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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 CanvasMatrix4 class
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27
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28 This class implements a 4x4 matrix. It has functions which
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29 duplicate the functionality of the OpenGL matrix stack and
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30 glut functions.
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31
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32 IDL:
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33
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34 [
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35 Constructor(in CanvasMatrix4 matrix), // copy passed matrix into new CanvasMatrix4
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36 Constructor(in sequence<float> array) // create new CanvasMatrix4 with 16 floats (row major)
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37 Constructor() // create new CanvasMatrix4 with identity matrix
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38 ]
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39 interface CanvasMatrix4 {
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40 attribute float m11;
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41 attribute float m12;
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42 attribute float m13;
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43 attribute float m14;
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44 attribute float m21;
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45 attribute float m22;
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46 attribute float m23;
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47 attribute float m24;
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48 attribute float m31;
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49 attribute float m32;
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50 attribute float m33;
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51 attribute float m34;
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52 attribute float m41;
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53 attribute float m42;
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54 attribute float m43;
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55 attribute float m44;
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56
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57 void load(in CanvasMatrix4 matrix); // copy the values from the passed matrix
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58 void load(in sequence<float> array); // copy 16 floats into the matrix
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59 sequence<float> getAsArray(); // return the matrix as an array of 16 floats
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60 WebGLFloatArray getAsCanvasFloatArray(); // return the matrix as a WebGLFloatArray with 16 values
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61 void makeIdentity(); // replace the matrix with identity
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62 void transpose(); // replace the matrix with its transpose
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63 void invert(); // replace the matrix with its inverse
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64
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65 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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66 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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67 void rotate(in float angle, // multiply the matrix by passed rotation values on the right
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68 in float x, in float y, in float z); // (angle is in degrees)
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69 void multRight(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
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70 void multLeft(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the left
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71 void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
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72 in float bottom, in float top,
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73 in float near, in float far);
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74 void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
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75 in float bottom, in float top,
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76 in float near, in float far);
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77 void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
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78 in float zNear, in float zFar);
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79 void lookat(in float eyex, in float eyey, in float eyez, // multiply the matrix by the passed lookat
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80 in float ctrx, in float ctry, in float ctrz, // values on the right
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81 in float upx, in float upy, in float upz);
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82 }
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83 */
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84
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85 CanvasMatrix4 = function(m)
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86 {
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87 if (typeof m == 'object') {
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88 if ("length" in m && m.length >= 16) {
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89 this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
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90 return;
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91 }
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92 else if (m instanceof CanvasMatrix4) {
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93 this.load(m);
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94 return;
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95 }
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96 }
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97 this.makeIdentity();
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98 }
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99
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100 CanvasMatrix4.prototype.load = function()
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101 {
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102 if (arguments.length == 1 && typeof arguments[0] == 'object') {
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103 var matrix = arguments[0];
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104
