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26
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1 /*
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2 * Copyright (C) 2009 Apple Inc. All Rights Reserved.
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3 *
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4 * Redistribution and use in source and binary forms, with or without
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5 * modification, are permitted provided that the following conditions
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6 * are met:
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7 * 1. Redistributions of source code must retain the above copyright
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8 * notice, this list of conditions and the following disclaimer.
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9 * 2. Redistributions in binary form must reproduce the above copyright
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10 * notice, this list of conditions and the following disclaimer in the
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11 * documentation and/or other materials provided with the distribution.
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12 *
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13 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
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14 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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15 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
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17 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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18 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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19 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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20 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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21 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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23 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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24 */
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25
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26 // J3DI (Jedi) - A support library for WebGL.
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27
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28 /*
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29 J3DI Math Classes. Currently includes:
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30
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31 J3DIMatrix4 - A 4x4 Matrix
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32 */
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33
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34 /*
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35 J3DIMatrix4 class
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36
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37 This class implements a 4x4 matrix. It has functions which duplicate the
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38 functionality of the OpenGL matrix stack and glut functions. On browsers
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39 that support it, CSSMatrix is used to accelerate operations.
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40
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41 IDL:
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42
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43 [
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44 Constructor(in J3DIMatrix4 matrix), // copy passed matrix into new J3DIMatrix4
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45 Constructor(in sequence<float> array) // create new J3DIMatrix4 with 16 floats (row major)
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46 Constructor() // create new J3DIMatrix4 with identity matrix
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47 ]
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48 interface J3DIMatrix4 {
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49 void load(in J3DIMatrix4 matrix); // copy the values from the passed matrix
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50 void load(in sequence<float> array); // copy 16 floats into the matrix
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51 sequence<float> getAsArray(); // return the matrix as an array of 16 floats
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52 Float32Array getAsFloat32Array(); // return the matrix as a Float32Array with 16 values
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53 void setUniform(in WebGLRenderingContext ctx, // Send the matrix to the passed uniform location in the passed context
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54 in WebGLUniformLocation loc,
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55 in boolean transpose);
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56 void makeIdentity(); // replace the matrix with identity
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57 void transpose(); // replace the matrix with its transpose
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58 void invert(); // replace the matrix with its inverse
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59
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60 void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
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61 void translate(in J3DVector3 v); // multiply the matrix by passed translation values on the right
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62 void scale(in float x, in float y, in float z); // multiply the matrix by passed scale values on the right
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63 void scale(in J3DVector3 v); // multiply the matrix by passed scale values on the right
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64 void rotate(in float angle, // multiply the matrix by passed rotation values on the right
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65 in float x, in float y, in float z); // (angle is in degrees)
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66 void rotate(in float angle, in J3DVector3 v); // multiply the matrix by passed rotation values on the right
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67 // (angle is in degrees)
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68 void multiply(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
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69 void divide(in float divisor); // divide the matrix by the passed divisor
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70 void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
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71 in float bottom, in float top,
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72 in float near, in float far);
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73 void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
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74 in float bottom, in float top,
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75 in float near, in float far);
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76 void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
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77 in float zNear, in float zFar);
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78 void lookat(in J3DVector3 eye, // multiply the matrix by the passed lookat
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79 in J3DVector3 center, in J3DVector3 up); // values on the right
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80 bool decompose(in J3DVector3 translate, // decompose the matrix into the passed vector
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81 in J3DVector3 rotate,
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82 in J3DVector3 scale,
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83 in J3DVector3 skew,
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84 in sequence<float> perspective);
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85 }
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86
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87 [
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88 Constructor(in J3DVector3 vector), // copy passed vector into new J3DVector3
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89 Constructor(in sequence<float> array) // create new J3DVector3 with 3 floats from array
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90 Constructor(in float x, in float y, in float z) // create new J3DVector3 with 3 floats
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91 Constructor() // create new J3DVector3 with (0,0,0)
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92 ]
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93 interface J3DVector3 {
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94 void load(in J3DVector3 vector); // copy the values from the passed vector
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95 void load(in sequence<float> array); // copy 3 floats into the vector from array
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96 void load(in float x, in float y, in float z); // copy 3 floats into the vector
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97 sequence<float> getAsArray(); // return the vector as an array of 3 floats
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98 Float32Array getAsFloat32Array(); // return the matrix as a Float32Array with 16 values
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99 void multMatrix(in J3DIMatrix4 matrix); // multiply the vector by the passed matrix (on the right)
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100 float vectorLength(); // return the length of the vector
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101 float dot(); // return the dot product of the vector
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102 void cross(in J3DVector3 v); // replace the vector with vector x v
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103 void divide(in float divisor); // divide the vector by the passed divisor
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104 }
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105 */
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106
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107 J3DIHasCSSMatrix = false;
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108 J3DIHasCSSMatrixCopy = false;
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109 /*
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110 if ("WebKitCSSMatrix" in window && ("media" in window && window.media.matchMedium("(-webkit-transform-3d)")) ||
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111 ("styleMedia" in window && window.styleMedia.matchMedium("(-webkit-transform-3d)"))) {
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112 J3DIHasCSSMatrix = true;
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113 if ("copy" in WebKitCSSMatrix.prototype)
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114 J3DIHasCSSMatrixCopy = true;
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115 }
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116 */
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117
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118 // console.log("J3DIHasCSSMatrix="+J3DIHasCSSMatrix);
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119 // console.log("J3DIHasCSSMatrixCopy="+J3DIHasCSSMatrixCopy);
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120
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121 //
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122 // J3DIMatrix4
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123 //
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124 J3DIMatrix4 = function(m)
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125 {
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126 if (J3DIHasCSSMatrix)
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127 this.$matrix = new WebKitCSSMatrix;
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128 else
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129 this.$matrix = new Object;
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130
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131 if (typeof m == 'object') {
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132 if ("length" in m && m.length >= 16) {
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133 this.load(m);
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134 return;
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135 }
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136 else if (m instanceof J3DIMatrix4) {
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137 this.load(m);
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138 return;
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139 }
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140 }
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141 this.makeIdentity();
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142 }
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143
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144 J3DIMatrix4.prototype.load = function()
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145 {
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146 if (arguments.length == 1 && typeof arguments[0] == 'object') {
