1 | // Graphics Programming Methods
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2 | // An Effective kd-tree Implementation
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3 | // László Szécsi
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4 | // 2003.
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5 |
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6 | // implementation of kd-tree methods
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7 |
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8 | #include "dxstdafx.h"
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9 | #include "KDTree.hpp"
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10 | #include <iostream>
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11 |
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12 | bool KDTree::traverse (const Ray& ray, HitRec& hitRec, float minT, float maxT)
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13 | {
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14 | // handle dirs parallel to axis here in advance
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15 | // will not need to check later for every node;
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16 | Vector dirInverts;
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17 | for(int i=0; i<3; i++)
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18 | dirInverts[i] = 1.0f / ray.dir[i];
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19 |
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20 | // hitRec.object = NULL;
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21 | hitRec.isIntersect = false;
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22 | hitRec.depth = FLT_MAX;
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23 |
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24 | float rayMin = minT;
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25 | float rayMax = maxT;
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26 |
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27 | unsigned int tNode = 0;
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28 | signed int stackPointer = -1;
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29 |
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30 | unsigned int leftChild;
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31 | unsigned int rightChild;
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32 |
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33 | for(;;)
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34 | {
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35 | bool isLeaf = !followChildren(tNode, leftChild, rightChild);
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36 |
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37 | if(isLeaf) // node is a leaf
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38 | {
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39 | Intersectable** leafList = ((Intersectable***)nodeTable)[tNode];
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40 | if(leafList) // leaf contains some objects
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41 | {
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42 | // first 4 bytes of leafList contains the length
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43 | unsigned int leafListLength = (unsigned int)*leafList;
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44 | Intersectable** leafListEnd = ++leafList + leafListLength;
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45 | for (Intersectable** objectIterator = leafList; objectIterator < leafListEnd; objectIterator++) {
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46 | if((*objectIterator) == forbidden) continue;
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47 | float depth;
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48 | // check if this test was already done
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49 | if (ray.id != (*objectIterator)->lastTestedRayId)
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50 | (*objectIterator)->intersect (ray, depth, minT, maxT);
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51 | else
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52 | depth = (*objectIterator)->lastTestedRayResult.depth;
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53 | // intersection is acceptable only if it is within the node volume
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54 | if ((*objectIterator)->lastTestedRayResult.isIntersect &&
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55 | depth < hitRec.depth &&
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56 | depth > rayMin - epsilon &&
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57 | depth < rayMax + epsilon)
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58 | hitRec = (*objectIterator)->lastTestedRayResult;
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59 | }
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60 |
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61 | if(hitRec.isIntersect)
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62 | return true;
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63 | else
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64 | if(stackPointer >= 0)
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65 | {
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66 | //have not found anything on this branch, pop the other one from stack
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67 | rayMin = traverseStack[stackPointer].rayMin;
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68 | rayMax = traverseStack[stackPointer].rayMax;
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69 | tNode = traverseStack[stackPointer].tNode;
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70 | stackPointer--;
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71 | }
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72 | else
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73 | return false;
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74 | }
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75 | else
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76 | {
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77 | //leaf is empty
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78 | if(stackPointer >= 0)
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79 | {
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80 | rayMin = traverseStack[stackPointer].rayMin;
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81 | rayMax = traverseStack[stackPointer].rayMax;
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82 | tNode = traverseStack[stackPointer].tNode;
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83 | stackPointer--;
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84 | }
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85 | else
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86 | return false;
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87 | }
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88 | }
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89 | else //not a leaf, go deeper
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90 | {
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91 | // gather cutting plane information from the nodeTable
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92 | float nodeValue = nodeTable[tNode];
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93 | unsigned char axis = *(unsigned int*)(&nodeValue) & 0x00000003;
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94 | unsigned int bitfield = *(unsigned int*)(&nodeValue) & 0xfffffffc;
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95 | float cutPlane = *(float*)(&bitfield);
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96 |
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97 | float origCoord = ray.origin[axis];
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98 | float dirCoord = dirInverts[axis];
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99 |
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100 | // calculate cutting plane - ray intersection distance 't'
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101 | register float t = (cutPlane - origCoord) * dirCoord;
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102 |
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103 | // find the child volume nearer to the origin
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104 | unsigned int nearNode = rightChild;
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105 | unsigned int farNode = leftChild;
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106 | if(origCoord + epsilon < cutPlane)
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107 | {
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108 | nearNode = leftChild;
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109 | farNode = rightChild;
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110 | }
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111 | else
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112 | if( origCoord < cutPlane + epsilon ) // origin is on the plane
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113 | if( dirCoord < 0 ) // direction decides
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114 | {
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115 | tNode = leftChild; continue;
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116 | }
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117 | else
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118 | {
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119 | tNode = rightChild; continue;
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120 | }
