1212 lines
37 KiB
JavaScript
1212 lines
37 KiB
JavaScript
// Copyright 2011 The Closure Library Authors. All Rights Reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS-IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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/**
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* @fileoverview Implements 3x3 matrices and their related functions which are
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* compatible with WebGL. The API is structured to avoid unnecessary memory
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* allocations. The last parameter will typically be the output vector and
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* an object can be both an input and output parameter to all methods except
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* where noted. Matrix operations follow the mathematical form when multiplying
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* vectors as follows: resultVec = matrix * vec.
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*
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* The matrices are stored in column-major order.
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*
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*/
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goog.provide('goog.vec.Mat3');
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goog.require('goog.vec');
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/** @typedef {goog.vec.Float32} */ goog.vec.Mat3.Float32;
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/** @typedef {goog.vec.Float64} */ goog.vec.Mat3.Float64;
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/** @typedef {goog.vec.Number} */ goog.vec.Mat3.Number;
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/** @typedef {goog.vec.AnyType} */ goog.vec.Mat3.AnyType;
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// The following two types are deprecated - use the above types instead.
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/** @typedef {Float32Array} */ goog.vec.Mat3.Type;
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/** @typedef {goog.vec.ArrayType} */ goog.vec.Mat3.Mat3Like;
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/**
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* Creates the array representation of a 3x3 matrix of Float32.
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* The use of the array directly instead of a class reduces overhead.
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* The returned matrix is cleared to all zeros.
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*
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* @return {!goog.vec.Mat3.Float32} The new matrix.
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*/
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goog.vec.Mat3.createFloat32 = function() {
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return new Float32Array(9);
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};
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/**
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* Creates the array representation of a 3x3 matrix of Float64.
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* The returned matrix is cleared to all zeros.
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*
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* @return {!goog.vec.Mat3.Float64} The new matrix.
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*/
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goog.vec.Mat3.createFloat64 = function() {
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return new Float64Array(9);
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};
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/**
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* Creates the array representation of a 3x3 matrix of Number.
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* The returned matrix is cleared to all zeros.
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*
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* @return {!goog.vec.Mat3.Number} The new matrix.
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*/
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goog.vec.Mat3.createNumber = function() {
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var a = new Array(9);
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goog.vec.Mat3.setFromValues(a,
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0, 0, 0,
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0, 0, 0,
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0, 0, 0);
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return a;
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};
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/**
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* Creates the array representation of a 3x3 matrix of Float32.
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* The returned matrix is cleared to all zeros.
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*
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* @deprecated Use createFloat32.
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* @return {!goog.vec.Mat3.Type} The new matrix.
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*/
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goog.vec.Mat3.create = function() {
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return goog.vec.Mat3.createFloat32();
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};
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/**
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* Creates a 3x3 identity matrix of Float32.
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*
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* @return {!goog.vec.Mat3.Float32} The new 9 element array.
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*/
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goog.vec.Mat3.createFloat32Identity = function() {
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var mat = goog.vec.Mat3.createFloat32();
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mat[0] = mat[4] = mat[8] = 1;
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return mat;
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};
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/**
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* Creates a 3x3 identity matrix of Float64.
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*
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* @return {!goog.vec.Mat3.Float64} The new 9 element array.
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*/
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goog.vec.Mat3.createFloat64Identity = function() {
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var mat = goog.vec.Mat3.createFloat64();
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mat[0] = mat[4] = mat[8] = 1;
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return mat;
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};
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/**
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* Creates a 3x3 identity matrix of Number.
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* The returned matrix is cleared to all zeros.
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*
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* @return {!goog.vec.Mat3.Number} The new 9 element array.
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*/
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goog.vec.Mat3.createNumberIdentity = function() {
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var a = new Array(9);
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goog.vec.Mat3.setFromValues(a,
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1, 0, 0,
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0, 1, 0,
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0, 0, 1);
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return a;
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};
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/**
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* Creates the array representation of a 3x3 matrix of Float32.
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* The returned matrix is cleared to all zeros.
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*
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* @deprecated Use createFloat32Identity.
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* @return {!goog.vec.Mat3.Type} The new 9 element array.
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*/
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goog.vec.Mat3.createIdentity = function() {
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return goog.vec.Mat3.createFloat32Identity();
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};
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/**
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* Creates a 3x3 matrix of Float32 initialized from the given array.
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*
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* @param {goog.vec.Mat3.AnyType} matrix The array containing the
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* matrix values in column major order.
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* @return {!goog.vec.Mat3.Float32} The new, nine element array.
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*/
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goog.vec.Mat3.createFloat32FromArray = function(matrix) {
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var newMatrix = goog.vec.Mat3.createFloat32();
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goog.vec.Mat3.setFromArray(newMatrix, matrix);
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return newMatrix;
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};
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/**
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* Creates a 3x3 matrix of Float32 initialized from the given values.
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*
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* @param {number} v00 The values at (0, 0).
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* @param {number} v10 The values at (1, 0).
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* @param {number} v20 The values at (2, 0).
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* @param {number} v01 The values at (0, 1).
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* @param {number} v11 The values at (1, 1).
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* @param {number} v21 The values at (2, 1).