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105 if ("length" in matrix && matrix.length == 16) {
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106 this.m11 = matrix[0];
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107 this.m12 = matrix[1];
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108 this.m13 = matrix[2];
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109 this.m14 = matrix[3];
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110
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111 this.m21 = matrix[4];
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112 this.m22 = matrix[5];
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113 this.m23 = matrix[6];
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114 this.m24 = matrix[7];
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115
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116 this.m31 = matrix[8];
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117 this.m32 = matrix[9];
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118 this.m33 = matrix[10];
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119 this.m34 = matrix[11];
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120
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121 this.m41 = matrix[12];
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122 this.m42 = matrix[13];
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123 this.m43 = matrix[14];
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124 this.m44 = matrix[15];
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125 return;
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126 }
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127
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128 if (arguments[0] instanceof CanvasMatrix4) {
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129
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130 this.m11 = matrix.m11;
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131 this.m12 = matrix.m12;
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132 this.m13 = matrix.m13;
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133 this.m14 = matrix.m14;
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134
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135 this.m21 = matrix.m21;
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136 this.m22 = matrix.m22;
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137 this.m23 = matrix.m23;
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138 this.m24 = matrix.m24;
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139
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140 this.m31 = matrix.m31;
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141 this.m32 = matrix.m32;
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142 this.m33 = matrix.m33;
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143 this.m34 = matrix.m34;
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144
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145 this.m41 = matrix.m41;
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146 this.m42 = matrix.m42;
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147 this.m43 = matrix.m43;
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148 this.m44 = matrix.m44;
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149 return;
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150 }
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151 }
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152
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153 this.makeIdentity();
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154 }
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155
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156 CanvasMatrix4.prototype.getAsArray = function()
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157 {
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158 return [
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159 this.m11, this.m12, this.m13, this.m14,
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160 this.m21, this.m22, this.m23, this.m24,
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161 this.m31, this.m32, this.m33, this.m34,
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162 this.m41, this.m42, this.m43, this.m44
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163 ];
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164 }
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165
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166 CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
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167 {
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168 return new WebGLFloatArray(this.getAsArray());
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169 }
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170
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171 CanvasMatrix4.prototype.makeIdentity = function()
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172 {
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173 this.m11 = 1;
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174 this.m12 = 0;
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175 this.m13 = 0;
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176 this.m14 = 0;
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177
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178 this.m21 = 0;
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179 this.m22 = 1;
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180 this.m23 = 0;
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181 this.m24 = 0;
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182
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183 this.m31 = 0;
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184 this.m32 = 0;
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185 this.m33 = 1;
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186 this.m34 = 0;
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187
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188 this.m41 = 0;
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189 this.m42 = 0;
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190 this.m43 = 0;
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191 this.m44 = 1;
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192 }
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193
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194 CanvasMatrix4.prototype.transpose = function()
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195 {
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196 var tmp = this.m12;
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197 this.m12 = this.m21;
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198 this.m21 = tmp;
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199
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200 tmp = this.m13;
