 + a3 * v1 + a5;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a mat2d
|
|
|
+ *
|
|
|
+ * @param {mat2d} a matrix to represent as a string
|
|
|
+ * @returns {String} string representation of the matrix
|
|
|
+ */
|
|
|
+mat2d.str = function (a) {
|
|
|
+ return 'mat2d(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' +
|
|
|
+ a[3] + ', ' + a[4] + ', ' + a[5] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns Frobenius norm of a mat2d
|
|
|
+ *
|
|
|
+ * @param {mat2d} a the matrix to calculate Frobenius norm of
|
|
|
+ * @returns {Number} Frobenius norm
|
|
|
+ */
|
|
|
+mat2d.frob = function (a) {
|
|
|
+ return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + 1))
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.mat2d = mat2d;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class 3x3 Matrix
|
|
|
+ * @name mat3
|
|
|
+ */
|
|
|
+
|
|
|
+var mat3 = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new identity mat3
|
|
|
+ *
|
|
|
+ * @returns {mat3} a new 3x3 matrix
|
|
|
+ */
|
|
|
+mat3.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(9);
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = 1;
|
|
|
+ out[5] = 0;
|
|
|
+ out[6] = 0;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copies the upper-left 3x3 values into the given mat3.
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving 3x3 matrix
|
|
|
+ * @param {mat4} a the source 4x4 matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.fromMat4 = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[4];
|
|
|
+ out[4] = a[5];
|
|
|
+ out[5] = a[6];
|
|
|
+ out[6] = a[8];
|
|
|
+ out[7] = a[9];
|
|
|
+ out[8] = a[10];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new mat3 initialized with values from an existing matrix
|
|
|
+ *
|
|
|
+ * @param {mat3} a matrix to clone
|
|
|
+ * @returns {mat3} a new 3x3 matrix
|
|
|
+ */
|
|
|
+mat3.clone = function(a) {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(9);
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[5];
|
|
|
+ out[6] = a[6];
|
|
|
+ out[7] = a[7];
|
|
|
+ out[8] = a[8];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one mat3 to another
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the source matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.copy = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[5];
|
|
|
+ out[6] = a[6];
|
|
|
+ out[7] = a[7];
|
|
|
+ out[8] = a[8];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set a mat3 to the identity matrix
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.identity = function(out) {
|
|
|
+ out[0] = 1;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = 1;
|
|
|
+ out[5] = 0;
|
|
|
+ out[6] = 0;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Transpose the values of a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the source matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.transpose = function(out, a) {
|
|
|
+ // If we are transposing ourselves we can skip a few steps but have to cache some values
|
|
|
+ if (out === a) {
|
|
|
+ var a01 = a[1], a02 = a[2], a12 = a[5];
|
|
|
+ out[1] = a[3];
|
|
|
+ out[2] = a[6];
|
|
|
+ out[3] = a01;
|
|
|
+ out[5] = a[7];
|
|
|
+ out[6] = a02;
|
|
|
+ out[7] = a12;
|
|
|
+ } else {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[3];
|
|
|
+ out[2] = a[6];
|
|
|
+ out[3] = a[1];
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[7];
|
|
|
+ out[6] = a[2];
|
|
|
+ out[7] = a[5];
|
|
|
+ out[8] = a[8];
|
|
|
+ }
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Inverts a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the source matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.invert = function(out, a) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8],
|
|
|
+
|
|
|
+ b01 = a22 * a11 - a12 * a21,
|
|
|
+ b11 = -a22 * a10 + a12 * a20,
|
|
|
+ b21 = a21 * a10 - a11 * a20,
|
|
|
+
|
|
|
+ // Calculate the determinant
|
|
|
+ det = a00 * b01 + a01 * b11 + a02 * b21;
|
|
|
+
|
|
|
+ if (!det) {
|
|
|
+ return null;
|
|
|
+ }
|
|
|
+ det = 1.0 / det;
|
|
|
+
|
|
|
+ out[0] = b01 * det;
|
|
|
+ out[1] = (-a22 * a01 + a02 * a21) * det;
|
|
|
+ out[2] = (a12 * a01 - a02 * a11) * det;
|
|
|
+ out[3] = b11 * det;
|
|
|
+ out[4] = (a22 * a00 - a02 * a20) * det;
|
|
|
+ out[5] = (-a12 * a00 + a02 * a10) * det;
|
|
|
+ out[6] = b21 * det;
|
|
|
+ out[7] = (-a21 * a00 + a01 * a20) * det;
|
|
|
+ out[8] = (a11 * a00 - a01 * a10) * det;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the adjugate of a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the source matrix
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.adjoint = function(out, a) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8];
|
|
|
+
|
|
|
+ out[0] = (a11 * a22 - a12 * a21);
|
|
|
+ out[1] = (a02 * a21 - a01 * a22);
|
|
|
+ out[2] = (a01 * a12 - a02 * a11);
|
|
|
+ out[3] = (a12 * a20 - a10 * a22);
|
|
|
+ out[4] = (a00 * a22 - a02 * a20);
|
|
|
+ out[5] = (a02 * a10 - a00 * a12);
|
|
|
+ out[6] = (a10 * a21 - a11 * a20);
|
|
|
+ out[7] = (a01 * a20 - a00 * a21);
|
|
|
+ out[8] = (a00 * a11 - a01 * a10);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the determinant of a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} a the source matrix
|
|
|
+ * @returns {Number} determinant of a
|
|
|
+ */
|
|
|
+mat3.determinant = function (a) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8];
|
|
|
+
|
|
|
+ return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two mat3's
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the first operand
|
|
|
+ * @param {mat3} b the second operand
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.multiply = function (out, a, b) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8],
|
|
|
+
|
|
|
+ b00 = b[0], b01 = b[1], b02 = b[2],
|
|
|
+ b10 = b[3], b11 = b[4], b12 = b[5],
|
|
|
+ b20 = b[6], b21 = b[7], b22 = b[8];
|
|
|
+
|
|
|
+ out[0] = b00 * a00 + b01 * a10 + b02 * a20;
|
|
|
+ out[1] = b00 * a01 + b01 * a11 + b02 * a21;
|
|
|
+ out[2] = b00 * a02 + b01 * a12 + b02 * a22;
|
|
|
+
|
|
|
+ out[3] = b10 * a00 + b11 * a10 + b12 * a20;
|
|
|
+ out[4] = b10 * a01 + b11 * a11 + b12 * a21;
|
|
|
+ out[5] = b10 * a02 + b11 * a12 + b12 * a22;
|
|
|
+
|
|
|
+ out[6] = b20 * a00 + b21 * a10 + b22 * a20;
|
|
|
+ out[7] = b20 * a01 + b21 * a11 + b22 * a21;
|
|
|
+ out[8] = b20 * a02 + b21 * a12 + b22 * a22;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link mat3.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+mat3.mul = mat3.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Translate a mat3 by the given vector
