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1 // 3D Cube Rotation |
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2 // http://www.speich.net/computer/moztesting/3d.htm |
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3 // Created by Simon Speich |
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4 |
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5 var Q = new Array(); |
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6 var MTrans = new Array(); // transformation matrix |
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7 var MQube = new Array(); // position information of qube |
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8 var I = new Array(); // entity matrix |
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9 var Origin = new Object(); |
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10 var Testing = new Object(); |
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11 var LoopTimer; |
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12 |
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13 var DisplArea = new Object(); |
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14 DisplArea.Width = 300; |
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15 DisplArea.Height = 300; |
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16 |
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17 function DrawLine(From, To) { |
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18 var x1 = From.V[0]; |
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19 var x2 = To.V[0]; |
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20 var y1 = From.V[1]; |
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21 var y2 = To.V[1]; |
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22 var dx = Math.abs(x2 - x1); |
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23 var dy = Math.abs(y2 - y1); |
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24 var x = x1; |
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25 var y = y1; |
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26 var IncX1, IncY1; |
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27 var IncX2, IncY2; |
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28 var Den; |
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29 var Num; |
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30 var NumAdd; |
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31 var NumPix; |
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32 |
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33 if (x2 >= x1) { IncX1 = 1; IncX2 = 1; } |
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34 else { IncX1 = -1; IncX2 = -1; } |
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35 if (y2 >= y1) { IncY1 = 1; IncY2 = 1; } |
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36 else { IncY1 = -1; IncY2 = -1; } |
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37 if (dx >= dy) { |
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38 IncX1 = 0; |
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39 IncY2 = 0; |
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40 Den = dx; |
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41 Num = dx / 2; |
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42 NumAdd = dy; |
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43 NumPix = dx; |
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44 } |
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45 else { |
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46 IncX2 = 0; |
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47 IncY1 = 0; |
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48 Den = dy; |
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49 Num = dy / 2; |
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50 NumAdd = dx; |
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51 NumPix = dy; |
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52 } |
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53 |
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54 NumPix = Math.round(Q.LastPx + NumPix); |
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55 |
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56 var i = Q.LastPx; |
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57 for (; i < NumPix; i++) { |
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58 Num += NumAdd; |
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59 if (Num >= Den) { |
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60 Num -= Den; |
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61 x += IncX1; |
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62 y += IncY1; |
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63 } |
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64 x += IncX2; |
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65 y += IncY2; |
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66 } |
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67 Q.LastPx = NumPix; |
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68 } |
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69 |
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70 function CalcCross(V0, V1) { |
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71 var Cross = new Array(); |
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72 Cross[0] = V0[1]*V1[2] - V0[2]*V1[1]; |
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73 Cross[1] = V0[2]*V1[0] - V0[0]*V1[2]; |
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74 Cross[2] = V0[0]*V1[1] - V0[1]*V1[0]; |
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75 return Cross; |
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76 } |
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77 |
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78 function CalcNormal(V0, V1, V2) { |
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79 var A = new Array(); var B = new Array(); |
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80 for (var i = 0; i < 3; i++) { |
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81 A[i] = V0[i] - V1[i]; |
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82 B[i] = V2[i] - V1[i]; |
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83 } |
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84 A = CalcCross(A, B); |
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85 var Length = Math.sqrt(A[0]*A[0] + A[1]*A[1] + A[2]*A[2]); |
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86 for (var i = 0; i < 3; i++) A[i] = A[i] / Length; |
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87 A[3] = 1; |
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88 return A; |
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89 } |
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90 |
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91 function CreateP(X,Y,Z) { |
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92 this.V = [X,Y,Z,1]; |
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93 } |
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94 |
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95 // multiplies two matrices |
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96 function MMulti(M1, M2) { |
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97 var M = [[],[],[],[]]; |
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98 var i = 0; |
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99 var j = 0; |
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100 for (; i < 4; i++) { |
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101 j = 0; |
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102 for (; j < 4; j++) M[i][j] = M1[i][0] * M2[0][j] + M1[i][1] * M2[1][j] + M1[i][2] * M2[2][j] + M1[i][3] * M2[3][j]; |
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103 } |
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104 return M; |
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105 } |
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106 |
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107 //multiplies matrix with vector |
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108 function VMulti(M, V) { |
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109 var Vect = new Array(); |
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110 var i = 0; |
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111 for (;i < 4; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2] + M[i][3] * V[3]; |
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112 return Vect; |
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113 } |
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114 |
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115 function VMulti2(M, V) { |
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116 var Vect = new Array(); |
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117 var i = 0; |
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118 for (;i < 3; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2]; |
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119 return Vect; |
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120 } |
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121 |
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122 // add to matrices |