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201 this.m13 = this.m31;
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202 this.m31 = tmp;
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203
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204 tmp = this.m14;
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205 this.m14 = this.m41;
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206 this.m41 = tmp;
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207
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208 tmp = this.m23;
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209 this.m23 = this.m32;
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210 this.m32 = tmp;
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211
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212 tmp = this.m24;
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213 this.m24 = this.m42;
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214 this.m42 = tmp;
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215
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216 tmp = this.m34;
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217 this.m34 = this.m43;
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218 this.m43 = tmp;
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219 }
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220
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221 CanvasMatrix4.prototype.invert = function()
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222 {
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223 // Calculate the 4x4 determinant
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224 // If the determinant is zero,
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225 // then the inverse matrix is not unique.
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226 var det = this._determinant4x4();
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227
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228 if (Math.abs(det) < 1e-8)
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229 return null;
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230
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231 this._makeAdjoint();
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232
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233 // Scale the adjoint matrix to get the inverse
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234 this.m11 /= det;
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235 this.m12 /= det;
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236 this.m13 /= det;
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237 this.m14 /= det;
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238
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239 this.m21 /= det;
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240 this.m22 /= det;
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241 this.m23 /= det;
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242 this.m24 /= det;
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243
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244 this.m31 /= det;
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245 this.m32 /= det;
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246 this.m33 /= det;
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247 this.m34 /= det;
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248
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249 this.m41 /= det;
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250 this.m42 /= det;
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251 this.m43 /= det;
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252 this.m44 /= det;
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253 }
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254
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255 CanvasMatrix4.prototype.translate = function(x,y,z)
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256 {
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257 if (x == undefined)
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258 x = 0;
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259 if (y == undefined)
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260 y = 0;
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261 if (z == undefined)
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262 z = 0;
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263
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264 var matrix = new CanvasMatrix4();
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265 matrix.m41 = x;
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266 matrix.m42 = y;
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267 matrix.m43 = z;
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268
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269 this.multRight(matrix);
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270 }
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271
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272 CanvasMatrix4.prototype.scale = function(x,y,z)
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273 {
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274 if (x == undefined)
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275 x = 1;
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276 if (z == undefined) {
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277 if (y == undefined) {
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278 y = x;
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279 z = x;
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280 }
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281 else
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282 z = 1;
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283 }
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284 else if (y == undefined)
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285 y = x;
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286
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287 var matrix = new CanvasMatrix4();
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288 matrix.m11 = x;
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289 matrix.m22 = y;
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290 matrix.m33 = z;
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291
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292 this.multRight(matrix);
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293 }
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294
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295 CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
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296 {
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297 // angles are in degrees. Switch to radians
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298 angle = angle / 180 * Math.PI;