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* @param {number} v02 The values at (0, 2).
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* @param {number} v12 The values at (1, 2).
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* @param {number} v22 The values at (2, 2).
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* @return {!goog.vec.Mat3.Float32} The new, nine element array.
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*/
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goog.vec.Mat3.createFloat32FromValues = function(
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v00, v10, v20, v01, v11, v21, v02, v12, v22) {
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var newMatrix = goog.vec.Mat3.createFloat32();
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goog.vec.Mat3.setFromValues(
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newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
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return newMatrix;
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};
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/**
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* Creates a clone of a 3x3 matrix of Float32.
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*
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* @param {goog.vec.Mat3.Float32} matrix The source 3x3 matrix.
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* @return {!goog.vec.Mat3.Float32} The new 3x3 element matrix.
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*/
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goog.vec.Mat3.cloneFloat32 = goog.vec.Mat3.createFloat32FromArray;
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/**
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* Creates a 3x3 matrix of Float64 initialized from the given array.
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*
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* @param {goog.vec.Mat3.AnyType} matrix The array containing the
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* matrix values in column major order.
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* @return {!goog.vec.Mat3.Float64} The new, nine element array.
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*/
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goog.vec.Mat3.createFloat64FromArray = function(matrix) {
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var newMatrix = goog.vec.Mat3.createFloat64();
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goog.vec.Mat3.setFromArray(newMatrix, matrix);
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return newMatrix;
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};
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/**
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* Creates a 3x3 matrix of Float64 initialized from the given values.
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*
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* @param {number} v00 The values at (0, 0).
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* @param {number} v10 The values at (1, 0).
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* @param {number} v20 The values at (2, 0).
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* @param {number} v01 The values at (0, 1).
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* @param {number} v11 The values at (1, 1).
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* @param {number} v21 The values at (2, 1).
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* @param {number} v02 The values at (0, 2).
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* @param {number} v12 The values at (1, 2).
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* @param {number} v22 The values at (2, 2).
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* @return {!goog.vec.Mat3.Float64} The new, nine element array.
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*/
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goog.vec.Mat3.createFloat64FromValues = function(
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v00, v10, v20, v01, v11, v21, v02, v12, v22) {
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var newMatrix = goog.vec.Mat3.createFloat64();
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goog.vec.Mat3.setFromValues(
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newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
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return newMatrix;
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};
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/**
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* Creates a clone of a 3x3 matrix of Float64.
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*
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* @param {goog.vec.Mat3.Float64} matrix The source 3x3 matrix.
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* @return {!goog.vec.Mat3.Float64} The new 3x3 element matrix.
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*/
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goog.vec.Mat3.cloneFloat64 = goog.vec.Mat3.createFloat64FromArray;
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/**
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* Creates a 3x3 matrix of Float32 initialized from the given array.
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*
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* @deprecated Use createFloat32FromArray.
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* @param {goog.vec.Mat3.Mat3Like} matrix The array containing the
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* matrix values in column major order.
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* @return {!goog.vec.Mat3.Type} The new, nine element array.
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*/
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goog.vec.Mat3.createFromArray = function(matrix) {
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var newMatrix = goog.vec.Mat3.createFloat32();
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goog.vec.Mat3.setFromArray(newMatrix, matrix);
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return newMatrix;
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};
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/**
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* Creates a 3x3 matrix of Float32 initialized from the given values.
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*
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* @deprecated Use createFloat32FromValues.
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* @param {number} v00 The values at (0, 0).
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* @param {number} v10 The values at (1, 0).
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* @param {number} v20 The values at (2, 0).
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* @param {number} v01 The values at (0, 1).
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* @param {number} v11 The values at (1, 1).
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* @param {number} v21 The values at (2, 1).
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* @param {number} v02 The values at (0, 2).
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* @param {number} v12 The values at (1, 2).
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* @param {number} v22 The values at (2, 2).
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* @return {!goog.vec.Mat3.Type} The new, nine element array.
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*/
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goog.vec.Mat3.createFromValues = function(
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v00, v10, v20, v01, v11, v21, v02, v12, v22) {
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var newMatrix = goog.vec.Mat3.create();
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goog.vec.Mat3.setFromValues(
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newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
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return newMatrix;
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};
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/**
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* Creates a clone of a 3x3 matrix of Float32.
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*
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* @deprecated Use cloneFloat32.
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* @param {goog.vec.Mat3.Mat3Like} matrix The source 3x3 matrix.
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* @return {!goog.vec.Mat3.Type} The new 3x3 element matrix.
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*/
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goog.vec.Mat3.clone = goog.vec.Mat3.createFromArray;
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/**
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* Retrieves the element at the requested row and column.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix containing the value to
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* retrieve.
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* @param {number} row The row index.
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* @param {number} column The column index.
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* @return {number} The element value at the requested row, column indices.
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*/
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goog.vec.Mat3.getElement = function(mat, row, column) {
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return mat[row + column * 3];
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};
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/**
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* Sets the element at the requested row and column.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix containing the value to
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* retrieve.
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* @param {number} row The row index.
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* @param {number} column The column index.