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the matrix to translate
|
|
|
+ * @param {vec2} v vector to translate by
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.translate = function(out, a, v) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8],
|
|
|
+ x = v[0], y = v[1];
|
|
|
+
|
|
|
+ out[0] = a00;
|
|
|
+ out[1] = a01;
|
|
|
+ out[2] = a02;
|
|
|
+
|
|
|
+ out[3] = a10;
|
|
|
+ out[4] = a11;
|
|
|
+ out[5] = a12;
|
|
|
+
|
|
|
+ out[6] = x * a00 + y * a10 + a20;
|
|
|
+ out[7] = x * a01 + y * a11 + a21;
|
|
|
+ out[8] = x * a02 + y * a12 + a22;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a mat3 by the given angle
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat3} out
|
|
|
+ */
|
|
|
+mat3.rotate = function (out, a, rad) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2],
|
|
|
+ a10 = a[3], a11 = a[4], a12 = a[5],
|
|
|
+ a20 = a[6], a21 = a[7], a22 = a[8],
|
|
|
+
|
|
|
+ s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = c * a00 + s * a10;
|
|
|
+ out[1] = c * a01 + s * a11;
|
|
|
+ out[2] = c * a02 + s * a12;
|
|
|
+
|
|
|
+ out[3] = c * a10 - s * a00;
|
|
|
+ out[4] = c * a11 - s * a01;
|
|
|
+ out[5] = c * a12 - s * a02;
|
|
|
+
|
|
|
+ out[6] = a20;
|
|
|
+ out[7] = a21;
|
|
|
+ out[8] = a22;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales the mat3 by the dimensions in the given vec2
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat3} a the matrix to rotate
|
|
|
+ * @param {vec2} v the vec2 to scale the matrix by
|
|
|
+ * @returns {mat3} out
|
|
|
+ **/
|
|
|
+mat3.scale = function(out, a, v) {
|
|
|
+ var x = v[0], y = v[1];
|
|
|
+
|
|
|
+ out[0] = x * a[0];
|
|
|
+ out[1] = x * a[1];
|
|
|
+ out[2] = x * a[2];
|
|
|
+
|
|
|
+ out[3] = y * a[3];
|
|
|
+ out[4] = y * a[4];
|
|
|
+ out[5] = y * a[5];
|
|
|
+
|
|
|
+ out[6] = a[6];
|
|
|
+ out[7] = a[7];
|
|
|
+ out[8] = a[8];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copies the values from a mat2d into a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} out the receiving matrix
|
|
|
+ * @param {mat2d} a the matrix to copy
|
|
|
+ * @returns {mat3} out
|
|
|
+ **/
|
|
|
+mat3.fromMat2d = function(out, a) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = 0;
|
|
|
+
|
|
|
+ out[3] = a[2];
|
|
|
+ out[4] = a[3];
|
|
|
+ out[5] = 0;
|
|
|
+
|
|
|
+ out[6] = a[4];
|
|
|
+ out[7] = a[5];
|
|
|
+ out[8] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+* Calculates a 3x3 matrix from the given quaternion
|
|
|
+*
|
|
|
+* @param {mat3} out mat3 receiving operation result
|
|
|
+* @param {quat} q Quaternion to create matrix from
|
|
|
+*
|
|
|
+* @returns {mat3} out
|
|
|
+*/
|
|
|
+mat3.fromQuat = function (out, q) {
|
|
|
+ var x = q[0], y = q[1], z = q[2], w = q[3],
|
|
|
+ x2 = x + x,
|
|
|
+ y2 = y + y,
|
|
|
+ z2 = z + z,
|
|
|
+
|
|
|
+ xx = x * x2,
|
|
|
+ yx = y * x2,
|
|
|
+ yy = y * y2,
|
|
|
+ zx = z * x2,
|
|
|
+ zy = z * y2,
|
|
|
+ zz = z * z2,
|
|
|
+ wx = w * x2,
|
|
|
+ wy = w * y2,
|
|
|
+ wz = w * z2;
|
|
|
+
|
|
|
+ out[0] = 1 - yy - zz;
|
|
|
+ out[3] = yx - wz;
|
|
|
+ out[6] = zx + wy;
|
|
|
+
|
|
|
+ out[1] = yx + wz;
|
|
|
+ out[4] = 1 - xx - zz;
|
|
|
+ out[7] = zy - wx;
|
|
|
+
|
|
|
+ out[2] = zx - wy;
|
|
|
+ out[5] = zy + wx;
|
|
|
+ out[8] = 1 - xx - yy;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+* Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
|
|
|
+*
|
|
|
+* @param {mat3} out mat3 receiving operation result
|
|
|
+* @param {mat4} a Mat4 to derive the normal matrix from
|
|
|
+*
|
|
|
+* @returns {mat3} out
|
|
|
+*/
|
|
|
+mat3.normalFromMat4 = function (out, a) {
|
|
|
+ var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
|
|
|
+ a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
|
|
|
+ a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
|
|
|
+ a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
|
|
|
+
|
|
|
+ b00 = a00 * a11 - a01 * a10,
|
|
|
+ b01 = a00 * a12 - a02 * a10,
|
|
|
+ b02 = a00 * a13 - a03 * a10,
|
|
|
+ b03 = a01 * a12 - a02 * a11,
|
|
|
+ b04 = a01 * a13 - a03 * a11,
|
|
|
+ b05 = a02 * a13 - a03 * a12,
|
|
|
+ b06 = a20 * a31 - a21 * a30,
|
|
|
+ b07 = a20 * a32 - a22 * a30,
|
|
|
+ b08 = a20 * a33 - a23 * a30,
|
|
|
+ b09 = a21 * a32 - a22 * a31,
|
|
|
+ b10 = a21 * a33 - a23 * a31,
|
|
|
+ b11 = a22 * a33 - a23 * a32,
|
|
|
+
|
|
|
+ // Calculate the determinant
|
|
|
+ det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
|
|
|
+
|
|
|
+ if (!det) {
|
|
|
+ return null;
|
|
|
+ }
|
|
|
+ det = 1.0 / det;
|
|
|
+
|
|
|
+ out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
|
|
|
+ out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
|
|
|
+ out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
|
|
|
+
|
|
|
+ out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
|
|
|
+ out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
|
|
|
+ out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
|
|
|
+
|
|
|
+ out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
|
|
|
+ out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
|
|
|
+ out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} mat matrix to represent as a string
|
|
|
+ * @returns {String} string representation of the matrix
|
|
|
+ */
|
|
|
+mat3.str = function (a) {
|
|
|
+ return 'mat3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' +
|
|
|
+ a[3] + ', ' + a[4] + ', ' + a[5] + ', ' +
|
|
|
+ a[6] + ', ' + a[7] + ', ' + a[8] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns Frobenius norm of a mat3
|
|
|
+ *
|
|
|
+ * @param {mat3} a the matrix to calculate Frobenius norm of
|
|
|
+ * @returns {Number} Frobenius norm
|
|
|
+ */
|
|
|
+mat3.frob = function (a) {
|
|
|
+ return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2)))
|
|
|
+};
|
|
|
+
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.mat3 = mat3;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
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+ list of conditions and the following disclaimer.
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+ * Redistributions in binary form must reproduce the above copyright notice,
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+ this list of conditions and the following disclaimer in the documentation
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+ and/or other materials provided with the distribution.