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299
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300 angle /= 2;
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301 var sinA = Math.sin(angle);
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302 var cosA = Math.cos(angle);
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303 var sinA2 = sinA * sinA;
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304
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305 // normalize
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306 var length = Math.sqrt(x * x + y * y + z * z);
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307 if (length == 0) {
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308 // bad vector, just use something reasonable
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309 x = 0;
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310 y = 0;
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311 z = 1;
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312 } else if (length != 1) {
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313 x /= length;
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314 y /= length;
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315 z /= length;
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316 }
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317
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318 var mat = new CanvasMatrix4();
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319
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320 // optimize case where axis is along major axis
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321 if (x == 1 && y == 0 && z == 0) {
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322 mat.m11 = 1;
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323 mat.m12 = 0;
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324 mat.m13 = 0;
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325 mat.m21 = 0;
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326 mat.m22 = 1 - 2 * sinA2;
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327 mat.m23 = 2 * sinA * cosA;
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328 mat.m31 = 0;
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329 mat.m32 = -2 * sinA * cosA;
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330 mat.m33 = 1 - 2 * sinA2;
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331 mat.m14 = mat.m24 = mat.m34 = 0;
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332 mat.m41 = mat.m42 = mat.m43 = 0;
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333 mat.m44 = 1;
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334 } else if (x == 0 && y == 1 && z == 0) {
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335 mat.m11 = 1 - 2 * sinA2;
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336 mat.m12 = 0;
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337 mat.m13 = -2 * sinA * cosA;
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338 mat.m21 = 0;
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339 mat.m22 = 1;
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340 mat.m23 = 0;
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341 mat.m31 = 2 * sinA * cosA;
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342 mat.m32 = 0;
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343 mat.m33 = 1 - 2 * sinA2;
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344 mat.m14 = mat.m24 = mat.m34 = 0;
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345 mat.m41 = mat.m42 = mat.m43 = 0;
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346 mat.m44 = 1;
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347 } else if (x == 0 && y == 0 && z == 1) {
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348 mat.m11 = 1 - 2 * sinA2;
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349 mat.m12 = 2 * sinA * cosA;
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350 mat.m13 = 0;
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351 mat.m21 = -2 * sinA * cosA;
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352 mat.m22 = 1 - 2 * sinA2;
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353 mat.m23 = 0;
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354 mat.m31 = 0;
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355 mat.m32 = 0;
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356 mat.m33 = 1;
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357 mat.m14 = mat.m24 = mat.m34 = 0;
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358 mat.m41 = mat.m42 = mat.m43 = 0;
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359 mat.m44 = 1;
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360 } else {
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361 var x2 = x*x;
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362 var y2 = y*y;
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363 var z2 = z*z;
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364
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365 mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
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366 mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
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367 mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
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368 mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
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369 mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
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370 mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
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371 mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
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372 mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
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373 mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
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374 mat.m14 = mat.m24 = mat.m34 = 0;
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375 mat.m41 = mat.m42 = mat.m43 = 0;
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376 mat.m44 = 1;
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377 }
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378 this.multRight(mat);
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379 }
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380
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381 CanvasMatrix4.prototype.multRight = function(mat)
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382 {
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383 var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21
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384 + this.m13 * mat.m31 + this.m14 * mat.m41);
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385 var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22