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* @param {number} value The value to set at the requested row, column.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setElement = function(mat, row, column, value) {
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mat[row + column * 3] = value;
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return mat;
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};
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/**
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* Initializes the matrix from the set of values. Note the values supplied are
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* in column major order.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the
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* values.
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* @param {number} v00 The values at (0, 0).
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* @param {number} v10 The values at (1, 0).
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* @param {number} v20 The values at (2, 0).
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* @param {number} v01 The values at (0, 1).
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* @param {number} v11 The values at (1, 1).
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* @param {number} v21 The values at (2, 1).
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* @param {number} v02 The values at (0, 2).
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* @param {number} v12 The values at (1, 2).
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* @param {number} v22 The values at (2, 2).
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setFromValues = function(
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mat, v00, v10, v20, v01, v11, v21, v02, v12, v22) {
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mat[0] = v00;
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mat[1] = v10;
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mat[2] = v20;
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mat[3] = v01;
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mat[4] = v11;
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mat[5] = v21;
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mat[6] = v02;
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mat[7] = v12;
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mat[8] = v22;
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return mat;
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};
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/**
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* Sets the matrix from the array of values stored in column major order.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
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* @param {goog.vec.Mat3.AnyType} values The column major ordered
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* array of values to store in the matrix.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setFromArray = function(mat, values) {
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mat[0] = values[0];
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mat[1] = values[1];
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mat[2] = values[2];
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mat[3] = values[3];
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mat[4] = values[4];
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mat[5] = values[5];
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mat[6] = values[6];
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mat[7] = values[7];
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mat[8] = values[8];
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return mat;
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};
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/**
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* Sets the matrix from the array of values stored in row major order.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
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* @param {goog.vec.Mat3.AnyType} values The row major ordered array
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* of values to store in the matrix.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setFromRowMajorArray = function(mat, values) {
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mat[0] = values[0];
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mat[1] = values[3];
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mat[2] = values[6];
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mat[3] = values[1];
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mat[4] = values[4];
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mat[5] = values[7];
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mat[6] = values[2];
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mat[7] = values[5];
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mat[8] = values[8];
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return mat;
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};
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/**
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* Sets the diagonal values of the matrix from the given values.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
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* @param {number} v00 The values for (0, 0).
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* @param {number} v11 The values for (1, 1).
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* @param {number} v22 The values for (2, 2).
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setDiagonalValues = function(mat, v00, v11, v22) {
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mat[0] = v00;
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mat[4] = v11;
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mat[8] = v22;
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return mat;
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};
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/**
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* Sets the diagonal values of the matrix from the given vector.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
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* @param {goog.vec.Vec3.AnyType} vec The vector containing the values.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setDiagonal = function(mat, vec) {
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mat[0] = vec[0];
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mat[4] = vec[1];
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mat[8] = vec[2];
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return mat;
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};
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/**
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* Sets the specified column with the supplied values.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to recieve the values.
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* @param {number} column The column index to set the values on.
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* @param {number} v0 The value for row 0.
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* @param {number} v1 The value for row 1.
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* @param {number} v2 The value for row 2.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setColumnValues = function(mat, column, v0, v1, v2) {
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var i = column * 3;
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mat[i] = v0;
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mat[i + 1] = v1;
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mat[i + 2] = v2;
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return mat;
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};
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/**
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* Sets the specified column with the value from the supplied array.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
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* @param {number} column The column index to set the values on.
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* @param {goog.vec.Vec3.AnyType} vec The vector elements for the column.
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* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.setColumn = function(mat, column, vec) {
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var i = column * 3;
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mat[i] = vec[0];
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mat[i + 1] = vec[1];
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mat[i + 2] = vec[2];
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return mat;
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};
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/**
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* Retrieves the specified column from the matrix into the given vector
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* array.
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*
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* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the values.
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* @param {number} column The column to get the values from.
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* @param {goog.vec.Vec3.AnyType} vec The vector elements to receive the
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* column.
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* @return {goog.vec.Vec3.AnyType} return vec so that operations can be
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* chained together.
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*/
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goog.vec.Mat3.getColumn = function(mat, column, vec) {
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var i = column * 3;
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vec[0] = mat[i];
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vec[1] = mat[i + 1];
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vec[2] = mat[i + 2];
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return vec;
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};
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/**
|
|
* Sets the columns of the matrix from the set of vector elements.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
|
|
* @param {goog.vec.Vec3.AnyType} vec0 The values for column 0.
|
|
* @param {goog.vec.Vec3.AnyType} vec1 The values for column 1.
|
|
* @param {goog.vec.Vec3.AnyType} vec2 The values for column 2.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.setColumns = function(mat, vec0, vec1, vec2) {
|
|
goog.vec.Mat3.setColumn(mat, 0, vec0);
|
|
goog.vec.Mat3.setColumn(mat, 1, vec1);
|
|
goog.vec.Mat3.setColumn(mat, 2, vec2);
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Retrieves the column values from the given matrix into the given vector
|
|
* elements.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the columns.
|
|
* @param {goog.vec.Vec3.AnyType} vec0 The vector to receive column 0.
|
|
* @param {goog.vec.Vec3.AnyType} vec1 The vector to receive column 1.