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147 var matrix;
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148
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149 if (arguments[0] instanceof J3DIMatrix4) {
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150 matrix = arguments[0].$matrix;
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151
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152 this.$matrix.m11 = matrix.m11;
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153 this.$matrix.m12 = matrix.m12;
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154 this.$matrix.m13 = matrix.m13;
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155 this.$matrix.m14 = matrix.m14;
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156
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157 this.$matrix.m21 = matrix.m21;
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158 this.$matrix.m22 = matrix.m22;
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159 this.$matrix.m23 = matrix.m23;
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160 this.$matrix.m24 = matrix.m24;
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161
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162 this.$matrix.m31 = matrix.m31;
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163 this.$matrix.m32 = matrix.m32;
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164 this.$matrix.m33 = matrix.m33;
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165 this.$matrix.m34 = matrix.m34;
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166
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167 this.$matrix.m41 = matrix.m41;
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168 this.$matrix.m42 = matrix.m42;
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169 this.$matrix.m43 = matrix.m43;
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170 this.$matrix.m44 = matrix.m44;
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171 return;
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172 }
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173 else
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174 matrix = arguments[0];
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175
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176 if ("length" in matrix && matrix.length >= 16) {
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177 this.$matrix.m11 = matrix[0];
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178 this.$matrix.m12 = matrix[1];
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179 this.$matrix.m13 = matrix[2];
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180 this.$matrix.m14 = matrix[3];
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181
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182 this.$matrix.m21 = matrix[4];
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183 this.$matrix.m22 = matrix[5];
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184 this.$matrix.m23 = matrix[6];
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185 this.$matrix.m24 = matrix[7];
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186
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187 this.$matrix.m31 = matrix[8];
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188 this.$matrix.m32 = matrix[9];
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189 this.$matrix.m33 = matrix[10];
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190 this.$matrix.m34 = matrix[11];
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191
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192 this.$matrix.m41 = matrix[12];
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193 this.$matrix.m42 = matrix[13];
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194 this.$matrix.m43 = matrix[14];
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195 this.$matrix.m44 = matrix[15];
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196 return;
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197 }
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198 }
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199
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200 this.makeIdentity();
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201 }
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202
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203 J3DIMatrix4.prototype.getAsArray = function()
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204 {
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205 return [
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206 this.$matrix.m11, this.$matrix.m12, this.$matrix.m13, this.$matrix.m14,
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207 this.$matrix.m21, this.$matrix.m22, this.$matrix.m23, this.$matrix.m24,
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208 this.$matrix.m31, this.$matrix.m32, this.$matrix.m33, this.$matrix.m34,
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209 this.$matrix.m41, this.$matrix.m42, this.$matrix.m43, this.$matrix.m44
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210 ];
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211 }
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212
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213 J3DIMatrix4.prototype.getAsFloat32Array = function()
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214 {
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215 if (J3DIHasCSSMatrixCopy) {
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216 var array = new Float32Array(16);
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217 this.$matrix.copy(array);
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218 return array;
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219 }
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220 return new Float32Array(this.getAsArray());
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221 }
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222
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223 J3DIMatrix4.prototype.setUniform = function(ctx, loc, transpose)
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224 {
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225 if (J3DIMatrix4.setUniformArray == undefined) {
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226 J3DIMatrix4.setUniformWebGLArray = new Float32Array(16);
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227 J3DIMatrix4.setUniformArray = new Array(16);
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228 }
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229
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230 if (J3DIHasCSSMatrixCopy)
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231 this.$matrix.copy(J3DIMatrix4.setUniformWebGLArray);
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232 else {
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233 J3DIMatrix4.setUniformArray[0] = this.$matrix.m11;
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234 J3DIMatrix4.setUniformArray[1] = this.$matrix.m12;
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235 J3DIMatrix4.setUniformArray[2] = this.$matrix.m13;
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236 J3DIMatrix4.setUniformArray[3] = this.$matrix.m14;
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237 J3DIMatrix4.setUniformArray[4] = this.$matrix.m21;
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238 J3DIMatrix4.setUniformArray[5] = this.$matrix.m22;
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239 J3DIMatrix4.setUniformArray[6] = this.$matrix.m23;
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240 J3DIMatrix4.setUniformArray[7] = this.$matrix.m24;
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241 J3DIMatrix4.setUniformArray[8] = this.$matrix.m31;
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242 J3DIMatrix4.setUniformArray[9] = this.$matrix.m32;
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243 J3DIMatrix4.setUniformArray[10] = this.$matrix.m33;
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244 J3DIMatrix4.setUniformArray[11] = this.$matrix.m34;
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245 J3DIMatrix4.setUniformArray[12] = this.$matrix.m41;
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246 J3DIMatrix4.setUniformArray[13] = this.$matrix.m42;
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247 J3DIMatrix4.setUniformArray[14] = this.$matrix.m43;
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248 J3DIMatrix4.setUniformArray[15] = this.$matrix.m44;
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249
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250 J3DIMatrix4.setUniformWebGLArray.set(J3DIMatrix4.setUniformArray);
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251 }
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252
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253 ctx.uniformMatrix4fv(loc, transpose, J3DIMatrix4.setUniformWebGLArray);
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254 }
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255
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256 J3DIMatrix4.prototype.makeIdentity = function()
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257 {
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258 this.$matrix.m11 = 1;
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259 this.$matrix.m12 = 0;
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260 this.$matrix.m13 = 0;
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261 this.$matrix.m14 = 0;
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262
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263 this.$matrix.m21 = 0;
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264 this.$matrix.m22 = 1;
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265 this.$matrix.m23 = 0;
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266 this.$matrix.m24 = 0;
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267
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268 this.$matrix.m31 = 0;
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269 this.$matrix.m32 = 0;
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270 this.$matrix.m33 = 1;
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271 this.$matrix.m34 = 0;
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272
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273 this.$matrix.m41 = 0;
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274 this.$matrix.m42 = 0;
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275 this.$matrix.m43 = 0;
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276 this.$matrix.m44 = 1;
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277 }
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278
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279 J3DIMatrix4.prototype.transpose = function()
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280 {
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281 var tmp = this.$matrix.m12;
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282 this.$matrix.m12 = this.$matrix.m21;
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283 this.$matrix.m21 = tmp;
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284
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285 tmp = this.$matrix.m13;
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286 this.$matrix.m13 = this.$matrix.m31;
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287 this.$matrix.m31 = tmp;
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288
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289 tmp = this.$matrix.m14;
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290 this.$matrix.m14 = this.$matrix.m41;
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291 this.$matrix.m41 = tmp;
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292
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293 tmp = this.$matrix.m23;
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294 this.$matrix.m23 = this.$matrix.m32;
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295 this.$matrix.m32 = tmp;
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296
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297 tmp = this.$matrix.m24;
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298 this.$matrix.m24 = this.$matrix.m42;
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299 this.$matrix.m42 = tmp;
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300
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301 tmp = this.$matrix.m34;
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302 this.$matrix.m34 = this.$matrix.m43;
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303 this.$matrix.m43 = tmp;
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304 }
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305
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306 J3DIMatrix4.prototype.invert = function()
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307 {
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308 if (J3DIHasCSSMatrix) {
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309 this.$matrix = this.$matrix.inverse();
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310 return;
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311 }
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312
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313 // Calculate the 4x4 determinant
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314 // If the determinant is zero,
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315 // then the inverse matrix is not unique.