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121 |
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122 | if(t <= 0 || rayMax + epsilon < t )
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123 | // whole interval on near cell
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124 | tNode = nearNode;
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125 | else
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126 | {
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127 | if(t < rayMin - epsilon)
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128 | // whole interval on far cell
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129 | tNode = farNode;
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130 | else
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131 | {
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132 | // both cells
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133 | // push far branch to stack
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134 | stackPointer++;
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135 | traverseStack[stackPointer].rayMin = t;
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136 | traverseStack[stackPointer].rayMax = rayMax;
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137 | traverseStack[stackPointer].tNode = farNode;
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138 | // near branch is next to traverse
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139 | tNode = nearNode;
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140 | rayMax = t;
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141 | }
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142 | }
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143 | }
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144 | }
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145 | return false;
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146 | }
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147 |
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148 | bool KDTree::traverseBackSide (const Ray& ray, HitRec& hitRec, float minT, float maxT)
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149 | {
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150 | // handle dirs parallel to axis here in advance
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151 | // will not need to check later for every node;
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152 | Vector dirInverts;
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153 | for(int i=0; i<3; i++)
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154 | dirInverts[i] = 1.0f / ray.dir[i];
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155 |
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156 | // hitRec.object = NULL;
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157 | hitRec.isIntersect = false;
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158 | hitRec.depth = FLT_MAX;
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159 |
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160 | float rayMin = minT;
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161 | float rayMax = maxT;
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162 |
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163 | unsigned int tNode = 0;
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164 | signed int stackPointer = -1;
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165 |
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166 | unsigned int leftChild;
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167 | unsigned int rightChild;
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168 |
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169 | for(;;)
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170 | {
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171 | bool isLeaf = !followChildren(tNode, leftChild, rightChild);
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172 |
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173 | if(isLeaf) // node is a leaf
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174 | {
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175 | Intersectable** leafList = ((Intersectable***)nodeTable)[tNode];
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176 | if(leafList) // leaf contains some objects
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177 | {
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178 | // first 4 bytes of leafList contains the length
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179 | unsigned int leafListLength = (unsigned int)*leafList;
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180 | Intersectable** leafListEnd = ++leafList + leafListLength;
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181 | for (Intersectable** objectIterator = leafList; objectIterator < leafListEnd; objectIterator++) {
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182 | // if((*objectIterator) == forbidden) continue;
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183 | float depth;
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184 | // check if this test was already done
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185 | if (ray.id != (*objectIterator)->lastTestedRayId)
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186 | (*objectIterator)->intersectBackSide (ray, depth, minT, maxT);
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187 | else
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188 | depth = (*objectIterator)->lastTestedRayResult.depth;
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189 | // intersection is acceptable only if it is within the node volume
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190 | if ((*objectIterator)->lastTestedRayResult.isIntersect &&
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191 | depth < hitRec.depth &&
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192 | depth > rayMin - epsilon &&
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193 | depth < rayMax + epsilon)
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194 | hitRec = (*objectIterator)->lastTestedRayResult;
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195 | }
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196 |
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197 | if(hitRec.isIntersect)
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198 | return true;
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199 | else
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200 | if(stackPointer >= 0)
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201 | {
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202 | //have not found anything on this branch, pop the other one from stack
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203 | rayMin = traverseStack[stackPointer].rayMin;
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204 | rayMax = traverseStack[stackPointer].rayMax;
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205 | tNode = traverseStack[stackPointer].tNode;
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206 | stackPointer--;
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207 | }
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208 | else
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209 | return false;
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210 | }
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211 | else
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212 | {
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213 | //leaf is empty
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214 | if(stackPointer >= 0)
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215 | {
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216 | rayMin = traverseStack[stackPointer].rayMin;
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217 | rayMax = traverseStack[stackPointer].rayMax;
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218 | tNode = traverseStack[stackPointer].tNode;
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219 | stackPointer--;
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220 | }
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221 | else
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222 | return false;
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223 | }
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224 | }
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225 | else //not a leaf, go deeper
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226 | {
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227 | // gather cutting plane information from the nodeTable
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228 | float nodeValue = nodeTable[tNode];
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229 | unsigned char axis = *(unsigned int*)(&nodeValue) & 0x00000003;
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230 | unsigned int bitfield = *(unsigned int*)(&nodeValue) & 0xfffffffc;
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231 | float cutPlane = *(float*)(&bitfield);
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232 |
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233 | float origCoord = ray.origin[axis];
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234 | float dirCoord = dirInverts[axis];
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235 |
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236 | // calculate cutting plane - ray intersection distance 't'
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237 | register float t = (cutPlane - origCoord) * dirCoord;
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238 |
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239 | // find the child volume nearer to the origin