|
|
* @param {goog.vec.Vec3.AnyType} vec2 The vector to receive column 2.
|
|
*/
|
|
goog.vec.Mat3.getColumns = function(mat, vec0, vec1, vec2) {
|
|
goog.vec.Mat3.getColumn(mat, 0, vec0);
|
|
goog.vec.Mat3.getColumn(mat, 1, vec1);
|
|
goog.vec.Mat3.getColumn(mat, 2, vec2);
|
|
};
|
|
|
|
|
|
/**
|
|
* Sets the row values from the supplied values.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
|
|
* @param {number} row The index of the row to receive the values.
|
|
* @param {number} v0 The value for column 0.
|
|
* @param {number} v1 The value for column 1.
|
|
* @param {number} v2 The value for column 2.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.setRowValues = function(mat, row, v0, v1, v2) {
|
|
mat[row] = v0;
|
|
mat[row + 3] = v1;
|
|
mat[row + 6] = v2;
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Sets the row values from the supplied vector.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the row values.
|
|
* @param {number} row The index of the row.
|
|
* @param {goog.vec.Vec3.AnyType} vec The vector containing the values.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.setRow = function(mat, row, vec) {
|
|
mat[row] = vec[0];
|
|
mat[row + 3] = vec[1];
|
|
mat[row + 6] = vec[2];
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Retrieves the row values into the given vector.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the values.
|
|
* @param {number} row The index of the row supplying the values.
|
|
* @param {goog.vec.Vec3.AnyType} vec The vector to receive the row.
|
|
* @return {goog.vec.Vec3.AnyType} return vec so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.getRow = function(mat, row, vec) {
|
|
vec[0] = mat[row];
|
|
vec[1] = mat[row + 3];
|
|
vec[2] = mat[row + 6];
|
|
return vec;
|
|
};
|
|
|
|
|
|
/**
|
|
* Sets the rows of the matrix from the supplied vectors.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
|
|
* @param {goog.vec.Vec3.AnyType} vec0 The values for row 0.
|
|
* @param {goog.vec.Vec3.AnyType} vec1 The values for row 1.
|
|
* @param {goog.vec.Vec3.AnyType} vec2 The values for row 2.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.setRows = function(mat, vec0, vec1, vec2) {
|
|
goog.vec.Mat3.setRow(mat, 0, vec0);
|
|
goog.vec.Mat3.setRow(mat, 1, vec1);
|
|
goog.vec.Mat3.setRow(mat, 2, vec2);
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Retrieves the rows of the matrix into the supplied vectors.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to supplying the values.
|
|
* @param {goog.vec.Vec3.AnyType} vec0 The vector to receive row 0.
|
|
* @param {goog.vec.Vec3.AnyType} vec1 The vector to receive row 1.
|
|
* @param {goog.vec.Vec3.AnyType} vec2 The vector to receive row 2.
|
|
*/
|
|
goog.vec.Mat3.getRows = function(mat, vec0, vec1, vec2) {
|
|
goog.vec.Mat3.getRow(mat, 0, vec0);
|
|
goog.vec.Mat3.getRow(mat, 1, vec1);
|
|
goog.vec.Mat3.getRow(mat, 2, vec2);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix the zero matrix.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so operations can be chained.
|
|
*/
|
|
goog.vec.Mat3.makeZero = function(mat) {
|
|
mat[0] = 0;
|
|
mat[1] = 0;
|
|
mat[2] = 0;
|
|
mat[3] = 0;
|
|
mat[4] = 0;
|
|
mat[5] = 0;
|
|
mat[6] = 0;
|
|
mat[7] = 0;
|
|
mat[8] = 0;
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix the identity matrix.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so operations can be chained.
|
|
*/
|
|
goog.vec.Mat3.makeIdentity = function(mat) {
|
|
mat[0] = 1;
|
|
mat[1] = 0;
|
|
mat[2] = 0;
|
|
mat[3] = 0;
|
|
mat[4] = 1;
|
|
mat[5] = 0;
|
|
mat[6] = 0;
|
|
mat[7] = 0;
|
|
mat[8] = 1;
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Performs a per-component addition of the matrices mat0 and mat1, storing
|
|
* the result into resultMat.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat0 The first addend.
|
|
* @param {goog.vec.Mat3.AnyType} mat1 The second addend.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to
|
|
* receive the results (may be either mat0 or mat1).
|
|
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.addMat = function(mat0, mat1, resultMat) {
|
|
resultMat[0] = mat0[0] + mat1[0];
|
|
resultMat[1] = mat0[1] + mat1[1];
|
|
resultMat[2] = mat0[2] + mat1[2];
|
|
resultMat[3] = mat0[3] + mat1[3];
|
|
resultMat[4] = mat0[4] + mat1[4];
|
|
resultMat[5] = mat0[5] + mat1[5];
|
|
resultMat[6] = mat0[6] + mat1[6];
|
|
resultMat[7] = mat0[7] + mat1[7];
|
|
resultMat[8] = mat0[8] + mat1[8];
|
|
return resultMat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Performs a per-component subtraction of the matrices mat0 and mat1,
|
|
* storing the result into resultMat.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat0 The minuend.