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316 var det = this._determinant4x4();
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317
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318 if (Math.abs(det) < 1e-8)
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319 return null;
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320
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321 this._makeAdjoint();
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322
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323 // Scale the adjoint matrix to get the inverse
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324 this.$matrix.m11 /= det;
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325 this.$matrix.m12 /= det;
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326 this.$matrix.m13 /= det;
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327 this.$matrix.m14 /= det;
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328
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329 this.$matrix.m21 /= det;
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330 this.$matrix.m22 /= det;
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331 this.$matrix.m23 /= det;
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332 this.$matrix.m24 /= det;
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333
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334 this.$matrix.m31 /= det;
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335 this.$matrix.m32 /= det;
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336 this.$matrix.m33 /= det;
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337 this.$matrix.m34 /= det;
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338
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339 this.$matrix.m41 /= det;
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340 this.$matrix.m42 /= det;
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341 this.$matrix.m43 /= det;
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342 this.$matrix.m44 /= det;
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343 }
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344
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345 J3DIMatrix4.prototype.translate = function(x,y,z)
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346 {
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347 if (typeof x == 'object' && "length" in x) {
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348 var t = x;
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349 x = t[0];
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350 y = t[1];
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351 z = t[2];
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352 }
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353 else {
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354 if (x == undefined)
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355 x = 0;
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356 if (y == undefined)
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357 y = 0;
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358 if (z == undefined)
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359 z = 0;
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360 }
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361
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362 if (J3DIHasCSSMatrix) {
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363 this.$matrix = this.$matrix.translate(x, y, z);
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364 return;
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365 }
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366
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367 var matrix = new J3DIMatrix4();
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368 matrix.$matrix.m41 = x;
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369 matrix.$matrix.m42 = y;
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370 matrix.$matrix.m43 = z;
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371
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372 this.multiply(matrix);
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373 }
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374
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375 J3DIMatrix4.prototype.scale = function(x,y,z)
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376 {
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377 if (typeof x == 'object' && "length" in x) {
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378 var t = x;
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379 x = t[0];
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380 y = t[1];
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381 z = t[2];
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382 }
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383 else {
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384 if (x == undefined)
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385 x = 1;
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|
|
386 if (z == undefined) {
|
|
|
387 if (y == undefined) {