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240 | unsigned int nearNode = rightChild;
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241 | unsigned int farNode = leftChild;
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242 | if(origCoord + epsilon < cutPlane)
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243 | {
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244 | nearNode = leftChild;
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245 | farNode = rightChild;
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246 | }
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247 | else
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248 | if( origCoord < cutPlane + epsilon ) // origin is on the plane
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249 | if( dirCoord < 0 ) // direction decides
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250 | {
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251 | tNode = leftChild; continue;
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252 | }
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253 | else
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254 | {
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255 | tNode = rightChild; continue;
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256 | }
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257 |
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258 | if(t <= 0 || rayMax + epsilon < t )
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259 | // whole interval on near cell
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260 | tNode = nearNode;
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261 | else
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262 | {
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263 | if(t < rayMin - epsilon)
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264 | // whole interval on far cell
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265 | tNode = farNode;
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266 | else
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267 | {
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268 | // both cells
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269 | // push far branch to stack
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270 | stackPointer++;
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271 | traverseStack[stackPointer].rayMin = t;
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272 | traverseStack[stackPointer].rayMax = rayMax;
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273 | traverseStack[stackPointer].tNode = farNode;
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274 | // near branch is next to traverse
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275 | tNode = nearNode;
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276 | rayMax = t;
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277 | }
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278 | }
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279 | }
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280 | }
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281 | return false;
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282 | }
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283 |
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284 | void KDTree::deleteLeaves(unsigned int nodeID)
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285 | {
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286 | unsigned int rc;
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287 | unsigned int lc;
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288 | if(!followChildren(nodeID, lc, rc))
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289 | {
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290 | Intersectable** leafList = *(Intersectable***)&nodeTable[nodeID];
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291 | if(leafList)
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292 | {
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293 | delete leafList;
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294 | return;
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295 | }
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296 | return;
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297 | }
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298 | deleteLeaves(lc);
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299 | deleteLeaves(rc);
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300 | }
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301 |
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302 | bool KDTree::followChildren(unsigned int& parent, unsigned int &leftChild, unsigned int &rightChild)
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303 | {
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304 | unsigned int subPos = parent & nCacheLineNodes; // position within cache line
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305 | unsigned int supPos = parent & ~nCacheLineNodes; // cache line index
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306 | unsigned int leafBit = ((*(unsigned int *)&nodeTable[parent | nCacheLineNodes]) >> subPos) & 0x1;
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307 | if(leafBit) // node is a leaf, has no children
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308 | return false; // leftChild & rightChild unchanged
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309 | subPos = (subPos << 1) + 1; // index of left child
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310 | if(subPos >= nCacheLineNodes) // out of cache line, node is pointer node
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311 | {
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312 | parent = ((unsigned int*)nodeTable)[parent]; // follow pointer
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313 | subPos = parent & nCacheLineNodes; // same procedure with new parent node
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314 | supPos = parent & ~nCacheLineNodes; // referenced node cannot be leaf
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315 | subPos = (subPos << 1) + 1; // or pointer node
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316 | }
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317 | leftChild = (parent & ~nCacheLineNodes) | subPos; // recombine parent and node address
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318 | rightChild = (parent & ~nCacheLineNodes) | subPos + 1;
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319 | return true;
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320 | }
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321 |
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322 | // retrieve would-have-been child nodes of a leaf node, if they are not in a last row
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323 | bool KDTree::getFreeNodes(unsigned int leaf, unsigned int& leftFree, unsigned int& rightFree)
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324 | {
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325 | unsigned int subPos = leaf & nCacheLineNodes; // position within cache line
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326 | unsigned int supPos = leaf & ~nCacheLineNodes; // cache line index
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327 | subPos = (subPos << 1) + 1; // index of left child position
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328 | if(subPos < nCacheLineNodes) // within cache line, may have free children positions
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329 | {
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330 | unsigned int grandSubPos = ((subPos + 1) << 1) + 2; // rightmost grandchild
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331 | if(grandSubPos >= nCacheLineNodes) // children are on last row
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332 | return false; // not suitable for free nodes
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333 | leftFree = (leaf & ~nCacheLineNodes) | subPos;
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334 | rightFree = (leaf & ~nCacheLineNodes) | subPos + 1;
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335 | return true;
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336 | }
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337 | else
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338 | return false; // leaf is on last row, has no free children
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339 | }
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340 |
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341 | bool KDTree::isLeaf(unsigned int xnode)
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342 | {
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343 | return ((*(unsigned int *)&nodeTable[xnode | nCacheLineNodes]) >> (xnode & nCacheLineNodes)) & 0x1;
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344 | }
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345 |
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346 | float KDTree::getBoundValue(unsigned int * extremeIndex, unsigned char axis)
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347 | {
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348 | //if Most Significant Bit of 'extremeIndex' is 1, take the maximum
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349 | //if Most Significant Bit of 'extremeIndex' is 0, take the minimum
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350 | unsigned int index = *extremeIndex;
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351 | return (index & 0x80000000)?