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386 + this.m13 * mat.m32 + this.m14 * mat.m42);
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387 var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23
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388 + this.m13 * mat.m33 + this.m14 * mat.m43);
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389 var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24
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390 + this.m13 * mat.m34 + this.m14 * mat.m44);
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391
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392 var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21
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393 + this.m23 * mat.m31 + this.m24 * mat.m41);
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394 var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22
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395 + this.m23 * mat.m32 + this.m24 * mat.m42);
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396 var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23
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397 + this.m23 * mat.m33 + this.m24 * mat.m43);
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|
398 var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24
|
|
|
399 + this.m23 * mat.m34 + this.m24 * mat.m44);
|
|
|
400
|
|
|
401 var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21
|
|
|
402 + this.m33 * mat.m31 + this.m34 * mat.m41);
|
|
|
403 var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22
|
|
|
404 + this.m33 * mat.m32 + this.m34 * mat.m42);
|
|
|
405 var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23
|
|
|
406 + this.m33 * mat.m33 + this.m34 * mat.m43);
|
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|
407 var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24
|
|
|
408 + this.m33 * mat.m34 + this.m34 * mat.m44);
|
|
|
409
|
|
|
410 var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21
|
|
|
411 + this.m43 * mat.m31 + this.m44 * mat.m41);
|
|
|
412 var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22
|
|
|
413 + this.m43 * mat.m32 + this.m44 * mat.m42);
|
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|
414 var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23
|
|
|
415 + this.m43 * mat.m33 + this.m44 * mat.m43);
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|
416 var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24
|
|
|
417 + this.m43 * mat.m34 + this.m44 * mat.m44);
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|
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418
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|
|
419 this.m11 = m11;
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|
420 this.m12 = m12;
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|
421 this.m13 = m13;
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422 this.m14 = m14;
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423
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424 this.m21 = m21;
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425 this.m22 = m22;
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426 this.m23 = m23;
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427 this.m24 = m24;
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428
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429 this.m31 = m31;
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430 this.m32 = m32;
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431 this.m33 = m33;
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432 this.m34 = m34;
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433
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434 this.m41 = m41;
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435 this.m42 = m42;
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436 this.m43 = m43;
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437 this.m44 = m44;
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|
|
438 }
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439
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|
440 CanvasMatrix4.prototype.multLeft = function(mat)
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|
441 {
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|
442 var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21
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|
443 + mat.m13 * this.m31 + mat.m14 * this.m41);
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|
444 var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22
|
|
|
445 + mat.m13 * this.m32 + mat.m14 * this.m42);
|
|
|
446 var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23
|
|
|
447 + mat.m13 * this.m33 + mat.m14 * this.m43);
|
|
|
448 var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24
|
|
|
449 + mat.m13 * this.m34 + mat.m14 * this.m44);
|
|
|
450
|
|
|
451 var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21
|
|
|
452 + mat.m23 * this.m31 + mat.m24 * this.m41);
|
|
|
453 var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22
|
|
|
454 + mat.m23 * this.m32 + mat.m24 * this.m42);
|
|
|
455 var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23
|
|
|
456 + mat.m23 * this.m33 + mat.m24 * this.m43);
|
|
|
457 var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24
|
|
|
458 + mat.m23 * this.m34 + mat.m24 * this.m44);
|
|
|
459
|
|
|
460 var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21
|
|
|
461 + mat.m33 * this.m31 + mat.m34 * this.m41);
|
|
|
462 var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22
|
|
|
463 + mat.m33 * this.m32 + mat.m34 * this.m42);
|
|
|
464 var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23
|
|
|
465 + mat.m33 * this.m33 + mat.m34 * this.m43);
|
|
|
466 var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24
|
|
|
467 + mat.m33 * this.m34 + mat.m34 * this.m44);
|
|
|
468
|
|
|
469 var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21
|
|
|
470 + mat.m43 * this.m31 + mat.m44 * this.m41);
|
|
|
471 var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22
|
|
|
472 + mat.m43 * this.m32 + mat.m44 * this.m42);
|
|
|
473 var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23
|
|
|
474 + mat.m43 * this.m33 + mat.m44 * this.m43);
|
|
|
475 var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24
|
|
|
476 + mat.m43 * this.m34 + mat.m44 * this.m44);
|
|
|
477
|
|
|
478 this.m11 = m11;
|
|
|
479 this.m12 = m12;
|
|
|
480 this.m13 = m13;
|
|
|
481 this.m14 = m14;
|
|
|
482
|
|
|
483 this.m21 = m21;
|
|
|
484 this.m22 = m22;
|
|
|
485 this.m23 = m23;
|
|
|
486 this.m24 = m24;
|
|
|
487
|
|
|
488 this.m31 = m31;
|
|
|
489 this.m32 = m32;
|
|
|
490 this.m33 = m33;
|
|
|
491 this.m34 = m34;
|
|
|
492
|
|
|
493 this.m41 = m41;
|
|
|
494 this.m42 = m42;
|
|
|
495 this.m43 = m43;
|
|
|
496 this.m44 = m44;
|
|
|
497 }
|
|
|
498
|
|
|
499 CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
|
|
|
500 {
|
|
|
501 var tx = (left + right) / (left - right);