|
|
|
388 y = x;
|
|
|
389 z = x;
|
|
|
390 }
|
|
|
391 else
|
|
|
392 z = 1;
|
|
|
393 }
|
|
|
394 else if (y == undefined)
|
|
|
395 y = x;
|
|
|
396 }
|
|
|
397
|
|
|
398 if (J3DIHasCSSMatrix) {
|
|
|
399 this.$matrix = this.$matrix.scale(x, y, z);
|
|
|
400 return;
|
|
|
401 }
|
|
|
402
|
|
|
403 var matrix = new J3DIMatrix4();
|
|
|
404 matrix.$matrix.m11 = x;
|
|
|
405 matrix.$matrix.m22 = y;
|
|
|
406 matrix.$matrix.m33 = z;
|
|
|
407
|
|
|
408 this.multiply(matrix);
|
|
|
409 }
|
|
|
410
|
|
|
411 J3DIMatrix4.prototype.rotate = function(angle,x,y,z)
|
|
|
412 {
|
|
|
413 // Forms are (angle, x,y,z), (angle,vector), (angleX, angleY, angleZ), (angle)
|
|
|
414 if (typeof x == 'object' && "length" in x) {
|
|
|
415 var t = x;
|
|
|
416 x = t[0];
|
|
|
417 y = t[1];
|
|
|
418 z = t[2];
|
|
|
419 }
|
|
|
420 else {
|
|
|
421 if (arguments.length == 1) {
|
|
|
422 x = 0;
|
|
|
423 y = 0;
|
|
|
424 z = 1;
|
|
|
425 }
|
|
|
426 else if (arguments.length == 3) {
|
|
|
427 this.rotate(angle, 1,0,0); // about X axis
|
|
|
428 this.rotate(x, 0,1,0); // about Y axis
|
|
|
429 this.rotate(y, 0,0,1); // about Z axis
|
|
|
430 return;
|
|
|
431 }
|
|
|
432 }
|
|
|
433
|
|
|
434 if (J3DIHasCSSMatrix) {
|
|
|
435 this.$matrix = this.$matrix.rotateAxisAngle(x, y, z, angle);
|
|
|
436 return;
|
|
|
437 }
|
|
|
438
|
|
|
439 // angles are in degrees. Switch to radians
|
|
|
440 angle = angle / 180 * Math.PI;
|
|
|
441
|
|
|
442 angle /= 2;
|
|
|
443 var sinA = Math.sin(angle);
|
|
|
444 var cosA = Math.cos(angle);
|
|
|
445 var sinA2 = sinA * sinA;
|
|
|
446
|
|
|
447 // normalize
|
|
|
448 var len = Math.sqrt(x * x + y * y + z * z);
|
|
|
449 if (len == 0) {
|
|
|
450 // bad vector, just use something reasonable
|
|
|
451 x = 0;
|
|
|
452 y = 0;
|
|
|
453 z = 1;
|
|
|
454 } else if (len != 1) {
|
|
|
455 x /= len;
|
|
|
456 y /= len;
|
|
|
457 z /= len;
|
|
|
458 }
|
|
|
459
|
|
|
460 var mat = new J3DIMatrix4();
|
|
|
461
|
|
|
462 // optimize case where axis is along major axis
|
|
|
463 if (x == 1 && y == 0 && z == 0) {
|
|
|
464 mat.$matrix.m11 = 1;
|
|
|
465 mat.$matrix.m12 = 0;
|
|
|
466 mat.$matrix.m13 = 0;
|
|
|
467 mat.$matrix.m21 = 0;
|
|
|
468 mat.$matrix.m22 = 1 - 2 * sinA2;
|
|
|
469 mat.$matrix.m23 = 2 * sinA * cosA;
|
|
|
470 mat.$matrix.m31 = 0;
|
|
|
471 mat.$matrix.m32 = -2 * sinA * cosA;
|
|
|
472 mat.$matrix.m33 = 1 - 2 * sinA2;
|
|
|
473 mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
|
474 mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
|
475 mat.$matrix.m44 = 1;
|
|
|
476 } else if (x == 0 && y == 1 && z == 0) {
|
|
|
477 mat.$matrix.m11 = 1 - 2 * sinA2;
|
|
|
478 mat.$matrix.m12 = 0;
|
|
|
479 mat.$matrix.m13 = -2 * sinA * cosA;
|
|
|
480 mat.$matrix.m21 = 0;
|
|
|
481 mat.$matrix.m22 = 1;
|
|
|
482 mat.$matrix.m23 = 0;
|
|
|
483 mat.$matrix.m31 = 2 * sinA * cosA;
|
|
|
484 mat.$matrix.m32 = 0;
|
|
|
485 mat.$matrix.m33 = 1 - 2 * sinA2;
|
|
|
486 mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
|
487 mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
|
488 mat.$matrix.m44 = 1;
|
|
|
489 } else if (x == 0 && y == 0 && z == 1) {
|
|
|
490 mat.$matrix.m11 = 1 - 2 * sinA2;
|
|
|
491 mat.$matrix.m12 = 2 * sinA * cosA;
|
|
|
492 mat.$matrix.m13 = 0;
|
|
|
493 mat.$matrix.m21 = -2 * sinA * cosA;
|
|
|
494 mat.$matrix.m22 = 1 - 2 * sinA2;
|
|
|
495 mat.$matrix.m23 = 0;
|
|
|
496 mat.$matrix.m31 = 0;
|
|
|
497 mat.$matrix.m32 = 0;
|
|
|
498 mat.$matrix.m33 = 1;
|
|
|
499 mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
|
500 mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
|
501 mat.$matrix.m44 = 1;
|
|
|
502 } else {
|
|
|
503 var x2 = x*x;
|
|
|
504 var y2 = y*y;
|
|
|
505 var z2 = z*z;
|
|
|
506
|
|
|
507 mat.$matrix.m11 = 1 - 2 * (y2 + z2) * sinA2;
|
|
|
508 mat.$matrix.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
|
|
|
509 mat.$matrix.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
|
|
|
510 mat.$matrix.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
|
|
|
511 mat.$matrix.m22 = 1 - 2 * (z2 + x2) * sinA2;
|
|
|
512 mat.$matrix.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
|
|
|
513 mat.$matrix.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
|
|
|
514 mat.$matrix.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
|
|
|
515 mat.$matrix.m33 = 1 - 2 * (x2 + y2) * sinA2;
|
|
|
516 mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
|
517 mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
|
518 mat.$matrix.m44 = 1;
|
|
|
519 }
|
|
|
520 this.multiply(mat);
|
|
|
521 }
|
|
|
522
|
|
|
523 J3DIMatrix4.prototype.multiply = function(mat)
|
|
|
524 {
|
|
|
525 if (J3DIHasCSSMatrix) {
|
|
|
526 this.$matrix = this.$matrix.multiply(mat.$matrix);
|
|
|
527 return;
|
|
|
528 }
|
|
|
529
|
|
|
530 var m11 = (mat.$matrix.m11 * this.$matrix.m11 + mat.$matrix.m12 * this.$matrix.m21
|
|
|
531 + mat.$matrix.m13 * this.$matrix.m31 + mat.$matrix.m14 * this.$matrix.m41);
|
|
|
532 var m12 = (mat.$matrix.m11 * this.$matrix.m12 + mat.$matrix.m12 * this.$matrix.m22
|
|
|
533 + mat.$matrix.m13 * this.$matrix.m32 + mat.$matrix.m14 * this.$matrix.m42);
|
|
|
534 var m13 = (mat.$matrix.m11 * this.$matrix.m13 + mat.$matrix.m12 * this.$matrix.m23
|
|
|
535 + mat.$matrix.m13 * this.$matrix.m33 + mat.$matrix.m14 * this.$matrix.m43);