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123 function MAdd(M1, M2) { |
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124 var M = [[],[],[],[]]; |
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125 var i = 0; |
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126 var j = 0; |
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127 for (; i < 4; i++) { |
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128 j = 0; |
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129 for (; j < 4; j++) M[i][j] = M1[i][j] + M2[i][j]; |
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130 } |
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131 return M; |
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132 } |
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133 |
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134 function Translate(M, Dx, Dy, Dz) { |
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135 var T = [ |
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136 [1,0,0,Dx], |
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137 [0,1,0,Dy], |
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138 [0,0,1,Dz], |
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139 [0,0,0,1] |
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140 ]; |
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141 return MMulti(T, M); |
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142 } |
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143 |
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144 function RotateX(M, Phi) { |
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145 var a = Phi; |
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146 a *= Math.PI / 180; |
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147 var Cos = Math.cos(a); |
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148 var Sin = Math.sin(a); |
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149 var R = [ |
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150 [1,0,0,0], |
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151 [0,Cos,-Sin,0], |
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152 [0,Sin,Cos,0], |
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153 [0,0,0,1] |
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154 ]; |
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155 return MMulti(R, M); |
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156 } |
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157 |
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158 function RotateY(M, Phi) { |
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159 var a = Phi; |
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160 a *= Math.PI / 180; |
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161 var Cos = Math.cos(a); |
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162 var Sin = Math.sin(a); |
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163 var R = [ |
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164 [Cos,0,Sin,0], |
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165 [0,1,0,0], |
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166 [-Sin,0,Cos,0], |
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167 [0,0,0,1] |
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168 ]; |
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169 return MMulti(R, M); |
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170 } |
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171 |
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172 function RotateZ(M, Phi) { |
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173 var a = Phi; |
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174 a *= Math.PI / 180; |
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175 var Cos = Math.cos(a); |
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176 var Sin = Math.sin(a); |
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177 var R = [ |
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178 [Cos,-Sin,0,0], |
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179 [Sin,Cos,0,0], |
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180 [0,0,1,0], |
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181 [0,0,0,1] |
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182 ]; |
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183 return MMulti(R, M); |
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184 } |
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185 |
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186 function DrawQube() { |
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187 // calc current normals |
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188 var CurN = new Array(); |
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189 var i = 5; |
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190 Q.LastPx = 0; |
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191 for (; i > -1; i--) CurN[i] = VMulti2(MQube, Q.Normal[i]); |
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192 if (CurN[0][2] < 0) { |
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193 if (!Q.Line[0]) { DrawLine(Q[0], Q[1]); Q.Line[0] = true; }; |
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194 if (!Q.Line[1]) { DrawLine(Q[1], Q[2]); Q.Line[1] = true; }; |
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195 if (!Q.Line[2]) { DrawLine(Q[2], Q[3]); Q.Line[2] = true; }; |
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196 if (!Q.Line[3]) { DrawLine(Q[3], Q[0]); Q.Line[3] = true; }; |
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197 } |
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198 if (CurN[1][2] < 0) { |
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199 if (!Q.Line[2]) { DrawLine(Q[3], Q[2]); Q.Line[2] = true; }; |
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200 if (!Q.Line[9]) { DrawLine(Q[2], Q[6]); Q.Line[9] = true; }; |
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201 if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; }; |
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202 if (!Q.Line[10]) { DrawLine(Q[7], Q[3]); Q.Line[10] = true; }; |
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203 } |
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204 if (CurN[2][2] < 0) { |
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205 if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; }; |
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206 if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; }; |
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207 if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; }; |
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208 if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; }; |
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209 } |
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210 if (CurN[3][2] < 0) { |
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211 if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; }; |
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212 if (!Q.Line[8]) { DrawLine(Q[5], Q[1]); Q.Line[8] = true; }; |
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213 if (!Q.Line[0]) { DrawLine(Q[1], Q[0]); Q.Line[0] = true; }; |
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214 if (!Q.Line[11]) { DrawLine(Q[0], Q[4]); Q.Line[11] = true; }; |
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215 } |
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216 if (CurN[4][2] < 0) { |
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217 if (!Q.Line[11]) { DrawLine(Q[4], Q[0]); Q.Line[11] = true; }; |
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218 if (!Q.Line[3]) { DrawLine(Q[0], Q[3]); Q.Line[3] = true; }; |
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219 if (!Q.Line[10]) { DrawLine(Q[3], Q[7]); Q.Line[10] = true; }; |
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220 if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; }; |
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221 } |
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222 if (CurN[5][2] < 0) { |
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223 if (!Q.Line[8]) { DrawLine(Q[1], Q[5]); Q.Line[8] = true; }; |
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224 if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; }; |
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225 if (!Q.Line[9]) { DrawLine(Q[6], Q[2]); Q.Line[9] = true; }; |
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226 if (!Q.Line[1]) { DrawLine(Q[2], Q[1]); Q.Line[1] = true; }; |
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227 } |
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228 Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false]; |
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229 Q.LastPx = 0; |
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230 } |
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231 |
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232 function Loop() { |
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233 if (Testing.LoopCount > Testing.LoopMax) return; |
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234 var TestingStr = String(Testing.LoopCount); |