|
|
* @param {goog.vec.Mat3.AnyType} mat1 The subtrahend.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
|
|
* the results (may be either mat0 or mat1).
|
|
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.subMat = function(mat0, mat1, resultMat) {
|
|
resultMat[0] = mat0[0] - mat1[0];
|
|
resultMat[1] = mat0[1] - mat1[1];
|
|
resultMat[2] = mat0[2] - mat1[2];
|
|
resultMat[3] = mat0[3] - mat1[3];
|
|
resultMat[4] = mat0[4] - mat1[4];
|
|
resultMat[5] = mat0[5] - mat1[5];
|
|
resultMat[6] = mat0[6] - mat1[6];
|
|
resultMat[7] = mat0[7] - mat1[7];
|
|
resultMat[8] = mat0[8] - mat1[8];
|
|
return resultMat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Multiplies matrix mat0 with the given scalar, storing the result
|
|
* into resultMat.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} scalar The scalar value to multiple to each element of mat.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
|
|
* the results (may be mat).
|
|
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.multScalar = function(mat, scalar, resultMat) {
|
|
resultMat[0] = mat[0] * scalar;
|
|
resultMat[1] = mat[1] * scalar;
|
|
resultMat[2] = mat[2] * scalar;
|
|
resultMat[3] = mat[3] * scalar;
|
|
resultMat[4] = mat[4] * scalar;
|
|
resultMat[5] = mat[5] * scalar;
|
|
resultMat[6] = mat[6] * scalar;
|
|
resultMat[7] = mat[7] * scalar;
|
|
resultMat[8] = mat[8] * scalar;
|
|
return resultMat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Multiplies the two matrices mat0 and mat1 using matrix multiplication,
|
|
* storing the result into resultMat.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat0 The first (left hand) matrix.
|
|
* @param {goog.vec.Mat3.AnyType} mat1 The second (right hand) matrix.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
|
|
* the results (may be either mat0 or mat1).
|
|
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.multMat = function(mat0, mat1, resultMat) {
|
|
var a00 = mat0[0], a10 = mat0[1], a20 = mat0[2];
|
|
var a01 = mat0[3], a11 = mat0[4], a21 = mat0[5];
|
|
var a02 = mat0[6], a12 = mat0[7], a22 = mat0[8];
|
|
|
|
var b00 = mat1[0], b10 = mat1[1], b20 = mat1[2];
|
|
var b01 = mat1[3], b11 = mat1[4], b21 = mat1[5];
|
|
var b02 = mat1[6], b12 = mat1[7], b22 = mat1[8];
|
|
|
|
resultMat[0] = a00 * b00 + a01 * b10 + a02 * b20;
|
|
resultMat[1] = a10 * b00 + a11 * b10 + a12 * b20;
|
|
resultMat[2] = a20 * b00 + a21 * b10 + a22 * b20;
|
|
resultMat[3] = a00 * b01 + a01 * b11 + a02 * b21;
|
|
resultMat[4] = a10 * b01 + a11 * b11 + a12 * b21;
|
|
resultMat[5] = a20 * b01 + a21 * b11 + a22 * b21;
|
|
resultMat[6] = a00 * b02 + a01 * b12 + a02 * b22;
|
|
resultMat[7] = a10 * b02 + a11 * b12 + a12 * b22;
|
|
resultMat[8] = a20 * b02 + a21 * b12 + a22 * b22;
|
|
return resultMat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Transposes the given matrix mat storing the result into resultMat.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix to transpose.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
|
|
* the results (may be mat).
|
|
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.transpose = function(mat, resultMat) {
|
|
if (resultMat == mat) {
|
|
var a10 = mat[1], a20 = mat[2], a21 = mat[5];
|
|
resultMat[1] = mat[3];
|
|
resultMat[2] = mat[6];
|
|
resultMat[3] = a10;
|
|
resultMat[5] = mat[7];
|
|
resultMat[6] = a20;
|
|
resultMat[7] = a21;
|
|
} else {
|
|
resultMat[0] = mat[0];
|
|
resultMat[1] = mat[3];
|
|
resultMat[2] = mat[6];
|
|
resultMat[3] = mat[1];
|
|
resultMat[4] = mat[4];
|
|
resultMat[5] = mat[7];
|
|
resultMat[6] = mat[2];
|
|
resultMat[7] = mat[5];
|
|
resultMat[8] = mat[8];
|
|
}
|
|
return resultMat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Computes the inverse of mat0 storing the result into resultMat. If the
|
|
* inverse is defined, this function returns true, false otherwise.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat0 The matrix to invert.
|
|
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
|
|
* the result (may be mat0).
|
|
* @return {boolean} True if the inverse is defined. If false is returned,
|
|
* resultMat is not modified.