|
|
|
536 var m14 = (mat.$matrix.m11 * this.$matrix.m14 + mat.$matrix.m12 * this.$matrix.m24
|
|
|
537 + mat.$matrix.m13 * this.$matrix.m34 + mat.$matrix.m14 * this.$matrix.m44);
|
|
|
538
|
|
|
539 var m21 = (mat.$matrix.m21 * this.$matrix.m11 + mat.$matrix.m22 * this.$matrix.m21
|
|
|
540 + mat.$matrix.m23 * this.$matrix.m31 + mat.$matrix.m24 * this.$matrix.m41);
|
|
|
541 var m22 = (mat.$matrix.m21 * this.$matrix.m12 + mat.$matrix.m22 * this.$matrix.m22
|
|
|
542 + mat.$matrix.m23 * this.$matrix.m32 + mat.$matrix.m24 * this.$matrix.m42);
|
|
|
543 var m23 = (mat.$matrix.m21 * this.$matrix.m13 + mat.$matrix.m22 * this.$matrix.m23
|
|
|
544 + mat.$matrix.m23 * this.$matrix.m33 + mat.$matrix.m24 * this.$matrix.m43);
|
|
|
545 var m24 = (mat.$matrix.m21 * this.$matrix.m14 + mat.$matrix.m22 * this.$matrix.m24
|
|
|
546 + mat.$matrix.m23 * this.$matrix.m34 + mat.$matrix.m24 * this.$matrix.m44);
|
|
|
547
|
|
|
548 var m31 = (mat.$matrix.m31 * this.$matrix.m11 + mat.$matrix.m32 * this.$matrix.m21
|
|
|
549 + mat.$matrix.m33 * this.$matrix.m31 + mat.$matrix.m34 * this.$matrix.m41);
|
|
|
550 var m32 = (mat.$matrix.m31 * this.$matrix.m12 + mat.$matrix.m32 * this.$matrix.m22
|
|
|
551 + mat.$matrix.m33 * this.$matrix.m32 + mat.$matrix.m34 * this.$matrix.m42);
|
|
|
552 var m33 = (mat.$matrix.m31 * this.$matrix.m13 + mat.$matrix.m32 * this.$matrix.m23
|
|
|
553 + mat.$matrix.m33 * this.$matrix.m33 + mat.$matrix.m34 * this.$matrix.m43);
|
|
|
554 var m34 = (mat.$matrix.m31 * this.$matrix.m14 + mat.$matrix.m32 * this.$matrix.m24
|
|
|
555 + mat.$matrix.m33 * this.$matrix.m34 + mat.$matrix.m34 * this.$matrix.m44);
|
|
|
556
|
|
|
557 var m41 = (mat.$matrix.m41 * this.$matrix.m11 + mat.$matrix.m42 * this.$matrix.m21
|
|
|
558 + mat.$matrix.m43 * this.$matrix.m31 + mat.$matrix.m44 * this.$matrix.m41);
|
|
|
559 var m42 = (mat.$matrix.m41 * this.$matrix.m12 + mat.$matrix.m42 * this.$matrix.m22
|
|
|
560 + mat.$matrix.m43 * this.$matrix.m32 + mat.$matrix.m44 * this.$matrix.m42);
|
|
|
561 var m43 = (mat.$matrix.m41 * this.$matrix.m13 + mat.$matrix.m42 * this.$matrix.m23
|
|
|
562 + mat.$matrix.m43 * this.$matrix.m33 + mat.$matrix.m44 * this.$matrix.m43);
|
|
|
563 var m44 = (mat.$matrix.m41 * this.$matrix.m14 + mat.$matrix.m42 * this.$matrix.m24
|
|
|
564 + mat.$matrix.m43 * this.$matrix.m34 + mat.$matrix.m44 * this.$matrix.m44);
|
|
|
565
|
|
|
566 this.$matrix.m11 = m11;
|
|
|
567 this.$matrix.m12 = m12;
|
|
|
568 this.$matrix.m13 = m13;
|
|
|
569 this.$matrix.m14 = m14;
|
|
|
570
|
|
|
571 this.$matrix.m21 = m21;
|
|
|
572 this.$matrix.m22 = m22;
|
|
|
573 this.$matrix.m23 = m23;
|
|
|
574 this.$matrix.m24 = m24;
|
|
|
575
|
|
|
576 this.$matrix.m31 = m31;
|
|
|
577 this.$matrix.m32 = m32;
|
|
|
578 this.$matrix.m33 = m33;
|
|
|
579 this.$matrix.m34 = m34;
|
|
|
580
|
|
|
581 this.$matrix.m41 = m41;
|
|
|
582 this.$matrix.m42 = m42;
|
|
|
583 this.$matrix.m43 = m43;
|
|
|
584 this.$matrix.m44 = m44;
|
|
|
585 }
|
|
|
586
|
|
|
587 J3DIMatrix4.prototype.divide = function(divisor)
|
|
|
588 {
|
|
|
589 this.$matrix.m11 /= divisor;
|
|
|
590 this.$matrix.m12 /= divisor;
|
|
|
591 this.$matrix.m13 /= divisor;
|
|
|
592 this.$matrix.m14 /= divisor;
|
|
|
593
|
|
|
594 this.$matrix.m21 /= divisor;
|
|
|
595 this.$matrix.m22 /= divisor;
|
|
|
596 this.$matrix.m23 /= divisor;
|
|
|
597 this.$matrix.m24 /= divisor;
|
|
|
598
|
|
|
599 this.$matrix.m31 /= divisor;
|
|
|
600 this.$matrix.m32 /= divisor;
|
|
|
601 this.$matrix.m33 /= divisor;
|
|
|
602 this.$matrix.m34 /= divisor;
|
|
|
603
|
|
|
604 this.$matrix.m41 /= divisor;
|
|
|
605 this.$matrix.m42 /= divisor;
|
|
|
606 this.$matrix.m43 /= divisor;
|
|
|
607 this.$matrix.m44 /= divisor;
|
|
|
608
|
|
|
609 }
|
|
|
610
|
|
|
611 J3DIMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
|
|
|
612 {
|
|
|
613 var tx = (left + right) / (left - right);
|
|
|
614 var ty = (top + bottom) / (top - bottom);
|
|
|
615 var tz = (far + near) / (far - near);
|
|
|
616
|
|
|
617 var matrix = new J3DIMatrix4();
|
|
|
618 matrix.$matrix.m11 = 2 / (left - right);
|
|
|
619 matrix.$matrix.m12 = 0;
|
|
|
620 matrix.$matrix.m13 = 0;
|
|
|
621 matrix.$matrix.m14 = 0;
|
|
|
622 matrix.$matrix.m21 = 0;
|
|
|
623 matrix.$matrix.m22 = 2 / (top - bottom);
|
|
|
624 matrix.$matrix.m23 = 0;
|
|
|
625 matrix.$matrix.m24 = 0;
|
|
|
626 matrix.$matrix.m31 = 0;
|
|
|
627 matrix.$matrix.m32 = 0;
|
|
|
628 matrix.$matrix.m33 = -2 / (far - near);
|
|
|
629 matrix.$matrix.m34 = 0;
|
|
|
630 matrix.$matrix.m41 = tx;
|
|
|
631 matrix.$matrix.m42 = ty;
|
|
|
632 matrix.$matrix.m43 = tz;
|
|
|
633 matrix.$matrix.m44 = 1;
|
|
|
634
|
|
|
635 this.multiply(matrix);
|
|
|
636 }
|
|
|
637
|
|
|
638 J3DIMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
|
|
|
639 {
|
|
|
640 var matrix = new J3DIMatrix4();
|
|
|
641 var A = (right + left) / (right - left);
|
|
|
642 var B = (top + bottom) / (top - bottom);
|
|
|
643 var C = -(far + near) / (far - near);
|
|
|
644 var D = -(2 * far * near) / (far - near);
|
|
|
645
|
|
|
646 matrix.$matrix.m11 = (2 * near) / (right - left);
|
|
|
647 matrix.$matrix.m12 = 0;
|
|
|
648 matrix.$matrix.m13 = 0;
|
|
|
649 matrix.$matrix.m14 = 0;
|
|
|
650
|
|
|
651 matrix.$matrix.m21 = 0;
|
|
|