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352 | (objects[ index & 0x7fffffff]->bbox.maxPoint[axis]):
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353 | (objects[ index & 0x7fffffff]->bbox.minPoint[axis]);
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354 | }
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355 |
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356 | void KDTree::build(unsigned int nodeID, unsigned int* boundsArray, unsigned int nObjects, BoundingBox& limits, unsigned char axisNmask)
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357 | {
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358 | //separate the axisNmask parameter to axis and mask
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359 | unsigned char axis = axisNmask & 07;
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360 | unsigned char mask = axisNmask & 070;
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361 |
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362 | //calculate some values for the cost function
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363 | float costBase; // area of face perpendicular to axis
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364 | float costSteep; // half of circumference of face perpendicular to axis
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365 | // surface area / 2 = costBase + costSteep * (length of edge parallel to axis)
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366 | // cost = #(objects within volume) * surface area / 2
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367 | switch(axis)
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368 | {
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369 | case 0:
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370 | costBase = (limits.maxPoint.z - limits.minPoint.z)
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371 | * (limits.maxPoint.y - limits.minPoint.y);
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372 | costSteep = (limits.maxPoint.z - limits.minPoint.z)
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373 | + (limits.maxPoint.y - limits.minPoint.y);
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374 | break;
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375 | case 1:
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376 | costBase = (limits.maxPoint.x - limits.minPoint.x)
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377 | * (limits.maxPoint.z - limits.minPoint.z);
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378 | costSteep = (limits.maxPoint.x - limits.minPoint.x)
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379 | + (limits.maxPoint.z - limits.minPoint.z);
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380 | break;
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381 | case 2:
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382 | costBase = (limits.maxPoint.x - limits.minPoint.x)
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383 | * (limits.maxPoint.y - limits.minPoint.y);
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384 | costSteep = (limits.maxPoint.x - limits.minPoint.x)
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385 | + (limits.maxPoint.y - limits.minPoint.y);
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386 | break;
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387 | }
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388 |
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389 | // references to extrema (corresponding to 'axis') of node volume
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390 | float& limiMin = axis?((axis==1)?limits.minPoint.y:limits.minPoint.z):limits.minPoint.x;
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391 | float& limiMax = axis?((axis==1)?limits.maxPoint.y:limits.maxPoint.z):limits.maxPoint.x;
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392 |
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393 | //sort the the extrema of the objects
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394 | //we will need this to find the best splitting plane
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395 | quickSort(boundsArray, boundsArray + (nObjects << 1) - 1, axis);
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396 |
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397 | // the following code section could be used to find the spatial and object medians
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398 | // either to implement a simpler and less effective subdivision rule
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399 | // or to restrict optimum search to the median interval (between two median)
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400 | //***************************************************************************
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401 | // find the value for the spatial median.... easy