|
|
*/
|
|
goog.vec.Mat3.invert = function(mat0, resultMat) {
|
|
var a00 = mat0[0], a10 = mat0[1], a20 = mat0[2];
|
|
var a01 = mat0[3], a11 = mat0[4], a21 = mat0[5];
|
|
var a02 = mat0[6], a12 = mat0[7], a22 = mat0[8];
|
|
|
|
var t00 = a11 * a22 - a12 * a21;
|
|
var t10 = a12 * a20 - a10 * a22;
|
|
var t20 = a10 * a21 - a11 * a20;
|
|
var det = a00 * t00 + a01 * t10 + a02 * t20;
|
|
if (det == 0) {
|
|
return false;
|
|
}
|
|
|
|
var idet = 1 / det;
|
|
resultMat[0] = t00 * idet;
|
|
resultMat[3] = (a02 * a21 - a01 * a22) * idet;
|
|
resultMat[6] = (a01 * a12 - a02 * a11) * idet;
|
|
|
|
resultMat[1] = t10 * idet;
|
|
resultMat[4] = (a00 * a22 - a02 * a20) * idet;
|
|
resultMat[7] = (a02 * a10 - a00 * a12) * idet;
|
|
|
|
resultMat[2] = t20 * idet;
|
|
resultMat[5] = (a01 * a20 - a00 * a21) * idet;
|
|
resultMat[8] = (a00 * a11 - a01 * a10) * idet;
|
|
return true;
|
|
};
|
|
|
|
|
|
/**
|
|
* Returns true if the components of mat0 are equal to the components of mat1.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat0 The first matrix.
|
|
* @param {goog.vec.Mat3.AnyType} mat1 The second matrix.
|
|
* @return {boolean} True if the the two matrices are equivalent.
|
|
*/
|
|
goog.vec.Mat3.equals = function(mat0, mat1) {
|
|
return mat0.length == mat1.length &&
|
|
mat0[0] == mat1[0] && mat0[1] == mat1[1] && mat0[2] == mat1[2] &&
|
|
mat0[3] == mat1[3] && mat0[4] == mat1[4] && mat0[5] == mat1[5] &&
|
|
mat0[6] == mat1[6] && mat0[7] == mat1[7] && mat0[8] == mat1[8];
|
|
};
|
|
|
|
|
|
/**
|
|
* Transforms the given vector with the given matrix storing the resulting,
|
|
* transformed matrix into resultVec.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the transformation.
|
|
* @param {goog.vec.Vec3.AnyType} vec The vector to transform.
|
|
* @param {goog.vec.Vec3.AnyType} resultVec The vector to
|
|
* receive the results (may be vec).
|
|
* @return {goog.vec.Vec3.AnyType} return resultVec so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.multVec3 = function(mat, vec, resultVec) {
|
|
var x = vec[0], y = vec[1], z = vec[2];
|
|
resultVec[0] = x * mat[0] + y * mat[3] + z * mat[6];
|
|
resultVec[1] = x * mat[1] + y * mat[4] + z * mat[7];
|
|
resultVec[2] = x * mat[2] + y * mat[5] + z * mat[8];
|
|
return resultVec;
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a translation matrix with x and y
|
|
* translation values.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} x The translation along the x axis.
|
|
* @param {number} y The translation along the y axis.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeTranslate = function(mat, x, y) {
|
|
goog.vec.Mat3.makeIdentity(mat);
|
|
return goog.vec.Mat3.setColumnValues(mat, 2, x, y, 1);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a scale matrix with x, y, and z scale factors.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The 3x3 (9-element) matrix
|
|
* array to receive the new scale matrix.
|
|
* @param {number} x The scale along the x axis.
|
|
* @param {number} y The scale along the y axis.
|
|
* @param {number} z The scale along the z axis.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeScale = function(mat, x, y, z) {
|
|
goog.vec.Mat3.makeIdentity(mat);
|
|
return goog.vec.Mat3.setDiagonalValues(mat, x, y, z);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a rotation matrix with the given rotation
|
|
* angle about the axis defined by the vector (ax, ay, az).
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The rotation angle in radians.
|
|
* @param {number} ax The x component of the rotation axis.
|
|
* @param {number} ay The y component of the rotation axis.
|
|
* @param {number} az The z component of the rotation axis.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeRotate = function(mat, angle, ax, ay, az) {
|
|
var c = Math.cos(angle);
|
|
var d = 1 - c;
|
|
var s = Math.sin(angle);
|
|
|
|
return goog.vec.Mat3.setFromValues(mat,
|
|
ax * ax * d + c,
|
|
ax * ay * d + az * s,
|
|
ax * az * d - ay * s,
|
|
|
|
ax * ay * d - az * s,
|
|
ay * ay * d + c,
|
|
ay * az * d + ax * s,
|
|
|
|
ax * az * d + ay * s,
|
|
ay * az * d - ax * s,
|
|
az * az * d + c);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a rotation matrix with the given rotation
|
|
* angle about the X axis.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The rotation angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeRotateX = function(mat, angle) {
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
return goog.vec.Mat3.setFromValues(mat,
|
|
1, 0, 0,
|
|
0, c, s,
|
|
0, -s, c);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a rotation matrix with the given rotation
|
|
* angle about the Y axis.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The rotation angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeRotateY = function(mat, angle) {
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
return goog.vec.Mat3.setFromValues(mat,
|
|
c, 0, -s,
|
|
0, 1, 0,
|
|
s, 0, c);
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a rotation matrix with the given rotation
|
|
* angle about the Z axis.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The rotation angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeRotateZ = function(mat, angle) {
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
return goog.vec.Mat3.setFromValues(mat,
|
|
c, s, 0,
|
|
-s, c, 0,
|
|
0, 0, 1);
|
|
};
|
|
|
|
|
|
/**
|
|
* Rotate the given matrix by angle about the x,y,z axis. Equivalent to:
|
|
* goog.vec.Mat3.multMat(
|
|
* mat,
|
|
* goog.vec.Mat3.makeRotate(goog.vec.Mat3.create(), angle, x, y, z),
|
|
* mat);
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The angle in radians.