652 matrix.$matrix.m22 = 2 * near / (top - bottom);
|
|
|
653 matrix.$matrix.m23 = 0;
|
|
|
654 matrix.$matrix.m24 = 0;
|
|
|
655
|
|
|
656 matrix.$matrix.m31 = A;
|
|
|
657 matrix.$matrix.m32 = B;
|
|
|
658 matrix.$matrix.m33 = C;
|
|
|
659 matrix.$matrix.m34 = -1;
|
|
|
660
|
|
|
661 matrix.$matrix.m41 = 0;
|
|
|
662 matrix.$matrix.m42 = 0;
|
|
|
663 matrix.$matrix.m43 = D;
|
|
|
664 matrix.$matrix.m44 = 0;
|
|
|
665
|
|
|
666 this.multiply(matrix);
|
|
|
667 }
|
|
|
668
|
|
|
669 J3DIMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
|
|
|
670 {
|
|
|
671 var top = Math.tan(fovy * Math.PI / 360) * zNear;
|
|
|
672 var bottom = -top;
|
|
|
673 var left = aspect * bottom;
|
|
|
674 var right = aspect * top;
|
|
|
675 this.frustum(left, right, bottom, top, zNear, zFar);
|
|
|
676 }
|
|
|
677
|
|
|
678 J3DIMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
|
|
|
679 {
|
|
|
680 if (typeof eyez == 'object' && "length" in eyez) {
|
|
|
681 var t = eyez;
|
|
|
682 upx = t[0];
|
|
|
683 upy = t[1];
|
|
|
684 upz = t[2];
|
|
|
685
|
|
|
686 t = eyey;
|
|
|
687 centerx = t[0];
|
|
|
688 centery = t[1];
|
|
|
689 centerz = t[2];
|
|
|
690
|
|
|
691 t = eyex;
|
|
|
692 eyex = t[0];
|
|
|
693 eyey = t[1];
|
|
|
694 eyez = t[2];
|
|
|
695 }
|
|
|
696
|
|
|
697 var matrix = new J3DIMatrix4();
|
|
|
698
|
|
|
699 // Make rotation matrix
|
|
|
700
|
|
|
701 // Z vector
|
|
|
702 var zx = eyex - centerx;
|
|
|
703 var zy = eyey - centery;
|
|
|
704 var zz = eyez - centerz;
|
|
|
705 var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
|
|
|
706 if (mag) {
|
|
|
707 zx /= mag;
|
|
|
708 zy /= mag;
|
|
|
709 zz /= mag;
|
|
|
710 }
|
|
|
711
|
|
|
712 // Y vector
|
|
|
713 var yx = upx;
|
|
|
714 var yy = upy;
|
|
|
715 var yz = upz;
|
|
|
716
|
|
|
717 // X vector = Y cross Z
|
|
|
718 xx = yy * zz - yz * zy;
|
|
|
719 xy = -yx * zz + yz * zx;
|
|
|
720 xz = yx * zy - yy * zx;
|
|
|
721
|
|
|
722 // Recompute Y = Z cross X
|
|
|
723 yx = zy * xz - zz * xy;
|
|
|
724 yy = -zx * xz + zz * xx;
|
|
|
725 yx = zx * xy - zy * xx;
|
|
|
726
|
|
|
727 // cross product gives area of parallelogram, which is < 1.0 for
|
|
|
728 // non-perpendicular unit-length vectors; so normalize x, y here
|
|
|
729
|
|
|
730 mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
|
|
|
731 if (mag) {
|
|
|
732 xx /= mag;
|
|
|
733 xy /= mag;
|
|
|
734 xz /= mag;
|
|
|
735 }
|
|
|
736
|
|
|
737 mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
|
|
|
738 if (mag) {
|
|
|
739 yx /= mag;
|
|
|
740 yy /= mag;
|
|
|
741 yz /= mag;
|
|
|
742 }
|
|
|
743
|
|
|
744 matrix.$matrix.m11 = xx;
|
|
|
745 matrix.$matrix.m12 = xy;
|
|
|
746 matrix.$matrix.m13 = xz;
|
|
|
747 matrix.$matrix.m14 = 0;
|
|
|
748
|
|
|
749 matrix.$matrix.m21 = yx;
|
|
|
750 matrix.$matrix.m22 = yy;
|
|
|
751 matrix.$matrix.m23 = yz;
|
|
|
752 matrix.$matrix.m24 = 0;
|
|
|
753
|
|
|
754 matrix.$matrix.m31 = zx;
|
|
|
755 matrix.$matrix.m32 = zy;
|
|
|
756 matrix.$matrix.m33 = zz;
|
|
|
757 matrix.$matrix.m34 = 0;
|
|
|
758
|
|
|
759 matrix.$matrix.m41 = 0;
|
|
|
760 matrix.$matrix.m42 = 0;
|
|
|
761 matrix.$matrix.m43 = 0;
|
|
|
762 matrix.$matrix.m44 = 1;
|
|
|
763 matrix.translate(-eyex, -eyey, -eyez);
|
|
|
764
|
|
|
765 this.multiply(matrix);
|
|
|
766 }
|
|
|
767
|
|
|
768 // Returns true on success, false otherwise. All params are Array objects
|
|
|
769 J3DIMatrix4.prototype.decompose = function(_translate, _rotate, _scale, _skew, _perspective)
|
|
|
770 {
|
|
|
771 // Normalize the matrix.
|
|
|
772 if (this.$matrix.m44 == 0)
|
|
|
773 return false;
|
|
|
774
|
|
|
775 // Gather the params
|
|
|
776 var translate, rotate, scale, skew, perspective;
|
|
|
777
|
|
|
778 var translate = (_translate == undefined || !("length" in _translate)) ? new J3DIVector3 : _translate;
|
|
|
779 var rotate = (_rotate == undefined || !("length" in _rotate)) ? new J3DIVector3 : _rotate;
|
|
|
780 var scale = (_scale == undefined || !("length" in _scale)) ? new J3DIVector3 : _scale;
|
|
|
781 var skew = (_skew == undefined || !("length" in _skew)) ? new J3DIVector3 : _skew;
|
|
|
782 var perspective = (_perspective == undefined || !("length" in _perspective)) ? new Array(4) : _perspective;
|
|
|
783
|
|
|
784 var matrix = new J3DIMatrix4(this);
|
|
|
785
|
|
|
786 matrix.divide(matrix.$matrix.m44);
|
|
|
787
|
|
|
788 // perspectiveMatrix is used to solve for perspective, but it also provides
|
|
|
789 // an easy way to test for singularity of the upper 3x3 component.
|
|
|
790 var perspectiveMatrix = new J3DIMatrix4(matrix);
|
|
|
791
|
|
|
792 perspectiveMatrix.$matrix.m14 = 0;
|
|
|
793 perspectiveMatrix.$matrix.m24 = 0;
|
|
|
794 perspectiveMatrix.$matrix.m34 = 0;
|
|
|
795 perspectiveMatrix.$matrix.m44 = 1;
|
|
|
796
|
|
|
797 if (perspectiveMatrix._determinant4x4() == 0)
|
|
|
798 return false;
|
|
|
799
|
|
|
800 // First, isolate perspective.
|
|
|
801 if (matrix.$matrix.m14 != 0 || matrix.$matrix.m24 != 0 || matrix.$matrix.m34 != 0) {
|
|
|
802 // rightHandSide is the right hand side of the equation.
|
|
|
803 var rightHandSide = [ matrix.$matrix.m14, matrix.$matrix.m24, matrix.$matrix.m34, matrix.$matrix.m44 ];
|
|
|
804
|
|
|
805 // Solve the equation by inverting perspectiveMatrix and multiplying
|
|
|
806 // rightHandSide by the inverse.