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+
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+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
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+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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+
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+/**
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+ * @class 4x4 Matrix
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+ * @name mat4
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+ */
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+
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+var mat4 = {};
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+
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+/**
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+ * Creates a new identity mat4
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+ *
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+ * @returns {mat4} a new 4x4 matrix
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+ */
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+mat4.create = function() {
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+ var out = new GLMAT_ARRAY_TYPE(16);
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+ out[0] = 1;
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+ out[1] = 0;
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+ out[2] = 0;
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+ out[3] = 0;
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+ out[4] = 0;
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+ out[5] = 1;
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+ out[6] = 0;
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+ out[7] = 0;
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+ out[8] = 0;
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+ out[9] = 0;
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+ out[10] = 1;
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+ out[11] = 0;
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+ out[12] = 0;
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+ out[13] = 0;
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+ out[14] = 0;
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+ out[15] = 1;
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+ return out;
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+};
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+
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+/**
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+ * Creates a new mat4 initialized with values from an existing matrix
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+ *
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+ * @param {mat4} a matrix to clone
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+ * @returns {mat4} a new 4x4 matrix
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+ */
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+mat4.clone = function(a) {
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+ var out = new GLMAT_ARRAY_TYPE(16);
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+ out[0] = a[0];
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+ out[1] = a[1];
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+ out[2] = a[2];
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+ out[3] = a[3];
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+ out[4] = a[4];
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+ out[5] = a[5];
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+ out[6] = a[6];
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+ out[7] = a[7];
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+ out[8] = a[8];
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+ out[9] = a[9];
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+ out[10] = a[10];
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+ out[11] = a[11];
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+ out[12] = a[12];
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+ out[13] = a[13];
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+ out[14] = a[14];
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+ out[15] = a[15];
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+ return out;
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+};
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+
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+/**
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+ * Copy the values from one mat4 to another
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+ *
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+ * @param {mat4} out the receiving matrix
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+ * @param {mat4} a the source matrix
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+ * @returns {mat4} out
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+ */
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+mat4.copy = function(out, a) {
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+ out[0] = a[0];
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+ out[1] = a[1];
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+ out[2] = a[2];
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+ out[3] = a[3];
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+ out[4] = a[4];
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+ out[5] = a[5];
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+ out[6] = a[6];
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+ out[7] = a[7];
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+ out[8] = a[8];
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+ out[9] = a[9];
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+ out[10] = a[10];
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+ out[11] = a[11];
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+ out[12] = a[12];
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+ out[13] = a[13];
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+ out[14] = a[14];
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+ out[15] = a[15];
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+ return out;
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+};
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+
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+/**
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+ * Set a mat4 to the identity matrix
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+ *
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+ * @param {mat4} out the receiving matrix
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+ * @returns {mat4} out
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+ */
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+mat4.identity = function(out) {
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+ out[0] = 1;
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+ out[1] = 0;
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+ out[2] = 0;
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+ out[3] = 0;
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+ out[4] = 0;
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+ out[5] = 1;
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+ out[6] = 0;
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+ out[7] = 0;
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+ out[8] = 0;
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+ out[9] = 0;
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+ out[10] = 1;
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+ out[11] = 0;
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+ out[12] = 0;
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+ out[13] = 0;
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+ out[14] = 0;
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+ out[15] = 1;
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+ return out;
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+};
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+
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+/**
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+ * Transpose the values of a mat4
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+ *
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+ * @param {mat4} out the receiving matrix
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+ * @param {mat4} a the source matrix
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+ * @returns {mat4} out
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+ */
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+mat4.transpose = function(out, a) {
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+ // If we are transposing ourselves we can skip a few steps but have to cache some values
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+ if (out === a) {
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+ var a01 = a[1], a02 = a[2], a03 = a[3],
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+ a12 = a[6], a13 = a[7],
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+ a23 = a[11];
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+
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+ out[1] = a[4];
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+ out[2] = a[8];
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+ out[3] = a[12];
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+ out[4] = a01;
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+ out[6] = a[9];
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+ out[7] = a[13];
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+ out[8] = a02;
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+ out[9] = a12;
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+ out[11] = a[14];
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+ out[12] = a03;
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+ out[13] = a13;
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+ out[14] = a23;
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+ } else {
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+ out[0] = a[0];
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+ out[1] = a[4];
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+ out[2] = a[8];
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+ out[3] = a[12];
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+ out[4] = a[1];
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+ out[5] = a[5];
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+ out[6] = a[9];
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+ out[7] = a[13];
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+ out[8] = a[2];
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+ out[9] = a[6];