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235 while (TestingStr.length < 3) TestingStr = "0" + TestingStr; |
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236 MTrans = Translate(I, -Q[8].V[0], -Q[8].V[1], -Q[8].V[2]); |
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237 MTrans = RotateX(MTrans, 1); |
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238 MTrans = RotateY(MTrans, 3); |
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239 MTrans = RotateZ(MTrans, 5); |
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240 MTrans = Translate(MTrans, Q[8].V[0], Q[8].V[1], Q[8].V[2]); |
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241 MQube = MMulti(MTrans, MQube); |
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242 var i = 8; |
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243 for (; i > -1; i--) { |
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244 Q[i].V = VMulti(MTrans, Q[i].V); |
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245 } |
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246 DrawQube(); |
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247 Testing.LoopCount++; |
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248 Loop(); |
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249 } |
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250 |
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251 function Init(CubeSize) { |
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252 // init/reset vars |
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253 Origin.V = [150,150,20,1]; |
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254 Testing.LoopCount = 0; |
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255 Testing.LoopMax = 50; |
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256 Testing.TimeMax = 0; |
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257 Testing.TimeAvg = 0; |
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258 Testing.TimeMin = 0; |
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259 Testing.TimeTemp = 0; |
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260 Testing.TimeTotal = 0; |
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261 Testing.Init = false; |
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262 |
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263 // transformation matrix |
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264 MTrans = [ |
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265 [1,0,0,0], |
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266 [0,1,0,0], |
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267 [0,0,1,0], |
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268 [0,0,0,1] |
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269 ]; |
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270 |
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271 // position information of qube |
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272 MQube = [ |
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273 [1,0,0,0], |
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274 [0,1,0,0], |
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275 [0,0,1,0], |
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276 [0,0,0,1] |
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277 ]; |
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278 |
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279 // entity matrix |
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280 I = [ |
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281 [1,0,0,0], |
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282 [0,1,0,0], |
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283 [0,0,1,0], |
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284 [0,0,0,1] |
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285 ]; |
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286 |
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287 // create qube |
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288 Q[0] = new CreateP(-CubeSize,-CubeSize, CubeSize); |
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289 Q[1] = new CreateP(-CubeSize, CubeSize, CubeSize); |
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290 Q[2] = new CreateP( CubeSize, CubeSize, CubeSize); |
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291 Q[3] = new CreateP( CubeSize,-CubeSize, CubeSize); |
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292 Q[4] = new CreateP(-CubeSize,-CubeSize,-CubeSize); |
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293 Q[5] = new CreateP(-CubeSize, CubeSize,-CubeSize); |
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294 Q[6] = new CreateP( CubeSize, CubeSize,-CubeSize); |
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295 Q[7] = new CreateP( CubeSize,-CubeSize,-CubeSize); |
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296 |
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297 // center of gravity |
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298 Q[8] = new CreateP(0, 0, 0); |
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299 |
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300 // anti-clockwise edge check |
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301 Q.Edge = [[0,1,2],[3,2,6],[7,6,5],[4,5,1],[4,0,3],[1,5,6]]; |
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302 |
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303 // calculate squad normals |
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304 Q.Normal = new Array(); |
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305 for (var i = 0; i < Q.Edge.length; i++) Q.Normal[i] = CalcNormal(Q[Q.Edge[i][0]].V, Q[Q.Edge[i][1]].V, Q[Q.Edge[i][2]].V); |
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306 |
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307 // line drawn ? |
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308 Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false]; |
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309 |
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310 // create line pixels |
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311 Q.NumPx = 9 * 2 * CubeSize; |
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312 for (var i = 0; i < Q.NumPx; i++) CreateP(0,0,0); |
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313 |
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314 MTrans = Translate(MTrans, Origin.V[0], Origin.V[1], Origin.V[2]); |
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315 MQube = MMulti(MTrans, MQube); |
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316 |
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317 var i = 0; |
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318 for (; i < 9; i++) { |
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319 Q[i].V = VMulti(MTrans, Q[i].V); |
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320 } |
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321 DrawQube(); |
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322 Testing.Init = true; |
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323 Loop(); |
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324 } |
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325 |
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326 for ( var i = 20; i <= 160; i *= 2 ) { |
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327 Init(i); |
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328 } |
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329 |
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330 var actual = ''; |
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331 for (var i = 0; i < Q.length; ++i) { |
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332 actual += Q[i].V + ';'; |
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333 } |
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334 var expected = "-116.618229186398,212.51135212951073,62.5094191967962,1;127.83701023614447,417.11611179082263,90.41153816299942,1;293.9570894432935,196.58093046570656,252.17789153139591,1;49.501850020750915,-8.02382919560505,224.275772565193,1;6.042910556709444,103.41906953429206,-212.1778915313964,1;250.49814997925202,308.02382919560387,-184.27577256519325,1;416.61822918640064,87.48864787048812,-22.509419196796493,1;172.1629897638581,-117.1161117908236,-50.41153816299975,1;150.0000000000007,149.99999999999952,20,1;"; |
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335 assertEq(actual, expected); |
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336 |
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337 Q = null; |
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338 MTrans = null; |
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339 MQube = null; |
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340 I = null; |
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341 Origin = null; |
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342 Testing = null; |
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343 LoopTime = null; |
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344 DisplArea = null; |
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345 |