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402 | // float spatialMedian = (limiMax + limiMin) / 2.0f;
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403 | //find the position in the array corresponding to the spatial median value
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404 | // unsigned int* spatialMedianPosition = findBound(boundsArray, nObjects << 1, spatialMedian, axis);
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405 | //find object median position (middle of array, surprise-surprise), and value
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406 | // unsigned int* objectMedianPosition = boundsArray + nObjects;
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407 | // float objectMedian = getBoundValue(objectMedianPosition, axis);
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408 | //****************************************************************************
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409 |
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410 | // find the value for the left and right "cutting off empty space" (COES) planes
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411 | // remember the object extrema are already sorted
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412 | float leftCoesCut = objects[boundsArray[0] & 0x7fffffff]->bbox.minPoint[axis];
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413 | float rightCoesCut = objects[boundsArray[(nObjects << 1)-1] & 0x7fffffff]->bbox.maxPoint[axis];
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414 |
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415 | if(rightCoesCut > limiMax)
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416 | rightCoesCut = limiMax;
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417 | if(leftCoesCut < limiMin)
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418 | leftCoesCut = limiMin;
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419 |
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420 | // find the estimated cost of ray casting after COES
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421 | float leftCoesCutCost = ((limiMax - leftCoesCut) * costSteep + costBase) * (nObjects);
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422 | float rightCoesCutCost = ((rightCoesCut - limiMin) * costSteep + costBase) * (nObjects);
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423 | // take care of numerical accuracy problems that arise when
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424 | // limiMin == limiMax (possible and allowed)
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425 | if(leftCoesCutCost < 0) leftCoesCutCost = FLT_MAX;
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426 | if(rightCoesCutCost < 0) rightCoesCutCost = FLT_MAX;
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427 |
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428 | // creep through array, evaluate cost for every possible cut,
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429 | // maintaining the counters for intersected and completely passed objects
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430 | int leftCount = 0; // objects on the left of current cut
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431 | int intersectedCount = 0; // object intersected by current cut
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432 |
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433 | // we may limit the search to a partition of the array, eg. the median interval
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434 | unsigned int* searchIntervalStart;
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435 | unsigned int* searchIntervalEnd;
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436 |
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437 | // full range optimum search
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438 | searchIntervalStart = boundsArray + 1;
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439 | searchIntervalEnd = boundsArray + (nObjects << 1) - 1;
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440 |
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441 | // these three variable identify the best cut found so far:
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442 | float minimumCostFound;
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443 | float minimumCostCut;
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444 | unsigned int* minimumCostPosition;
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445 |
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446 | // is left or right COES better? the better is our best candidate to start with
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447 | int minimumIntersected = 0;
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448 | int minimumLeft = 0;
|
---|
449 | if(leftCoesCutCost < rightCoesCutCost)
|
---|
450 | {
|
---|
451 | minimumCostFound = leftCoesCutCost;