|
|
|
807 var inversePerspectiveMatrix = new J3DIMatrix4(perspectiveMatrix);
|
|
|
808 inversePerspectiveMatrix.invert();
|
|
|
809 var transposedInversePerspectiveMatrix = new J3DIMatrix4(inversePerspectiveMatrix);
|
|
|
810 transposedInversePerspectiveMatrix.transpose();
|
|
|
811 transposedInversePerspectiveMatrix.multVecMatrix(perspective, rightHandSide);
|
|
|
812
|
|
|
813 // Clear the perspective partition
|
|
|
814 matrix.$matrix.m14 = matrix.$matrix.m24 = matrix.$matrix.m34 = 0
|
|
|
815 matrix.$matrix.m44 = 1;
|
|
|
816 }
|
|
|
817 else {
|
|
|
818 // No perspective.
|
|
|
819 perspective[0] = perspective[1] = perspective[2] = 0;
|
|
|
820 perspective[3] = 1;
|
|
|
821 }
|
|
|
822
|
|
|
823 // Next take care of translation
|
|
|
824 translate[0] = matrix.$matrix.m41
|
|
|
825 matrix.$matrix.m41 = 0
|
|
|
826 translate[1] = matrix.$matrix.m42
|
|
|
827 matrix.$matrix.m42 = 0
|
|
|
828 translate[2] = matrix.$matrix.m43
|
|
|
829 matrix.$matrix.m43 = 0
|
|
|
830
|
|
|
831 // Now get scale and shear. 'row' is a 3 element array of 3 component vectors
|
|
|
832 var row0 = new J3DIVector3(matrix.$matrix.m11, matrix.$matrix.m12, matrix.$matrix.m13);
|
|
|
833 var row1 = new J3DIVector3(matrix.$matrix.m21, matrix.$matrix.m22, matrix.$matrix.m23);
|
|
|
834 var row2 = new J3DIVector3(matrix.$matrix.m31, matrix.$matrix.m32, matrix.$matrix.m33);
|
|
|
835
|
|
|
836 // Compute X scale factor and normalize first row.
|
|
|
837 scale[0] = row0.vectorLength();
|
|
|
838 row0.divide(scale[0]);
|
|
|
839
|
|
|
840 // Compute XY shear factor and make 2nd row orthogonal to 1st.
|
|
|
841 skew[0] = row0.dot(row1);
|
|
|
842 row1.combine(row0, 1.0, -skew[0]);
|
|
|
843
|
|
|
844 // Now, compute Y scale and normalize 2nd row.
|
|
|
845 scale[1] = row1.vectorLength();
|
|
|
846 row1.divide(scale[1]);
|
|
|
847 skew[0] /= scale[1];
|
|
|
848
|
|
|
849 // Compute XZ and YZ shears, orthogonalize 3rd row
|
|
|
850 skew[1] = row1.dot(row2);
|
|
|
851 row2.combine(row0, 1.0, -skew[1]);
|
|
|
852 skew[2] = row1.dot(row2);
|
|
|
853 row2.combine(row1, 1.0, -skew[2]);
|
|
|
854
|
|
|
855 // Next, get Z scale and normalize 3rd row.
|
|
|
856 scale[2] = row2.vectorLength();
|
|
|
857 row2.divide(scale[2]);
|
|
|
858 skew[1] /= scale[2];
|
|
|
859 skew[2] /= scale[2];
|
|
|
860
|
|
|
861 // At this point, the matrix (in rows) is orthonormal.
|
|
|
862 // Check for a coordinate system flip. If the determinant
|
|
|
863 // is -1, then negate the matrix and the scaling factors.
|
|
|
864 var pdum3 = new J3DIVector3(row1);
|
|
|
865 pdum3.cross(row2);
|
|
|
866 if (row0.dot(pdum3) < 0) {
|
|
|
867 for (i = 0; i < 3; i++) {
|
|
|
868 scale[i] *= -1;
|
|
|
869 row[0][i] *= -1;
|
|
|
870 row[1][i] *= -1;
|
|
|
871 row[2][i] *= -1;
|
|
|
872 }
|
|
|
873 }
|
|
|
874
|
|
|
875 // Now, get the rotations out
|
|
|
876 rotate[1] = Math.asin(-row0[2]);
|
|
|
877 if (Math.cos(rotate[1]) != 0) {
|
|
|
878 rotate[0] = Math.atan2(row1[2], row2[2]);
|
|
|
879 rotate[2] = Math.atan2(row0[1], row0[0]);
|
|
|
880 }
|
|
|
881 else {
|
|
|
882 rotate[0] = Math.atan2(-row2[0], row1[1]);
|
|
|
883 rotate[2] = 0;
|
|
|
884 }
|
|
|
885
|
|
|
886 // Convert rotations to degrees
|
|
|
887 var rad2deg = 180 / Math.PI;
|
|
|
888 rotate[0] *= rad2deg;
|
|
|
889 rotate[1] *= rad2deg;
|
|
|
890 rotate[2] *= rad2deg;
|
|
|
891
|
|
|
892 return true;
|
|
|
893 }
|
|
|
894
|
|
|
895 J3DIMatrix4.prototype._determinant2x2 = function(a, b, c, d)
|
|
|
896 {
|
|
|
897 return a * d - b * c;
|
|
|
898 }
|
|
|
899
|
|
|
900 J3DIMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
|
|
|
901 {
|
|
|
902 return a1 * this._determinant2x2(b2, b3, c2, c3)
|
|
|
903 - b1 * this._determinant2x2(a2, a3, c2, c3)
|
|
|
904 + c1 * this._determinant2x2(a2, a3, b2, b3);
|
|
|
905 }
|
|
|
906
|
|
|
907 J3DIMatrix4.prototype._determinant4x4 = function()
|
|
|
908 {
|
|
|
909 var a1 = this.$matrix.m11;
|
|
|
910 var b1 = this.$matrix.m12;
|
|
|
911 var c1 = this.$matrix.m13;
|
|
|
912 var d1 = this.$matrix.m14;
|
|
|
913
|
|
|
914 var a2 = this.$matrix.m21;
|
|
|
915 var b2 = this.$matrix.m22;
|
|
|
916 var c2 = this.$matrix.m23;
|
|
|
917 var d2 = this.$matrix.m24;
|
|
|
918
|
|
|
919 var a3 = this.$matrix.m31;
|
|
|
920 var b3 = this.$matrix.m32;
|
|
|
921 var c3 = this.$matrix.m33;
|
|
|
922 var d3 = this.$matrix.m34;
|
|
|
923
|
|
|
924 var a4 = this.$matrix.m41;
|
|
|
925 var b4 = this.$matrix.m42;
|
|
|
926 var c4 = this.$matrix.m43;
|
|
|
927 var d4 = this.$matrix.m44;
|
|
|
928
|
|
|
929 return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
|
|
|
930 - b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
|
|
|
931 + c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
|
|
|
932 - d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
933 }
|
|
|
934
|
|
|
935 J3DIMatrix4.prototype._makeAdjoint = function()
|
|
|
936 {
|
|
|
937 var a1 = this.$matrix.m11;
|
|
|
938 var b1 = this.$matrix.m12;