|
|
* @param {number} x The x component of the rotation axis.
|
|
* @param {number} y The y component of the rotation axis.
|
|
* @param {number} z The z component of the rotation axis.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.rotate = function(mat, angle, x, y, z) {
|
|
var m00 = mat[0], m10 = mat[1], m20 = mat[2];
|
|
var m01 = mat[3], m11 = mat[4], m21 = mat[5];
|
|
var m02 = mat[6], m12 = mat[7], m22 = mat[8];
|
|
|
|
var cosAngle = Math.cos(angle);
|
|
var sinAngle = Math.sin(angle);
|
|
var diffCosAngle = 1 - cosAngle;
|
|
var r00 = x * x * diffCosAngle + cosAngle;
|
|
var r10 = x * y * diffCosAngle + z * sinAngle;
|
|
var r20 = x * z * diffCosAngle - y * sinAngle;
|
|
|
|
var r01 = x * y * diffCosAngle - z * sinAngle;
|
|
var r11 = y * y * diffCosAngle + cosAngle;
|
|
var r21 = y * z * diffCosAngle + x * sinAngle;
|
|
|
|
var r02 = x * z * diffCosAngle + y * sinAngle;
|
|
var r12 = y * z * diffCosAngle - x * sinAngle;
|
|
var r22 = z * z * diffCosAngle + cosAngle;
|
|
|
|
return goog.vec.Mat3.setFromValues(
|
|
mat,
|
|
m00 * r00 + m01 * r10 + m02 * r20,
|
|
m10 * r00 + m11 * r10 + m12 * r20,
|
|
m20 * r00 + m21 * r10 + m22 * r20,
|
|
|
|
m00 * r01 + m01 * r11 + m02 * r21,
|
|
m10 * r01 + m11 * r11 + m12 * r21,
|
|
m20 * r01 + m21 * r11 + m22 * r21,
|
|
|
|
m00 * r02 + m01 * r12 + m02 * r22,
|
|
m10 * r02 + m11 * r12 + m12 * r22,
|
|
m20 * r02 + m21 * r12 + m22 * r22);
|
|
};
|
|
|
|
|
|
/**
|
|
* Rotate the given matrix by angle about the x axis. Equivalent to:
|
|
* goog.vec.Mat3.multMat(
|
|
* mat,
|
|
* goog.vec.Mat3.makeRotateX(goog.vec.Mat3.create(), angle),
|
|
* mat);
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.rotateX = function(mat, angle) {
|
|
var m01 = mat[3], m11 = mat[4], m21 = mat[5];
|
|
var m02 = mat[6], m12 = mat[7], m22 = mat[8];
|
|
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
|
|
mat[3] = m01 * c + m02 * s;
|
|
mat[4] = m11 * c + m12 * s;
|
|
mat[5] = m21 * c + m22 * s;
|
|
mat[6] = m01 * -s + m02 * c;
|
|
mat[7] = m11 * -s + m12 * c;
|
|
mat[8] = m21 * -s + m22 * c;
|
|
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Rotate the given matrix by angle about the y axis. Equivalent to:
|
|
* goog.vec.Mat3.multMat(
|
|
* mat,
|
|
* goog.vec.Mat3.makeRotateY(goog.vec.Mat3.create(), angle),
|
|
* mat);
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.rotateY = function(mat, angle) {
|
|
var m00 = mat[0], m10 = mat[1], m20 = mat[2];
|
|
var m02 = mat[6], m12 = mat[7], m22 = mat[8];
|
|
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
|
|
mat[0] = m00 * c + m02 * -s;
|
|
mat[1] = m10 * c + m12 * -s;
|
|
mat[2] = m20 * c + m22 * -s;
|
|
mat[6] = m00 * s + m02 * c;
|
|
mat[7] = m10 * s + m12 * c;
|
|
mat[8] = m20 * s + m22 * c;
|
|
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Rotate the given matrix by angle about the z axis. Equivalent to:
|
|
* goog.vec.Mat3.multMat(
|
|
* mat,
|
|
* goog.vec.Mat3.makeRotateZ(goog.vec.Mat3.create(), angle),
|
|
* mat);
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} angle The angle in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.rotateZ = function(mat, angle) {
|
|
var m00 = mat[0], m10 = mat[1], m20 = mat[2];
|
|
var m01 = mat[3], m11 = mat[4], m21 = mat[5];
|
|
|
|
var c = Math.cos(angle);
|
|
var s = Math.sin(angle);
|
|
|
|
mat[0] = m00 * c + m01 * s;
|
|
mat[1] = m10 * c + m11 * s;
|
|
mat[2] = m20 * c + m21 * s;
|
|
mat[3] = m00 * -s + m01 * c;
|
|
mat[4] = m10 * -s + m11 * c;
|
|
mat[5] = m20 * -s + m21 * c;
|
|
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Makes the given 3x3 matrix a rotation matrix given Euler angles using
|
|
* the ZXZ convention.