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+ out[10] = a[10];
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+ out[11] = a[14];
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+ out[12] = a[3];
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+ out[13] = a[7];
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+ out[14] = a[11];
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+ out[15] = a[15];
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+ }
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+
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+ return out;
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+};
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+
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+/**
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+ * Inverts a mat4
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+ *
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+ * @param {mat4} out the receiving matrix
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+ * @param {mat4} a the source matrix
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+ * @returns {mat4} out
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+ */
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+mat4.invert = function(out, a) {
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+ var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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+ a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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+ a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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+ a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
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+
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+ b00 = a00 * a11 - a01 * a10,
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+ b01 = a00 * a12 - a02 * a10,
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+ b02 = a00 * a13 - a03 * a10,
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+ b03 = a01 * a12 - a02 * a11,
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+ b04 = a01 * a13 - a03 * a11,
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+ b05 = a02 * a13 - a03 * a12,
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+ b06 = a20 * a31 - a21 * a30,
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+ b07 = a20 * a32 - a22 * a30,
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+ b08 = a20 * a33 - a23 * a30,
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+ b09 = a21 * a32 - a22 * a31,
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+ b10 = a21 * a33 - a23 * a31,
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+ b11 = a22 * a33 - a23 * a32,
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+
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+ // Calculate the determinant
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+ det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
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+
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+ if (!det) {
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+ return null;
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+ }
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+ det = 1.0 / det;
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+
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+ out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
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+ out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
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+ out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
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+ out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
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+ out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
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+ out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
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+ out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
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+ out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
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+ out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
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+ out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
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+ out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
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+ out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
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+ out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
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+ out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
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+ out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
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+ out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
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+
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+ return out;
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+};
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+
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+/**
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+ * Calculates the adjugate of a mat4
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+ *
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+ * @param {mat4} out the receiving matrix
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+ * @param {mat4} a the source matrix
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+ * @returns {mat4} out
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+ */
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+mat4.adjoint = function(out, a) {
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+ var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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+ a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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+ a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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+ a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
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+
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+ out[0] = (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
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+ out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
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+ out[2] = (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
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+ out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
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+ out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
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+ out[5] = (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
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+ out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
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+ out[7] = (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
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+ out[8] = (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
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+ out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
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+ out[10] = (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
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+ out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
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+ out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
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+ out[13] = (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
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+ out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
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+ out[15] = (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));
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+ return out;
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+};
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+
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+/**
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+ * Calculates the determinant of a mat4
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+ *
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+ * @param {mat4} a the source matrix
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+ * @returns {Number} determinant of a
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+ */
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+mat4.determinant = function (a) {
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+ var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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+ a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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+ a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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+ a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
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+
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+ b00 = a00 * a11 - a01 * a10,
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+ b01 = a00 * a12 - a02 * a10,
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+ b02 = a00 * a13 - a03 * a10,
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+ b03 = a01 * a12 - a02 * a11,
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+ b04 = a01 * a13 - a03 * a11,
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+ b05 = a02 * a13 - a03 * a12,
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+ b06 = a20 * a31 - a21 * a30,
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+ b07 = a20 * a32 - a22 * a30,
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+ b08 = a20 * a33 - a23 * a30,
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+ b09 = a21 * a32 - a22 * a31,
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+ b10 = a21 * a33 - a23 * a31,
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+ b11 = a22 * a33 - a23 * a32;
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+
|
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+ // Calculate the determinant
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|
+ return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