|
|
|
939 var c1 = this.$matrix.m13;
|
|
|
940 var d1 = this.$matrix.m14;
|
|
|
941
|
|
|
942 var a2 = this.$matrix.m21;
|
|
|
943 var b2 = this.$matrix.m22;
|
|
|
944 var c2 = this.$matrix.m23;
|
|
|
945 var d2 = this.$matrix.m24;
|
|
|
946
|
|
|
947 var a3 = this.$matrix.m31;
|
|
|
948 var b3 = this.$matrix.m32;
|
|
|
949 var c3 = this.$matrix.m33;
|
|
|
950 var d3 = this.$matrix.m34;
|
|
|
951
|
|
|
952 var a4 = this.$matrix.m41;
|
|
|
953 var b4 = this.$matrix.m42;
|
|
|
954 var c4 = this.$matrix.m43;
|
|
|
955 var d4 = this.$matrix.m44;
|
|
|
956
|
|
|
957 // Row column labeling reversed since we transpose rows & columns
|
|
|
958 this.$matrix.m11 = this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
|
|
|
959 this.$matrix.m21 = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
|
|
|
960 this.$matrix.m31 = this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
|
|
|
961 this.$matrix.m41 = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
962
|
|
|
963 this.$matrix.m12 = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
|
|
|
964 this.$matrix.m22 = this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
|
|
|
965 this.$matrix.m32 = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
|
|
|
966 this.$matrix.m42 = this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
|
|
|
967
|
|
|
968 this.$matrix.m13 = this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
|
|
|
969 this.$matrix.m23 = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
|
|
|
970 this.$matrix.m33 = this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
|
|
|
971 this.$matrix.m43 = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
|
|
|
972
|
|
|
973 this.$matrix.m14 = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
|
|
|
974 this.$matrix.m24 = this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
|
|
|
975 this.$matrix.m34 = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
|
|
|
976 this.$matrix.m44 = this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
|
|
|
977 }
|
|
|
978
|
|
|
979 //
|
|
|
980 // J3DIVector3
|
|
|
981 //
|
|
|
982 J3DIVector3 = function(x,y,z)
|
|
|
983 {
|
|
|
984 this.load(x,y,z);
|
|
|
985 }
|
|
|
986
|
|
|
987 J3DIVector3.prototype.load = function(x,y,z)
|
|
|
988 {
|
|
|
989 if (typeof x == 'object' && "length" in x) {
|
|
|
990 this[0] = x[0];
|
|
|
991 this[1] = x[1];
|
|
|
992 this[2] = x[2];
|
|
|
993 }
|
|
|
994 else if (typeof x == 'number') {
|
|
|
995 this[0] = x;
|
|
|
996 this[1] = y;
|
|
|
997 this[2] = z;
|
|
|
998 }
|
|
|
999 else {
|
|
|
1000 this[0] = 0;
|
|
|
1001 this[1] = 0;
|
|
|
1002 this[2] = 0;
|
|
|
1003 }
|
|
|
1004 }
|
|
|
1005
|
|
|
1006 J3DIVector3.prototype.getAsArray = function()
|
|
|
1007 {
|
|
|
1008 return [ this[0], this[1], this[2] ];
|
|
|
1009 }
|
|
|
1010
|
|
|
1011 J3DIVector3.prototype.getAsFloat32Array = function()
|
|
|
1012 {
|
|
|
1013 return new Float32Array(this.getAsArray());
|
|
|
1014 }
|
|
|
1015
|
|
|
1016 J3DIVector3.prototype.vectorLength = function()
|
|
|
1017 {
|
|
|
1018 return Math.sqrt(this[0] * this[0] + this[1] * this[1] + this[2] * this[2]);
|
|
|
1019 }
|
|
|
1020
|
|
|
1021 J3DIVector3.prototype.divide = function(divisor)
|
|
|
1022 {
|
|
|
1023 this[0] /= divisor; this[1] /= divisor; this[2] /= divisor;
|
|
|
1024 }
|
|
|
1025
|
|
|
1026 J3DIVector3.prototype.cross = function(v)
|
|
|
1027 {
|
|
|
1028 this[0] = this[1] * v[2] - this[2] * v[1];
|
|
|
1029 this[1] = -this[0] * v[2] + this[2] * v[0];
|
|
|
1030 this[2] = this[0] * v[1] - this[1] * v[0];
|
|
|
1031 }
|
|
|
1032
|
|
|
1033 J3DIVector3.prototype.dot = function(v)
|
|
|
1034 {
|
|
|
1035 return this[0] * v[0] + this[1] * v[1] + this[2] * v[2];
|
|
|
1036 }
|
|
|
1037
|
|
|
1038 J3DIVector3.prototype.combine = function(v, ascl, bscl)
|
|
|
1039 {
|
|
|
1040 this[0] = (ascl * this[0]) + (bscl * v[0]);
|
|
|
1041 this[1] = (ascl * this[1]) + (bscl * v[1]);
|
|
|
1042 this[2] = (ascl * this[2]) + (bscl * v[2]);
|
|
|
1043 }
|
|
|
1044
|
|
|
1045 J3DIVector3.prototype.multVecMatrix = function(matrix)
|
|
|
1046 {
|
|
|
1047 var x = this[0];
|
|
|
1048 var y = this[1];
|
|
|
1049 var z = this[2];
|
|
|
1050
|
|
|
1051 this[0] = matrix.$matrix.m41 + x * matrix.$matrix.m11 + y * matrix.$matrix.m21 + z * matrix.$matrix.m31;
|
|
|
1052 this[1] = matrix.$matrix.m42 + x * matrix.$matrix.m12 + y * matrix.$matrix.m22 + z * matrix.$matrix.m32;
|
|
|
1053 this[2] = matrix.$matrix.m43 + x * matrix.$matrix.m13 + y * matrix.$matrix.m23 + z * matrix.$matrix.m33;
|
|
|
1054 var w = matrix.$matrix.m44 + x * matrix.$matrix.m14 + y * matrix.$matrix.m24 + z * matrix.$matrix.m34;
|
|
|
1055 if (w != 1 && w != 0) {
|
|
|
1056 this[0] /= w;
|
|
|
1057 this[1] /= w;
|
|
|
1058 this[2] /= w;
|
|
|
1059 }
|
|
|
1060 }
|
|
|
1061
|
|
|
1062 J3DIVector3.prototype.toString = function()
|
|
|
1063 {
|
|
|
1064 return "["+this[0]+","+this[1]+","+this[2]+"]";
|
|
|
1065 } |