|
|
* Given the euler angles [theta1, theta2, theta3], the rotation is defined as
|
|
* rotation = rotation_z(theta1) * rotation_x(theta2) * rotation_z(theta3),
|
|
* with theta1 in [0, 2 * pi], theta2 in [0, pi] and theta3 in [0, 2 * pi].
|
|
* rotation_x(theta) means rotation around the X axis of theta radians.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {number} theta1 The angle of rotation around the Z axis in radians.
|
|
* @param {number} theta2 The angle of rotation around the X axis in radians.
|
|
* @param {number} theta3 The angle of rotation around the Z axis in radians.
|
|
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
|
|
* chained.
|
|
*/
|
|
goog.vec.Mat3.makeEulerZXZ = function(mat, theta1, theta2, theta3) {
|
|
var c1 = Math.cos(theta1);
|
|
var s1 = Math.sin(theta1);
|
|
|
|
var c2 = Math.cos(theta2);
|
|
var s2 = Math.sin(theta2);
|
|
|
|
var c3 = Math.cos(theta3);
|
|
var s3 = Math.sin(theta3);
|
|
|
|
mat[0] = c1 * c3 - c2 * s1 * s3;
|
|
mat[1] = c2 * c1 * s3 + c3 * s1;
|
|
mat[2] = s3 * s2;
|
|
|
|
mat[3] = -c1 * s3 - c3 * c2 * s1;
|
|
mat[4] = c1 * c2 * c3 - s1 * s3;
|
|
mat[5] = c3 * s2;
|
|
|
|
mat[6] = s2 * s1;
|
|
mat[7] = -c1 * s2;
|
|
mat[8] = c2;
|
|
|
|
return mat;
|
|
};
|
|
|
|
|
|
/**
|
|
* Decomposes a rotation matrix into Euler angles using the ZXZ convention so
|
|
* that rotation = rotation_z(theta1) * rotation_x(theta2) * rotation_z(theta3),
|
|
* with theta1 in [0, 2 * pi], theta2 in [0, pi] and theta3 in [0, 2 * pi].
|
|
* rotation_x(theta) means rotation around the X axis of theta radians.
|
|
*
|
|
* @param {goog.vec.Mat3.AnyType} mat The matrix.
|
|
* @param {goog.vec.Vec3.AnyType} euler The ZXZ Euler angles in
|
|
* radians as [theta1, theta2, theta3].
|
|
* @param {boolean=} opt_theta2IsNegative Whether theta2 is in [-pi, 0] instead
|
|
* of the default [0, pi].
|
|
* @return {goog.vec.Vec3.AnyType} return euler so that operations can be
|
|
* chained together.
|
|
*/
|
|
goog.vec.Mat3.toEulerZXZ = function(mat, euler, opt_theta2IsNegative) {
|
|
// There is an ambiguity in the sign of sinTheta2 because of the sqrt.
|
|
var sinTheta2 = Math.sqrt(mat[2] * mat[2] + mat[5] * mat[5]);
|
|
|
|
// By default we explicitely constrain theta2 to be in [0, pi],
|
|
// so sinTheta2 is always positive. We can change the behavior and specify
|
|
// theta2 to be negative in [-pi, 0] with opt_Theta2IsNegative.
|
|
var signTheta2 = opt_theta2IsNegative ? -1 : 1;
|
|
|
|
if (sinTheta2 > goog.vec.EPSILON) {
|
|
euler[2] = Math.atan2(mat[2] * signTheta2, mat[5] * signTheta2);
|
|
euler[1] = Math.atan2(sinTheta2 * signTheta2, mat[8]);
|
|
euler[0] = Math.atan2(mat[6] * signTheta2, -mat[7] * signTheta2);
|
|
} else {
|
|
// There is also an arbitrary choice for theta1 = 0 or theta2 = 0 here.
|
|
// We assume theta1 = 0 as some applications do not allow the camera to roll
|
|
// (i.e. have theta1 != 0).
|
|
euler[0] = 0;
|
|
euler[1] = Math.atan2(sinTheta2 * signTheta2, mat[8]);
|
|
euler[2] = Math.atan2(mat[1], mat[0]);
|
|
}
|
|
|
|
// Atan2 outputs angles in [-pi, pi] so we bring them back to [0, 2 * pi].
|
|
euler[0] = (euler[0] + Math.PI * 2) % (Math.PI * 2);
|
|
euler[2] = (euler[2] + Math.PI * 2) % (Math.PI * 2);
|
|
// For theta2 we want the angle to be in [0, pi] or [-pi, 0] depending on
|
|
// signTheta2.
|
|
euler[1] = ((euler[1] * signTheta2 + Math.PI * 2) % (Math.PI * 2)) *
|
|
signTheta2;
|
|
|
|
return euler;
|
|
};
|