|
|
|
+};
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+
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+/**
|
|
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+ * Multiplies two mat4's
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+ *
|
|
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+ * @param {mat4} out the receiving matrix
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+ * @param {mat4} a the first operand
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+ * @param {mat4} b the second operand
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+ * @returns {mat4} out
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+ */
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+mat4.multiply = function (out, a, b) {
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+ var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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+ a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
|
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+ a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
|
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|
+ a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
|
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+
|
|
|
+ // Cache only the current line of the second matrix
|
|
|
+ var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
|
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|
+ out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
|
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|
+ out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
|
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|
+ out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
|
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|
+ out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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+
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+ b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
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|
+ out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
|
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+ out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
|
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|
+ out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
|
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|
+ out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
|
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+
|
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+ b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
|
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+ out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
|
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|
+ out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
|
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|
+ out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
|
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|
+ out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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+
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+ b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
|
|
|
+ out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
|
|
|
+ out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
|
|
|
+ out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
|
|
|
+ out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link mat4.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+mat4.mul = mat4.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Translate a mat4 by the given vector
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to translate
|
|
|
+ * @param {vec3} v vector to translate by
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.translate = function (out, a, v) {
|
|
|
+ var x = v[0], y = v[1], z = v[2],
|
|
|
+ a00, a01, a02, a03,
|
|
|
+ a10, a11, a12, a13,
|
|
|
+ a20, a21, a22, a23;
|
|
|
+
|
|
|
+ if (a === out) {
|
|
|
+ out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
|
|
|
+ out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
|
|
|
+ out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
|
|
|
+ out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
|
|
|
+ } else {
|
|
|
+ a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
|
|
|
+ a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
|
|
|
+ a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
|
|
|
+
|
|
|
+ out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
|
|
|
+ out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
|
|
|
+ out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;
|
|
|
+
|
|
|
+ out[12] = a00 * x + a10 * y + a20 * z + a[12];
|
|
|
+ out[13] = a01 * x + a11 * y + a21 * z + a[13];
|
|
|
+ out[14] = a02 * x + a12 * y + a22 * z + a[14];
|
|
|
+ out[15] = a03 * x + a13 * y + a23 * z + a[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales the mat4 by the dimensions in the given vec3
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to scale
|
|
|
+ * @param {vec3} v the vec3 to scale the matrix by
|
|
|
+ * @returns {mat4} out
|
|
|
+ **/
|
|
|
+mat4.scale = function(out, a, v) {
|
|
|
+ var x = v[0], y = v[1], z = v[2];
|
|
|
+
|
|
|
+ out[0] = a[0] * x;
|
|
|
+ out[1] = a[1] * x;
|
|
|
+ out[2] = a[2] * x;
|
|
|
+ out[3] = a[3] * x;
|
|
|
+ out[4] = a[4] * y;
|
|
|
+ out[5] = a[5] * y;
|
|
|
+ out[6] = a[6] * y;
|
|
|
+ out[7] = a[7] * y;
|
|
|
+ out[8] = a[8] * z;
|
|
|
+ out[9] = a[9] * z;
|
|
|
+ out[10] = a[10] * z;
|
|
|
+ out[11] = a[11] * z;
|
|
|
+ out[12] = a[12];
|
|
|
+ out[13] = a[13];
|
|
|
+ out[14] = a[14];
|
|
|
+ out[15] = a[15];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a mat4 by the given angle
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @param {vec3} axis the axis to rotate around
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.rotate = function (out, a, rad, axis) {
|
|
|
+ var x = axis[0], y = axis[1], z = axis[2],
|
|
|
+ len = Math.sqrt(x * x + y * y + z * z),
|
|
|
+ s, c, t,
|
|
|
+ a00, a01, a02, a03,
|
|
|
+ a10, a11, a12, a13,
|
|
|
+ a20, a21, a22, a23,
|
|
|
+ b00, b01, b02,
|
|
|
+ b10, b11, b12,
|
|
|
+ b20, b21, b22;
|
|
|
+
|
|
|
+ if (Math.abs(len) < GLMAT_EPSILON) { return null; }
|
|
|
+
|
|
|
+ len = 1 / len;
|
|
|
+ x *= len;
|
|
|
+ y *= len;
|
|
|
+ z *= len;
|
|
|
+
|
|
|
+ s = Math.sin(rad);
|
|
|
+ c = Math.cos(rad);
|
|
|
+ t = 1 - c;
|
|
|
+
|
|
|
+ a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
|
|
|
+ a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
|
|
|
+ a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
|
|
|
+
|
|
|
+ // Construct the elements of the rotation matrix
|
|
|
+ b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s;
|
|
|
+ b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s;
|
|
|
+ b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c;
|
|
|
+
|
|
|
+ // Perform rotation-specific matrix multiplication
|
|
|
+ out[0] = a00 * b00 + a10 * b01 + a20 * b02;
|
|
|
+ out[1] = a01 * b00 + a11 * b01 + a21 * b02;
|
|
|
+ out[2] = a02 * b00 + a12 * b01 + a22 * b02;
|
|
|
+ out[3] = a03 * b00 + a13 * b01 + a23 * b02;
|
|
|
+ out[4] = a00 * b10 + a10 * b11 + a20 * b12;
|
|
|
+ out[5] = a01 * b10 + a11 * b11 + a21 * b12;
|
|
|
+ out[6] = a02 * b10 + a12 * b11 + a22 * b12;
|
|
|
+ out[7] = a03 * b10 + a13 * b11 + a23 * b12;
|
|
|
+ out[8] = a00 * b20 + a10 * b21 + a20 * b22;
|
|
|
+ out[9] = a01 * b20 + a11 * b21 + a21 * b22;
|
|
|
+ out[10] = a02 * b20 + a12 * b21 + a22 * b22;
|
|
|
+ out[11] = a03 * b20 + a13 * b21 + a23 * b22;
|
|
|
+
|
|
|
+ if (a !== out) { // If the source and destination differ, copy the unchanged last row
|
|
|
+ out[12] = a[12];
|
|
|
+ out[13] = a[13];
|
|
|
+ out[14] = a[14];
|
|
|
+ out[15] = a[15];
|
|
|
+ }
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a matrix by the given angle around the X axis
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.rotateX = function (out, a, rad) {
|
|
|
+ var s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad),
|
|
|
+ a10 = a[4],
|
|
|
+ a11 = a[5],
|
|
|
+ a12 = a[6],
|
|
|
+ a13 = a[7],
|
|
|
+ a20 = a[8],
|
|
|
+ a21 = a[9],
|
|
|
+ a22 = a[10],
|
|
|
+ a23 = a[11];
|
|
|
+
|
|
|
+ if (a !== out) { // If the source and destination differ, copy the unchanged rows
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ out[12] = a[12];
|
|
|
+ out[13] = a[13];
|
|
|
+ out[14] = a[14];
|
|
|
+ out[15] = a[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ // Perform axis-specific matrix multiplication
|
|
|
+ out[4] = a10 * c + a20 * s;
|
|
|
+ out[5] = a11 * c + a21 * s;
|
|
|
+ out[6] = a12 * c + a22 * s;
|
|
|
+ out[7] = a13 * c + a23 * s;
|
|
|
+ out[8] = a20 * c - a10 * s;
|
|
|
+ out[9] = a21 * c - a11 * s;
|
|
|
+ out[10] = a22 * c - a12 * s;
|
|
|
+ out[11] = a23 * c - a13 * s;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a matrix by the given angle around the Y axis
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.rotateY = function (out, a, rad) {
|
|
|
+ var s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad),
|
|
|
+ a00 = a[0],
|
|
|
+ a01 = a[1],
|
|
|
+ a02 = a[2],
|
|
|
+ a03 = a[3],
|
|
|
+ a20 = a[8],
|
|
|
+ a21 = a[9],
|
|
|
+ a22 = a[10],
|
|
|
+ a23 = a[11];
|
|
|
+
|
|
|
+ if (a !== out) { // If the source and destination differ, copy the unchanged rows
|
|
|
+ out[4] = a[4];
|
|
|
+ out[5] = a[5];
|
|
|
+ out[6] = a[6];
|
|
|
+ out[7] = a[7];
|
|
|
+ out[12] = a[12];
|
|
|
+ out[13] = a[13];
|
|
|
+ out[14] = a[14];
|
|
|
+ out[15] = a[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ // Perform axis-specific matrix multiplication
|
|
|
+ out[0] = a00 * c - a20 * s;
|
|
|
+ out[1] = a01 * c - a21 * s;
|
|
|
+ out[2] = a02 * c - a22 * s;
|
|
|
+ out[3] = a03 * c - a23 * s;
|
|
|
+ out[8] = a00 * s + a20 * c;
|
|
|
+ out[9] = a01 * s + a21 * c;
|
|
|
+ out[10] = a02 * s + a22 * c;
|
|
|
+ out[11] = a03 * s + a23 * c;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a matrix by the given angle around the Z axis
|
|
|
+ *
|
|
|
+ * @param {mat4} out the receiving matrix
|
|
|
+ * @param {mat4} a the matrix to rotate
|
|
|
+ * @param {Number} rad the angle to rotate the matrix by
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.rotateZ = function (out, a, rad) {
|
|
|
+ var s = Math.sin(rad),
|
|
|
+ c = Math.cos(rad),
|
|
|
+ a00 = a[0],
|
|
|
+ a01 = a[1],
|
|
|
+ a02 = a[2],
|
|
|
+ a03 = a[3],
|
|
|
+ a10 = a[4],
|
|
|
+ a11 = a[5],
|
|
|
+ a12 = a[6],
|
|
|
+ a13 = a[7];
|
|
|
+
|
|
|
+ if (a !== out) { // If the source and destination differ, copy the unchanged last row
|
|
|
+ out[8] = a[8];
|
|
|
+ out[9] = a[9];
|
|
|
+ out[10] = a[10];
|
|
|
+ out[11] = a[11];
|
|
|
+ out[12] = a[12];
|
|
|
+ out[13] = a[13];
|
|
|
+ out[14] = a[14];
|
|
|