|
---|
452 | minimumCostPosition = boundsArray;
|
---|
453 | minimumCostCut = leftCoesCut;
|
---|
454 | minimumIntersected = 0;
|
---|
455 | minimumLeft = 0;
|
---|
456 | }
|
---|
457 | else
|
---|
458 | {
|
---|
459 | minimumCostFound = rightCoesCutCost;
|
---|
460 | minimumCostPosition = boundsArray + (nObjects << 1);
|
---|
461 | minimumCostCut = rightCoesCut;
|
---|
462 | minimumIntersected = 0;
|
---|
463 | minimumLeft = nObjects;
|
---|
464 | }
|
---|
465 |
|
---|
466 | // creep up to the search interval... count objects
|
---|
467 | unsigned int* trace = boundsArray;
|
---|
468 | for(; trace< searchIntervalStart; trace++ )
|
---|
469 | {
|
---|
470 | if(*trace & 0x80000000)
|
---|
471 | {
|
---|
472 | intersectedCount--;
|
---|
473 | leftCount++;
|
---|
474 | }
|
---|
475 | else
|
---|
476 | intersectedCount++;
|
---|
477 | }
|
---|
478 | // evaluate the cost function, if better is found keep it
|
---|
479 | for(; trace< searchIntervalEnd; trace++ )
|
---|
480 | {
|
---|
481 | float cut = getBoundValue(trace, axis);
|
---|
482 | float costIfCutHere;
|
---|
483 | if(*trace & 0x80000000)
|
---|
484 | {
|
---|
485 | intersectedCount--;
|
---|
486 | leftCount++;
|
---|
487 | costIfCutHere =
|
---|
488 | (leftCount+intersectedCount) * ((cut - limiMin) * costSteep + costBase) +
|
---|
489 | (nObjects - leftCount) * ((limiMax - cut) * costSteep + costBase);
|
---|
490 | if(leftCount == 0 || leftCount + intersectedCount == nObjects )
|
---|
491 | costIfCutHere = FLT_MAX;
|
---|
492 | if(costIfCutHere < minimumCostFound ){
|
---|
493 | minimumCostFound = costIfCutHere;
|
---|
494 | minimumCostPosition = trace + 1;
|
---|
495 | minimumIntersected = intersectedCount;
|
---|
496 | minimumLeft = leftCount;
|
---|
497 | minimumCostCut = cut;
|
---|
498 | }
|
---|
499 | }
|
---|
500 | else
|
---|
501 | {
|
---|
502 | costIfCutHere =
|
---|
503 | (leftCount+intersectedCount) * ((cut - limiMin) * costSteep + costBase) +
|
---|
504 | (nObjects - leftCount) * ((limiMax - cut) * costSteep + costBase);
|
---|
505 | if(leftCount == 0 || leftCount + intersectedCount == nObjects)
|
---|
506 | costIfCutHere = FLT_MAX;
|
---|
507 | if(costIfCutHere < minimumCostFound)
|
---|
508 | {
|
---|
509 | minimumCostFound = costIfCutHere;
|
---|
510 | minimumCostPosition = trace;
|
---|
511 | minimumIntersected = intersectedCount;
|
---|
512 | minimumLeft = leftCount;
|
---|
513 | minimumCostCut = cut;
|
---|
514 | }
|
---|
515 | intersectedCount++;
|
---|
516 | }
|
---|
517 |
|
---|
518 | }
|
---|
519 |
|
---|
520 | // automatic termination, based on the cost estimation
|
---|
521 | if( minimumCostFound * 1.0001 >= nObjects * ((limiMax - limiMin) * costSteep + costBase))
|
---|
522 | {
|
---|
523 | // no appropriate splitting found, mark this axis as failed
|
---|
524 | mask |= (010 << axis);
|
---|
525 | if(mask != 070 && (nObjects != 1 || minimumCostFound < 10.0))
|
---|
526 | {
|
---|
527 | //if there is still a hopeful axis, do not split here, go on with another direction
|
---|
528 | do{ axis = (axis + 1)%3;
|
---|
529 | }while(mask & (010 << axis));
|
---|
530 | build(nodeID, boundsArray, nObjects, limits, mask | axis);
|
---|
531 | return;
|
---|
532 | }
|
---|
533 | // if all 3 have axes have already failed, stop here, make a leaf
|
---|
534 | // save leaf length and objects list
|
---|
535 | Intersectable** leafList = new Intersectable*[nObjects+1];
|
---|
536 | Intersectable** leafLoader = leafList;
|
---|
537 | *(unsigned int*)leafLoader = nObjects;
|
---|
538 | leafLoader++;
|
---|
539 | for(unsigned int* bubo = boundsArray;bubo < boundsArray + (nObjects << 1);bubo++)
|
---|
540 | if(!(*bubo & 0x80000000))
|
---|
541 | {
|
---|
542 | *leafLoader = *(objects + *bubo);
|
---|
543 | leafLoader++;
|
---|
544 | }
|
---|
545 | // make the node contain a pointer to the list
|
---|
546 | ((Intersectable ***)nodeTable)[nodeID] = leafList;
|
---|
547 | delete boundsArray;
|
---|
548 | //mark the node as a leaf
|
---|
549 | ((unsigned int*)nodeTable)[nodeID | nCacheLineNodes] |= (0x1 << (nodeID & nCacheLineNodes));
|
---|
550 | //add orphaned nodes to free node list
|
---|
551 | unsigned int lFree;
|
---|
552 | unsigned int rFree;
|
---|
553 | if(getFreeNodes(nodeID, lFree, rFree))
|
---|
554 | {
|
---|
555 | freeNodes->insert(lFree);
|
---|
556 | freeNodes->insert(rFree);
|
---|
557 | }
|
---|
558 | return;
|
---|
559 | }
|
---|
560 | // grant another chance to previously failed directions:
|
---|
561 | mask = 00;
|
---|
562 | // insert a back-pointer if necessary
|
---|
563 | nodeID = makePointer(nodeID);
|
---|
564 | // store the splitting plane value in the node
|
---|
565 | unsigned int bitfield = *(unsigned int*)(&minimumCostCut) & 0xfffffffc | axis;
|
---|
566 | nodeTable[nodeID] = *(float*)(&bitfield);
|
---|
567 | // mark node as a non-leaf node
|
---|
568 | *(unsigned int*)&nodeTable[nodeID | nCacheLineNodes] &= ~(0x1 << (nodeID & nCacheLineNodes));
|
---|
569 |
|
---|
570 | currentDepth++; if(currentDepth > depth) depth = currentDepth;
|
---|