|
|
|
502 var ty = (top + bottom) / (top - bottom);
|
|
|
503 var tz = (far + near) / (far - near);
|
|
|
504
|
|
|
505 var matrix = new CanvasMatrix4();
|
|
|
506 matrix.m11 = 2 / (left - right);
|
|
|
507 matrix.m12 = 0;
|
|
|
508 matrix.m13 = 0;
|
|
|
509 matrix.m14 = 0;
|
|
|
510 matrix.m21 = 0;
|
|
|
511 matrix.m22 = 2 / (top - bottom);
|
|
|
512 matrix.m23 = 0;
|
|
|
513 matrix.m24 = 0;
|
|
|
514 matrix.m31 = 0;
|
|
|
515 matrix.m32 = 0;
|
|
|
516 matrix.m33 = -2 / (far - near);
|
|
|
517 matrix.m34 = 0;
|
|
|
518 matrix.m41 = tx;
|
|
|
519 matrix.m42 = ty;
|
|
|
520 matrix.m43 = tz;
|
|
|
521 matrix.m44 = 1;
|
|
|
522
|
|
|
523 this.multRight(matrix);
|
|
|
524 }
|
|
|
525
|
|
|
526 CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
|
|
|
527 {
|
|
|
528 var matrix = new CanvasMatrix4();
|
|
|
529 var A = (right + left) / (right - left);
|
|
|
530 var B = (top + bottom) / (top - bottom);
|
|
|
531 var C = -(far + near) / (far - near);
|
|
|
532 var D = -(2 * far * near) / (far - near);
|
|
|
533
|
|
|
534 matrix.m11 = (2 * near) / (right - left);
|
|
|
535 matrix.m12 = 0;
|
|
|
536 matrix.m13 = 0;
|
|
|
537 matrix.m14 = 0;
|
|
|
538
|
|
|
539 matrix.m21 = 0;
|
|
|
540 matrix.m22 = 2 * near / (top - bottom);
|
|
|
541 matrix.m23 = 0;
|
|
|
542 matrix.m24 = 0;
|
|
|
543
|
|
|
544 matrix.m31 = A;
|
|
|
545 matrix.m32 = B;
|
|
|
546 matrix.m33 = C;
|
|
|
547 matrix.m34 = -1;
|
|
|
548
|
|
|
549 matrix.m41 = 0;
|
|
|
550 matrix.m42 = 0;
|
|
|
551 matrix.m43 = D;
|
|
|
552 matrix.m44 = 0;
|
|
|
553
|
|
|
554 this.multRight(matrix);
|
|
|
555 }
|
|
|
556
|
|
|
557 CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
|
|
|
558 {
|
|
|
559 var top = Math.tan(fovy * Math.PI / 360) * zNear;
|
|
|
560 var bottom = -top;
|
|
|
561 var left = aspect * bottom;
|
|
|
562 var right = aspect * top;
|
|
|
563 this.frustum(left, right, bottom, top, zNear, zFar);
|
|
|
564 }
|
|
|
565
|
|
|
566 CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
|
|
|
567 {
|
|
|
568 var matrix = new CanvasMatrix4();
|
|
|
569
|
|
|
570 // Make rotation matrix
|
|
|
571
|
|
|
572 // Z vector
|
|
|
573 var zx = eyex - centerx;
|
|
|
574 var zy = eyey - centery;
|
|
|
575 var zz = eyez - centerz;
|
|
|
576 var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
|
|
|
577 if (mag) {
|
|
|
578 zx /= mag;
|
|
|
579 zy /= mag;
|
|
|
580 zz /= mag;
|
|
|
581 }
|
|
|
582
|
|
|
583 // Y vector
|
|
|
584 var yx = upx;
|
|
|
585 var yy = upy;
|
|
|
586 var yz = upz;
|
|
|
587
|
|
|
588 // X vector = Y cross Z
|
|
|
589 xx = yy * zz - yz * zy;
|
|
|
590 xy = -yx * zz + yz * zx;
|
|
|
591 xz = yx * zy - yy * zx;
|
|
|
592
|
|
|
593 // Recompute Y = Z cross X
|
|
|
594 yx = zy * xz - zz * xy;
|
|
|
595 yy = -zx * xz + zz * xx;
|
|
|
596 yx = zx * xy - zy * xx;
|
|
|
597
|
|
|
598 // cross product gives area of parallelogram, which is < 1.0 for
|
|
|
599 // non-perpendicular unit-length vectors; so normalize x, y here
|
|
|
600
|
|
|
601 mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
|
|
|
602 if (mag) {
|
|
|
603 xx /= mag;
|
|
|
604 xy /= mag;
|
|
|
605 xz /= mag;
|
|
|
606 }
|
|
|
607
|
|
|
608 mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
|
|
|
609 if (mag) {
|
|
|
610 yx /= mag;
|
|
|
611 yy /= mag;
|
|
|
612 yz /= mag;
|
|
|
613 }
|
|
|
614
|
|
|
615 matrix.m11 = xx;
|
|
|
616 matrix.m12 = xy;
|
|
|
617 matrix.m13 = xz;
|
|
|
618 matrix.m14 = 0;
|
|
|
619
|
|
|
620 matrix.m21 = yx;
|
|
|
621 matrix.m22 = yy;
|
|
|
622 matrix.m23 = yz;
|
|
|
623 matrix.m24 = 0;
|
|
|
624
|
|
|
625 matrix.m31 = zx;
|
|
|
626 matrix.m32 = zy;
|
|
|
627 matrix.m33 = zz;
|
|
|
628 matrix.m34 = 0;
|
|
|
629
|
|
|
630 matrix.m41 = 0;
|
|
|
631 matrix.m42 = 0;
|
|
|
632 matrix.m43 = 0;
|
|
|
633 matrix.m44 = 1;
|
|
|
634 matrix.translate(-eyex, -eyey, -eyez);
|
|
|
635
|
|
|
636 this.multRight(matrix);
|
|
|
637 }
|
|
|
638
|
|
|
639 // Support functions
|
|
|
640 CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
|
|
|
641 {
|
|
|
642 return a * d - b * c;
|
|
|
643 }
|
|
|
644
|
|
|
645 CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
|
|
|
646 {
|
|
|
647 return a1 * this._determinant2x2(b2, b3, c2, c3)
|
|
|
648 - b1 * this._determinant2x2(a2, a3, c2, c3)
|
|
|
649 + c1 * this._determinant2x2(a2, a3, b2, b3);
|
|
|
650 }
|
|
|
651
|
|
|
652 CanvasMatrix4.prototype._determinant4x4 = function()
|
|
|
653 {
|
|
|
654 var a1 = this.m11;
|
|
|
655 var b1 = this.m12;
|
|
|
656 var c1 = this.m13;
|
|
|
657 var d1 = this.m14;
|
|
|
658
|
|
|
659 var a2 = this.m21;
|
|
|
660 var b2 = this.m22;
|
|
|
661 var c2 = this.m23;
|
|
|
662 var d2 = this.m24;
|
|
|
663
|
|
|
664 var a3 = this.m31;
|
|
|
665 var b3 = this.m32;
|
|
|
666 var c3 = this.m33;
|
|
|
667 var d3 = this.m34;
|
|
|
668
|
|
|
669 var a4 = this.m41;
|
|
|
670 var b4 = this.m42;
|
|
|
671 var c4 = this.m43;
|
|
|
672 var d4 = this.m44;
|
|
|
673
|
|
|
674 return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
|
|
|
675 - b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
|
|
|
676 + c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
|
|
|
677 - d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
678 }
|
|
|
679
|
|
|
680 CanvasMatrix4.prototype._makeAdjoint = function()
|
|
|
681 {
|
|
|
682 var a1 = this.m11;
|
|
|
683 var b1 = this.m12;
|
|
|
684 var c1 = this.m13;
|
|
|
685 var d1 = this.m14;
|
|
|
686
|
|
|
687 var a2 = this.m21;
|
|
|
688 var b2 = this.m22;
|
|
|
689 var c2 = this.m23;
|
|
|
690 var d2 = this.m24;
|
|
|
691
|
|
|
692 var a3 = this.m31;
|
|
|
693 var b3 = this.m32;
|
|
|
694 var c3 = this.m33;
|
|
|
695 var d3 = this.m34;
|
|
|
696
|
|
|
697 var a4 = this.m41;
|
|
|
698 var b4 = this.m42;
|
|
|
699 var c4 = this.m43;
|
|
|
700 var d4 = this.m44;
|
|
|
701
|
|
|
702 // Row column labeling reversed since we transpose rows & columns
|
|
|
703 this.m11 = this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
|
|
|
704 this.m21 = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
|
|
|
705 this.m31 = this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
|
|
|
706 this.m41 = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
707
|
|
|
708 this.m12 = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
|
|
|
709 this.m22 = this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
|
|
|
710 this.m32 = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
|
|
|
711 this.m42 = this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
|
|
|
712
|
|
|
713 this.m13 = this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
|
|
|
714 this.m23 = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
|
|
|
715 this.m33 = this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
|
|
|
716 this.m43 = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
|
|
|
717
|
|
|
718 this.m14 = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
|
|
|
719 this.m24 = this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
|
|
|
720 this.m34 = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
|
|
|
721 this.m44 = this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
|
|
|
722 } |