+ out[15] = a[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ // Perform axis-specific matrix multiplication
|
|
|
+ out[0] = a00 * c + a10 * s;
|
|
|
+ out[1] = a01 * c + a11 * s;
|
|
|
+ out[2] = a02 * c + a12 * s;
|
|
|
+ out[3] = a03 * c + a13 * s;
|
|
|
+ out[4] = a10 * c - a00 * s;
|
|
|
+ out[5] = a11 * c - a01 * s;
|
|
|
+ out[6] = a12 * c - a02 * s;
|
|
|
+ out[7] = a13 * c - a03 * s;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a matrix from a quaternion rotation and vector translation
|
|
|
+ * This is equivalent to (but much faster than):
|
|
|
+ *
|
|
|
+ * mat4.identity(dest);
|
|
|
+ * mat4.translate(dest, vec);
|
|
|
+ * var quatMat = mat4.create();
|
|
|
+ * quat4.toMat4(quat, quatMat);
|
|
|
+ * mat4.multiply(dest, quatMat);
|
|
|
+ *
|
|
|
+ * @param {mat4} out mat4 receiving operation result
|
|
|
+ * @param {quat4} q Rotation quaternion
|
|
|
+ * @param {vec3} v Translation vector
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.fromRotationTranslation = function (out, q, v) {
|
|
|
+ // Quaternion math
|
|
|
+ var x = q[0], y = q[1], z = q[2], w = q[3],
|
|
|
+ x2 = x + x,
|
|
|
+ y2 = y + y,
|
|
|
+ z2 = z + z,
|
|
|
+
|
|
|
+ xx = x * x2,
|
|
|
+ xy = x * y2,
|
|
|
+ xz = x * z2,
|
|
|
+ yy = y * y2,
|
|
|
+ yz = y * z2,
|
|
|
+ zz = z * z2,
|
|
|
+ wx = w * x2,
|
|
|
+ wy = w * y2,
|
|
|
+ wz = w * z2;
|
|
|
+
|
|
|
+ out[0] = 1 - (yy + zz);
|
|
|
+ out[1] = xy + wz;
|
|
|
+ out[2] = xz - wy;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = xy - wz;
|
|
|
+ out[5] = 1 - (xx + zz);
|
|
|
+ out[6] = yz + wx;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = xz + wy;
|
|
|
+ out[9] = yz - wx;
|
|
|
+ out[10] = 1 - (xx + yy);
|
|
|
+ out[11] = 0;
|
|
|
+ out[12] = v[0];
|
|
|
+ out[13] = v[1];
|
|
|
+ out[14] = v[2];
|
|
|
+ out[15] = 1;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+mat4.fromQuat = function (out, q) {
|
|
|
+ var x = q[0], y = q[1], z = q[2], w = q[3],
|
|
|
+ x2 = x + x,
|
|
|
+ y2 = y + y,
|
|
|
+ z2 = z + z,
|
|
|
+
|
|
|
+ xx = x * x2,
|
|
|
+ yx = y * x2,
|
|
|
+ yy = y * y2,
|
|
|
+ zx = z * x2,
|
|
|
+ zy = z * y2,
|
|
|
+ zz = z * z2,
|
|
|
+ wx = w * x2,
|
|
|
+ wy = w * y2,
|
|
|
+ wz = w * z2;
|
|
|
+
|
|
|
+ out[0] = 1 - yy - zz;
|
|
|
+ out[1] = yx + wz;
|
|
|
+ out[2] = zx - wy;
|
|
|
+ out[3] = 0;
|
|
|
+
|
|
|
+ out[4] = yx - wz;
|
|
|
+ out[5] = 1 - xx - zz;
|
|
|
+ out[6] = zy + wx;
|
|
|
+ out[7] = 0;
|
|
|
+
|
|
|
+ out[8] = zx + wy;
|
|
|
+ out[9] = zy - wx;
|
|
|
+ out[10] = 1 - xx - yy;
|
|
|
+ out[11] = 0;
|
|
|
+
|
|
|
+ out[12] = 0;
|
|
|
+ out[13] = 0;
|
|
|
+ out[14] = 0;
|
|
|
+ out[15] = 1;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a frustum matrix with the given bounds
|
|
|
+ *
|
|
|
+ * @param {mat4} out mat4 frustum matrix will be written into
|
|
|
+ * @param {Number} left Left bound of the frustum
|
|
|
+ * @param {Number} right Right bound of the frustum
|
|
|
+ * @param {Number} bottom Bottom bound of the frustum
|
|
|
+ * @param {Number} top Top bound of the frustum
|
|
|
+ * @param {Number} near Near bound of the frustum
|
|
|
+ * @param {Number} far Far bound of the frustum
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.frustum = function (out, left, right, bottom, top, near, far) {
|
|
|
+ var rl = 1 / (right - left),
|
|
|
+ tb = 1 / (top - bottom),
|
|
|
+ nf = 1 / (near - far);
|
|
|
+ out[0] = (near * 2) * rl;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = 0;
|
|
|
+ out[5] = (near * 2) * tb;
|
|
|
+ out[6] = 0;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = (right + left) * rl;
|
|
|
+ out[9] = (top + bottom) * tb;
|
|
|
+ out[10] = (far + near) * nf;
|
|
|
+ out[11] = -1;
|
|
|
+ out[12] = 0;
|
|
|
+ out[13] = 0;
|
|
|
+ out[14] = (far * near * 2) * nf;
|
|
|
+ out[15] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a perspective projection matrix with the given bounds
|
|
|
+ *
|
|
|
+ * @param {mat4} out mat4 frustum matrix will be written into
|
|
|
+ * @param {number} fovy Vertical field of view in radians
|
|
|
+ * @param {number} aspect Aspect ratio. typically viewport width/height
|
|
|
+ * @param {number} near Near bound of the frustum
|
|
|
+ * @param {number} far Far bound of the frustum
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.perspective = function (out, fovy, aspect, near, far) {
|
|
|
+ var f = 1.0 / Math.tan(fovy / 2),
|
|
|
+ nf = 1 / (near - far);
|
|
|
+ out[0] = f / aspect;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = 0;
|
|
|
+ out[5] = f;
|
|
|
+ out[6] = 0;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = 0;
|
|
|
+ out[9] = 0;
|
|
|
+ out[10] = (far + near) * nf;
|
|
|
+ out[11] = -1;
|
|
|
+ out[12] = 0;
|
|
|
+ out[13] = 0;
|
|
|
+ out[14] = (2 * far * near) * nf;
|
|
|
+ out[15] = 0;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a orthogonal projection matrix with the given bounds
|
|
|
+ *
|
|
|
+ * @param {mat4} out mat4 frustum matrix will be written into
|
|
|
+ * @param {number} left Left bound of the frustum
|
|
|
+ * @param {number} right Right bound of the frustum
|
|
|
+ * @param {number} bottom Bottom bound of the frustum
|
|
|
+ * @param {number} top Top bound of the frustum
|
|
|
+ * @param {number} near Near bound of the frustum
|
|
|
+ * @param {number} far Far bound of the frustum
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.ortho = function (out, left, right, bottom, top, near, far) {
|
|
|
+ var lr = 1 / (left - right),
|
|
|
+ bt = 1 / (bottom - top),
|
|
|
+ nf = 1 / (near - far);
|
|
|
+ out[0] = -2 * lr;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = 0;
|
|
|
+ out[5] = -2 * bt;
|
|
|
+ out[6] = 0;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = 0;
|
|
|
+ out[9] = 0;
|
|
|
+ out[10] = 2 * nf;
|
|
|
+ out[11] = 0;
|
|
|
+ out[12] = (left + right) * lr;
|
|
|
+ out[13] = (top + bottom) * bt;
|
|
|
+ out[14] = (far + near) * nf;
|
|
|
+ out[15] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Generates a look-at matrix with the given eye position, focal point, and up axis
|
|
|
+ *
|
|
|
+ * @param {mat4} out mat4 frustum matrix will be written into
|
|
|
+ * @param {vec3} eye Position of the viewer
|
|
|
+ * @param {vec3} center Point the viewer is looking at
|
|
|
+ * @param {vec3} up vec3 pointing up
|
|
|
+ * @returns {mat4} out
|
|
|
+ */
|
|
|
+mat4.lookAt = function (out, eye, center, up) {
|
|
|
+ var x0, x1, x2, y0, y1, y2, z0, z1, z2, len,
|
|
|
+ eyex = eye[0],
|
|
|
+ eyey = eye[1],
|
|
|
+ eyez = eye[2],
|
|
|
+ upx = up[0],
|
|
|
+ upy = up[1],
|
|
|
+ upz = up[2],
|
|
|
+ centerx = center[0],
|
|
|
+ centery = center[1],
|
|
|
+ centerz = center[2];
|
|
|
+
|
|
|
+ if (Math.abs(eyex - centerx) < GLMAT_EPSILON &&
|
|
|
+ Math.abs(eyey - centery) < GLMAT_EPSILON &&
|
|
|
+ Math.abs(eyez - centerz) < GLMAT_EPSILON) {
|
|
|
+ return mat4.identity(out);
|
|
|
+ }
|
|
|
+
|
|
|
+ z0 = eyex - centerx;
|
|
|
+ z1 = eyey - centery;
|
|
|
+ z2 = eyez - centerz;
|
|
|
+
|
|
|
+ len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
|
|
|
+ z0 *= len;
|
|
|
+ z1 *= len;
|
|
|
+ z2 *= len;
|
|
|
+
|
|
|
+ x0 = upy * z2 - upz * z1;
|
|
|
+ x1 = upz * z0 - upx * z2;
|
|
|
+ x2 = upx * z1 - upy * z0;
|
|
|
+ len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
|
|
|
+ if (!len) {
|
|
|
+ x0 = 0;
|
|
|
+ x1 = 0;
|
|
|
+ x2 = 0;
|
|
|
+ } else {
|
|
|
+ len = 1 / len;
|
|
|
+ x0 *= len;
|
|
|
+ x1 *= len;
|
|
|
+ x2 *= len;
|
|
|
+ }
|
|
|
+
|
|
|
+ y0 = z1 * x2 - z2 * x1;
|
|
|
+ y1 = z2 * x0 - z0 * x2;
|
|
|
+ y2 = z0 * x1 - z1 * x0;
|
|
|
+
|
|
|
+ len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
|
|
|
+ if (!len) {
|
|
|
+ y0 = 0;
|
|
|
+ y1 = 0;
|
|
|
+ y2 = 0;
|
|
|
+ } else {
|
|
|
+ len = 1 / len;
|
|
|
+ y0 *= len;
|
|
|
+ y1 *= len;
|
|
|
+ y2 *= len;
|
|
|
+ }
|
|
|
+
|
|
|
+ out[0] = x0;
|
|
|
+ out[1] = y0;
|
|
|
+ out[2] = z0;
|
|
|
+ out[3] = 0;
|
|
|
+ out[4] = x1;
|
|
|
+ out[5] = y1;
|
|
|
+ out[6] = z1;
|
|
|
+ out[7] = 0;
|
|
|
+ out[8] = x2;
|
|
|
+ out[9] = y2;
|
|
|
+ out[10] = z2;
|
|
|
+ out[11] = 0;
|
|
|
+ out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
|
|
|
+ out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
|
|
|
+ out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
|
|
|
+ out[15] = 1;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a mat4
|
|
|
+ *
|
|
|
+ * @param {mat4} mat matrix to represent as a string
|
|
|
+ * @returns {String} string representation of the matrix
|
|
|
+ */
|
|
|
+mat4.str = function (a) {
|
|
|
+ return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' +
|
|
|
+ a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' +
|
|
|
+ a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' +
|
|
|
+ a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns Frobenius norm of a mat4
|
|
|
+ *
|
|
|
+ * @param {mat4} a the matrix to calculate Frobenius norm of
|
|
|
+ * @returns {Number} Frobenius norm
|
|
|
+ */
|
|
|
+mat4.frob = function (a) {
|
|
|
+ return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2) + Math.pow(a[9], 2) + Math.pow(a[10], 2) + Math.pow(a[11], 2) + Math.pow(a[12], 2) + Math.pow(a[13], 2) + Math.pow(a[14], 2) + Math.pow(a[15], 2) ))
|
|
|
+};
|
|
|
+
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.mat4 = mat4;
|
|
|
+}
|
|
|
+;
|
|
|
+/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
|
|
|
+
|
|
|
+Redistribution and use in source and binary forms, with or without modification,
|
|
|
+are permitted provided that the following conditions are met:
|
|
|
+
|
|
|
+ * Redistributions of source code must retain the above copyright notice, this
|
|
|
+ list of conditions and the following disclaimer.
|
|
|
+ * Redistributions in binary form must reproduce the above copyright notice,
|
|
|
+ this list of conditions and the following disclaimer in the documentation
|
|
|
+ and/or other materials provided with the distribution.
|
|
|
+
|
|
|
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
|
|
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
|
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
|
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
|
|
|
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
|
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
|
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
|
|
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
|
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
+
|
|
|
+/**
|
|
|
+ * @class Quaternion
|
|
|
+ * @name quat
|
|
|
+ */
|
|
|
+
|
|
|
+var quat = {};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new identity quat
|
|
|
+ *
|
|
|
+ * @returns {quat} a new quaternion
|
|
|
+ */
|
|
|
+quat.create = function() {
|
|
|
+ var out = new GLMAT_ARRAY_TYPE(4);
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Sets a quaternion to represent the shortest rotation from one
|
|
|
+ * vector to another.
|
|
|
+ *
|
|
|
+ * Both vectors are assumed to be unit length.