571 |
|
---|
572 | // allocate child nodes, pass the objects on to them
|
---|
573 | unsigned int leftChildMade;
|
---|
574 | unsigned int rightChildMade;
|
---|
575 |
|
---|
576 | // handle the two branches, the one with less objects first
|
---|
577 | bool firstBranch = false;
|
---|
578 | bool rightBranchHasMoreObjects = (minimumLeft << 1) + minimumIntersected < nObjects;
|
---|
579 | followChildren(nodeID, leftChildMade, rightChildMade);
|
---|
580 | do
|
---|
581 | {
|
---|
582 | firstBranch = !firstBranch;
|
---|
583 | if(firstBranch && rightBranchHasMoreObjects
|
---|
584 | || !firstBranch && !rightBranchHasMoreObjects)
|
---|
585 | {
|
---|
586 | // left branch
|
---|
587 | if(minimumLeft + minimumIntersected)
|
---|
588 | {
|
---|
589 | // branch has objects
|
---|
590 | // create new object extrema array
|
---|
591 | BoundingBox diver = limits;
|
---|
592 | limiMax = minimumCostCut;
|
---|
593 | unsigned int * leftChildBounds = new unsigned int[(minimumLeft + minimumIntersected) << 1];
|
---|
594 | unsigned int* copycatLeft = leftChildBounds;
|
---|
595 | unsigned int* snoop = boundsArray;
|
---|
596 | for(; snoop < minimumCostPosition; snoop++)
|
---|
597 | {
|
---|
598 | // for every mimimum left of cutting plane
|
---|
599 | if(!(*snoop & 0x80000000))
|
---|
600 | {
|
---|
601 | // add one for the mimimum
|
---|
602 | *copycatLeft = *snoop;
|
---|
603 | copycatLeft++;
|
---|
604 | // add one for the maximum
|
---|
605 | *copycatLeft = *snoop | 0x80000000;
|
---|
606 | copycatLeft++;
|
---|
607 | }
|
---|
608 | }
|
---|
609 | unsigned char turnedAxis = axis;
|
---|
610 | do{ turnedAxis = (turnedAxis + 1)%3;
|
---|
611 | }while(mask & (010 << turnedAxis));
|
---|
612 | build(leftChildMade, leftChildBounds, minimumLeft + minimumIntersected, limits, mask | turnedAxis);
|
---|
613 | limits = diver;
|
---|
614 | }
|
---|
615 | else
|
---|
616 | {
|
---|
617 | // make empty leaf
|
---|
618 | unsigned int empty = leftChildMade;
|
---|
619 | (unsigned int *&)nodeTable[empty] = 0x0;
|
---|
620 | *(unsigned int*)&nodeTable[empty | nCacheLineNodes] |= 0x1 << (empty & nCacheLineNodes);
|
---|
621 | // add orphaned nodes to free list
|
---|
622 | unsigned int eleLeft;
|
---|
623 | unsigned int eleRight;
|
---|
624 | if(getFreeNodes(empty, eleLeft, eleRight))
|
---|
625 | {
|
---|
626 | freeNodes->insert(eleLeft);
|
---|
627 | freeNodes->insert(eleRight);
|
---|
628 | }
|
---|
629 | }
|
---|
630 | }
|
---|
631 | else
|
---|
632 | {
|
---|
633 | if(nObjects - minimumLeft)
|
---|
634 | {
|
---|
635 | BoundingBox diver = limits;
|
---|
636 | limiMin = minimumCostCut;
|
---|
637 |
|
---|
638 | // create new bounds array
|
---|
639 | unsigned int * rightChildBounds;
|
---|
640 | rightChildBounds = new unsigned int[(nObjects - minimumLeft) << 1 ];
|
---|
641 |
|
---|
642 | unsigned int* copycatRight = rightChildBounds;
|
---|
643 | unsigned int* snoop = minimumCostPosition;
|
---|
644 | for(; snoop < boundsArray + (nObjects << 1); snoop++)
|
---|
645 | {
|
---|
646 | // for every maximum right of cutting plane
|
---|
647 | if(*snoop & 0x80000000)
|
---|
648 | {
|
---|
649 | *copycatRight = *snoop & 0x7fffffff;
|
---|
650 | copycatRight++;
|
---|
651 | *copycatRight = *snoop;
|
---|
652 | copycatRight++;
|
---|
653 | }
|
---|
654 | }
|
---|
655 |
|
---|
656 | unsigned int turnedAxis = axis;
|
---|
657 | do{ turnedAxis = (turnedAxis + 1)%3;
|
---|
658 | }while(mask & (010 << turnedAxis));
|
---|
659 | build(rightChildMade, rightChildBounds, nObjects - minimumLeft, limits, mask | turnedAxis);
|
---|
660 | limits = diver;
|
---|
661 | }
|
---|
662 | else
|
---|
663 | {
|
---|
664 | // empty leaf
|
---|
665 | unsigned int empty = rightChildMade;
|
---|
666 | (unsigned int *&)nodeTable[empty] = 0x0;
|
---|
667 | *(unsigned int*)&nodeTable[empty | nCacheLineNodes] |= 0x1 << (empty & nCacheLineNodes);
|
---|
668 | // orphaned nodes
|
---|
669 | unsigned int eleLeft;
|
---|
670 | unsigned int eleRight;
|
---|
671 | if(getFreeNodes(empty, eleLeft, eleRight))
|
---|
672 | {
|
---|
673 | freeNodes->insert(eleLeft);
|
---|
674 | freeNodes->insert(eleRight);
|
---|
675 | }
|
---|
676 | }
|
---|
677 | }
|
---|
678 | }while(firstBranch);
|
---|
679 | currentDepth--;
|
---|
680 | delete boundsArray;
|
---|
681 | }
|
---|
682 |
|
---|
683 | void KDTree::quickSort(unsigned int *lo0, unsigned int* hi0, unsigned char axis)
|
---|
684 | {
|
---|
685 | if ( hi0 > lo0)
|
---|
686 | {
|
---|
687 | unsigned int* lo = lo0;
|
---|
688 | unsigned int* hi = hi0;
|
---|
689 |
|
---|
690 | // establish partition element as the midpoint of the array.
|
---|
691 | unsigned int* midPos =
|
---|
692 | lo0 + ( ((unsigned int)hi0 - (unsigned int)lo0) / sizeof(unsigned int) / 2);
|
---|
693 | unsigned int midIndex = *midPos;
|
---|
694 |
|
---|
695 | // loop through the array until indices cross
|
---|
696 | while( lo <= hi )
|
---|
697 | {
|
---|
698 | // find the first element that is greater than or equal to
|
---|
699 | // the partition element starting from the left Index.