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion.
|
|
|
+ * @param {vec3} a the initial vector
|
|
|
+ * @param {vec3} b the destination vector
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.rotationTo = (function() {
|
|
|
+ var tmpvec3 = vec3.create();
|
|
|
+ var xUnitVec3 = vec3.fromValues(1,0,0);
|
|
|
+ var yUnitVec3 = vec3.fromValues(0,1,0);
|
|
|
+
|
|
|
+ return function(out, a, b) {
|
|
|
+ var dot = vec3.dot(a, b);
|
|
|
+ if (dot < -0.999999) {
|
|
|
+ vec3.cross(tmpvec3, xUnitVec3, a);
|
|
|
+ if (vec3.length(tmpvec3) < 0.000001)
|
|
|
+ vec3.cross(tmpvec3, yUnitVec3, a);
|
|
|
+ vec3.normalize(tmpvec3, tmpvec3);
|
|
|
+ quat.setAxisAngle(out, tmpvec3, Math.PI);
|
|
|
+ return out;
|
|
|
+ } else if (dot > 0.999999) {
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+ } else {
|
|
|
+ vec3.cross(tmpvec3, a, b);
|
|
|
+ out[0] = tmpvec3[0];
|
|
|
+ out[1] = tmpvec3[1];
|
|
|
+ out[2] = tmpvec3[2];
|
|
|
+ out[3] = 1 + dot;
|
|
|
+ return quat.normalize(out, out);
|
|
|
+ }
|
|
|
+ };
|
|
|
+})();
|
|
|
+
|
|
|
+/**
|
|
|
+ * Sets the specified quaternion with values corresponding to the given
|
|
|
+ * axes. Each axis is a vec3 and is expected to be unit length and
|
|
|
+ * perpendicular to all other specified axes.
|
|
|
+ *
|
|
|
+ * @param {vec3} view the vector representing the viewing direction
|
|
|
+ * @param {vec3} right the vector representing the local "right" direction
|
|
|
+ * @param {vec3} up the vector representing the local "up" direction
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.setAxes = (function() {
|
|
|
+ var matr = mat3.create();
|
|
|
+
|
|
|
+ return function(out, view, right, up) {
|
|
|
+ matr[0] = right[0];
|
|
|
+ matr[3] = right[1];
|
|
|
+ matr[6] = right[2];
|
|
|
+
|
|
|
+ matr[1] = up[0];
|
|
|
+ matr[4] = up[1];
|
|
|
+ matr[7] = up[2];
|
|
|
+
|
|
|
+ matr[2] = -view[0];
|
|
|
+ matr[5] = -view[1];
|
|
|
+ matr[8] = -view[2];
|
|
|
+
|
|
|
+ return quat.normalize(out, quat.fromMat3(out, matr));
|
|
|
+ };
|
|
|
+})();
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new quat initialized with values from an existing quaternion
|
|
|
+ *
|
|
|
+ * @param {quat} a quaternion to clone
|
|
|
+ * @returns {quat} a new quaternion
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.clone = vec4.clone;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a new quat initialized with the given values
|
|
|
+ *
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @param {Number} w W component
|
|
|
+ * @returns {quat} a new quaternion
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.fromValues = vec4.fromValues;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Copy the values from one quat to another
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a the source quaternion
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.copy = vec4.copy;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set the components of a quat to the given values
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {Number} x X component
|
|
|
+ * @param {Number} y Y component
|
|
|
+ * @param {Number} z Z component
|
|
|
+ * @param {Number} w W component
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.set = vec4.set;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Set a quat to the identity quaternion
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.identity = function(out) {
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Sets a quat from the given angle and rotation axis,
|
|
|
+ * then returns it.
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {vec3} axis the axis around which to rotate
|
|
|
+ * @param {Number} rad the angle in radians
|
|
|
+ * @returns {quat} out
|
|
|
+ **/
|
|
|
+quat.setAxisAngle = function(out, axis, rad) {
|
|
|
+ rad = rad * 0.5;
|
|
|
+ var s = Math.sin(rad);
|
|
|
+ out[0] = s * axis[0];
|
|
|
+ out[1] = s * axis[1];
|
|
|
+ out[2] = s * axis[2];
|
|
|
+ out[3] = Math.cos(rad);
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Adds two quat's
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a the first operand
|
|
|
+ * @param {quat} b the second operand
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.add = vec4.add;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Multiplies two quat's
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a the first operand
|
|
|
+ * @param {quat} b the second operand
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.multiply = function(out, a, b) {
|
|
|
+ var ax = a[0], ay = a[1], az = a[2], aw = a[3],
|
|
|
+ bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
+
|
|
|
+ out[0] = ax * bw + aw * bx + ay * bz - az * by;
|
|
|
+ out[1] = ay * bw + aw * by + az * bx - ax * bz;
|
|
|
+ out[2] = az * bw + aw * bz + ax * by - ay * bx;
|
|
|
+ out[3] = aw * bw - ax * bx - ay * by - az * bz;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link quat.multiply}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.mul = quat.multiply;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Scales a quat by a scalar number
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving vector
|
|
|
+ * @param {quat} a the vector to scale
|
|
|
+ * @param {Number} b amount to scale the vector by
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.scale = vec4.scale;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a quaternion by the given angle about the X axis
|
|
|
+ *
|
|
|
+ * @param {quat} out quat receiving operation result
|
|
|
+ * @param {quat} a quat to rotate
|
|
|
+ * @param {number} rad angle (in radians) to rotate
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.rotateX = function (out, a, rad) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ var ax = a[0], ay = a[1], az = a[2], aw = a[3],
|
|
|
+ bx = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw + aw * bx;
|
|
|
+ out[1] = ay * bw + az * bx;
|
|
|
+ out[2] = az * bw - ay * bx;
|
|
|
+ out[3] = aw * bw - ax * bx;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a quaternion by the given angle about the Y axis
|
|
|
+ *
|
|
|
+ * @param {quat} out quat receiving operation result
|
|
|
+ * @param {quat} a quat to rotate
|
|
|
+ * @param {number} rad angle (in radians) to rotate
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.rotateY = function (out, a, rad) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ var ax = a[0], ay = a[1], az = a[2], aw = a[3],
|
|
|
+ by = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw - az * by;
|
|
|
+ out[1] = ay * bw + aw * by;
|
|
|
+ out[2] = az * bw + ax * by;
|
|
|
+ out[3] = aw * bw - ay * by;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Rotates a quaternion by the given angle about the Z axis
|
|
|
+ *
|
|
|
+ * @param {quat} out quat receiving operation result
|
|
|
+ * @param {quat} a quat to rotate
|
|
|
+ * @param {number} rad angle (in radians) to rotate
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.rotateZ = function (out, a, rad) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ var ax = a[0], ay = a[1], az = a[2], aw = a[3],
|
|
|
+ bz = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw + ay * bz;
|
|
|
+ out[1] = ay * bw - ax * bz;
|
|
|
+ out[2] = az * bw + aw * bz;
|
|
|
+ out[3] = aw * bw - az * bz;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the W component of a quat from the X, Y, and Z components.
|
|
|
+ * Assumes that quaternion is 1 unit in length.
|
|
|
+ * Any existing W component will be ignored.
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a quat to calculate W component of
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.calculateW = function (out, a) {
|
|
|
+ var x = a[0], y = a[1], z = a[2];
|
|
|
+
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the dot product of two quat's
|
|
|
+ *
|
|
|
+ * @param {quat} a the first operand
|
|
|
+ * @param {quat} b the second operand
|
|
|
+ * @returns {Number} dot product of a and b
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.dot = vec4.dot;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Performs a linear interpolation between two quat's
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a the first operand
|
|
|
+ * @param {quat} b the second operand
|
|
|
+ * @param {Number} t interpolation amount between the two inputs
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.lerp = vec4.lerp;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Performs a spherical linear interpolation between two quat
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a the first operand
|
|
|
+ * @param {quat} b the second operand
|
|
|
+ * @param {Number} t interpolation amount between the two inputs
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.slerp = function (out, a, b, t) {
|
|
|
+ // benchmarks:
|
|
|
+ // http://jsperf.com/quaternion-slerp-implementations
|
|
|
+
|
|
|
+ var ax = a[0], ay = a[1], az = a[2], aw = a[3],
|
|
|
+ bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
+
|
|
|
+ var omega, cosom, sinom, scale0, scale1;
|
|
|
+
|
|
|
+ // calc cosine
|
|
|
+ cosom = ax * bx + ay * by + az * bz + aw * bw;
|
|
|
+ // adjust signs (if necessary)
|
|
|
+ if ( cosom < 0.0 ) {
|
|
|
+ cosom = -cosom;
|
|
|
+ bx = - bx;
|
|
|
+ by = - by;
|
|
|
+ bz = - bz;
|
|
|
+ bw = - bw;
|
|
|
+ }
|
|
|
+ // calculate coefficients
|
|
|
+ if ( (1.0 - cosom) > 0.000001 ) {
|
|
|
+ // standard case (slerp)
|
|
|
+ omega = Math.acos(cosom);
|
|
|
+ sinom = Math.sin(omega);
|
|
|
+ scale0 = Math.sin((1.0 - t) * omega) / sinom;
|
|
|
+ scale1 = Math.sin(t * omega) / sinom;
|
|
|
+ } else {
|
|
|
+ // "from" and "to" quaternions are very close
|
|
|
+ // ... so we can do a linear interpolation
|
|
|
+ scale0 = 1.0 - t;
|
|
|
+ scale1 = t;
|
|
|
+ }
|
|
|
+ // calculate final values
|
|
|
+ out[0] = scale0 * ax + scale1 * bx;
|
|
|
+ out[1] = scale0 * ay + scale1 * by;
|
|
|
+ out[2] = scale0 * az + scale1 * bz;
|
|
|
+ out[3] = scale0 * aw + scale1 * bw;
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the inverse of a quat
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a quat to calculate inverse of
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.invert = function(out, a) {
|
|
|
+ var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3],
|
|
|
+ dot = a0*a0 + a1*a1 + a2*a2 + a3*a3,
|
|
|
+ invDot = dot ? 1.0/dot : 0;
|
|
|
+
|
|
|
+ // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
|
|
|
+
|
|
|
+ out[0] = -a0*invDot;
|
|
|
+ out[1] = -a1*invDot;
|
|
|
+ out[2] = -a2*invDot;
|
|
|
+ out[3] = a3*invDot;
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the conjugate of a quat
|
|
|
+ * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a quat to calculate conjugate of
|
|
|
+ * @returns {quat} out
|
|
|
+ */
|
|
|
+quat.conjugate = function (out, a) {
|
|
|
+ out[0] = -a[0];
|
|
|
+ out[1] = -a[1];
|
|
|
+ out[2] = -a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the length of a quat
|
|
|
+ *
|
|
|
+ * @param {quat} a vector to calculate length of
|
|
|
+ * @returns {Number} length of a
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.length = vec4.length;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link quat.length}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.len = quat.length;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Calculates the squared length of a quat
|
|
|
+ *
|
|
|
+ * @param {quat} a vector to calculate squared length of
|
|
|
+ * @returns {Number} squared length of a
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.squaredLength = vec4.squaredLength;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Alias for {@link quat.squaredLength}
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.sqrLen = quat.squaredLength;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Normalize a quat
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {quat} a quaternion to normalize
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.normalize = vec4.normalize;
|
|
|
+
|
|
|
+/**
|
|
|
+ * Creates a quaternion from the given 3x3 rotation matrix.
|
|
|
+ *
|
|
|
+ * NOTE: The resultant quaternion is not normalized, so you should be sure
|
|
|
+ * to renormalize the quaternion yourself where necessary.
|
|
|
+ *
|
|
|
+ * @param {quat} out the receiving quaternion
|
|
|
+ * @param {mat3} m rotation matrix
|
|
|
+ * @returns {quat} out
|
|
|
+ * @function
|
|
|
+ */
|
|
|
+quat.fromMat3 = function(out, m) {
|
|
|
+ // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
|
|
|
+ // article "Quaternion Calculus and Fast Animation".
|
|
|
+ var fTrace = m[0] + m[4] + m[8];
|
|
|
+ var fRoot;
|
|
|
+
|
|
|
+ if ( fTrace > 0.0 ) {
|
|
|
+ // |w| > 1/2, may as well choose w > 1/2
|
|
|
+ fRoot = Math.sqrt(fTrace + 1.0); // 2w
|
|
|
+ out[3] = 0.5 * fRoot;
|
|
|
+ fRoot = 0.5/fRoot; // 1/(4w)
|
|
|
+ out[0] = (m[5]-m[7])*fRoot;
|
|
|
+ out[1] = (m[6]-m[2])*fRoot;
|
|
|
+ out[2] = (m[1]-m[3])*fRoot;
|
|
|
+ } else {
|
|
|
+ // |w| <= 1/2
|
|
|
+ var i = 0;
|
|
|
+ if ( m[4] > m[0] )
|
|
|
+ i = 1;
|
|
|
+ if ( m[8] > m[i*3+i] )
|
|
|
+ i = 2;
|
|
|
+ var j = (i+1)%3;
|
|
|
+ var k = (i+2)%3;
|
|
|
+
|
|
|
+ fRoot = Math.sqrt(m[i*3+i]-m[j*3+j]-m[k*3+k] + 1.0);
|
|
|
+ out[i] = 0.5 * fRoot;
|
|
|
+ fRoot = 0.5 / fRoot;
|
|
|
+ out[3] = (m[j*3+k] - m[k*3+j]) * fRoot;
|
|
|
+ out[j] = (m[j*3+i] + m[i*3+j]) * fRoot;
|
|
|
+ out[k] = (m[k*3+i] + m[i*3+k]) * fRoot;
|
|
|
+ }
|
|
|
+
|
|
|
+ return out;
|
|
|
+};
|
|
|
+
|
|
|
+/**
|
|
|
+ * Returns a string representation of a quatenion
|
|
|
+ *
|
|
|
+ * @param {quat} vec vector to represent as a string
|
|
|
+ * @returns {String} string representation of the vector
|
|
|
+ */
|
|
|
+quat.str = function (a) {
|
|
|
+ return 'quat(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')';
|
|
|
+};
|
|
|
+
|
|
|
+if(typeof(exports) !== 'undefined') {
|
|
|
+ exports.quat = quat;
|
|
|
+}
|
|
|
+;
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+ })(shim.exports);
|
|
|
+})(this);
|
Josh Engebretson