|
---|
700 | // getBoundValue(lo, axis) < mid ) && *lo != midIndex)
|
---|
701 | while( ( lo < hi0 ) && ( compare(*lo, midIndex, axis)))
|
---|
702 | ++lo;
|
---|
703 |
|
---|
704 | // find an element that is smaller than or equal to
|
---|
705 | // the partition element starting from the right Index.
|
---|
706 | //( getBoundValue(hi, axis) > mid ) && *hi != midIndex)
|
---|
707 | while( ( hi > lo0 ) && ( compare(midIndex, *hi, axis)))
|
---|
708 | --hi;
|
---|
709 | // if the indices have not crossed, swap
|
---|
710 | if( lo <= hi )
|
---|
711 | {
|
---|
712 | unsigned int temp = *lo;
|
---|
713 | *lo = *hi;
|
---|
714 | *hi = temp;
|
---|
715 | ++lo;
|
---|
716 | --hi;
|
---|
717 | }
|
---|
718 | }
|
---|
719 | // If the right index has not reached the left side of array
|
---|
720 | // must now sort the left partition.
|
---|
721 | if( lo0 < hi )
|
---|
722 | quickSort( lo0, hi, axis);
|
---|
723 | // If the left index has not reached the right side of array
|
---|
724 | // must now sort the right partition.
|
---|
725 | if( lo < hi0 )
|
---|
726 | quickSort( lo, hi0, axis);
|
---|
727 | }
|
---|
728 | }
|
---|
729 |
|
---|
730 | KDTree::KDTree (Intersectable** iObjects, int nObjects){
|
---|
731 | // take parameters
|
---|
732 | this->nObjects = nObjects;
|
---|
733 | objects = iObjects;
|
---|
734 |
|
---|
735 | // determine bounding box
|
---|
736 | createBoundingBox (iObjects, nObjects);
|
---|
737 |
|
---|
738 | // determine error because of 21 bits mantissa representaion
|
---|
739 | float largest = 0.0f;
|
---|
740 | for(int i=0; i<3; i++)
|
---|
741 | if( boundingBox.maxPoint[i] > largest)
|
---|
742 | largest = boundingBox.maxPoint[i];
|
---|
743 | for(int o=0; o<3; o++)
|
---|
744 | if( - boundingBox.minPoint[o] > largest)
|
---|
745 | largest = - boundingBox.minPoint[o];
|
---|
746 | epsilon = largest / 524288.0f; // e = X * 2^19
|
---|
747 |
|
---|
748 | // set up memory structure constants
|
---|
749 | nCacheLineBytes = KDTREE_CACHE_LINE_BYTES;
|
---|
750 | // a cache line has 2^n - 1 nodes, plus 4 bytes (1 node) for leaf bits
|
---|
751 | nCacheLineNodes = nCacheLineBytes / sizeof(float) - 1;
|
---|
752 |
|
---|
753 | // size of cache line memory pool
|
---|
754 | maxNCacheLines = nObjects * 16 / nCacheLineNodes + 1;
|
---|
755 | // cache lines already allocated
|
---|
756 | nCacheLines = 1;
|
---|
757 |
|
---|
758 | unsigned int maxPossibleFree = maxNCacheLines * nCacheLineNodes / 2;
|
---|
759 | // allocate free nodes heap
|
---|
760 | freeNodes = new Heap<unsigned int>(maxPossibleFree);
|
---|
761 |
|
---|
762 | // allocate cache line memory pool (large size, will be shrinked after the build)
|
---|
763 | // nodes in cache line pool + offset correction
|
---|
764 | poolNodeTable = (float*)malloc(sizeof(float) *
|
---|
765 | ( maxNCacheLines * (nCacheLineNodes + 1) + nCacheLineNodes + 1 ));
|
---|
766 | nodeTable = (float*)(((unsigned int)poolNodeTable / nCacheLineBytes + 1) * nCacheLineBytes);
|
---|
767 |
|
---|
768 | // collect the initial object extremes to pass on to the build algorithm
|
---|
769 | unsigned int* objectBoundaries = new unsigned int[nObjects << 1];
|
---|
770 | for(unsigned int fill=0;fill<nObjects;fill++){
|
---|
771 | objectBoundaries[fill << 1] = fill & 0x7fffffff;
|
---|
772 | objectBoundaries[(fill << 1) + 1] = fill | 0x80000000;
|
---|
773 | }
|
---|
774 |
|
---|
775 | // GO! GO! GO!
|
---|
776 | depth = currentDepth = 1;
|
---|
777 | build(0, objectBoundaries, nObjects, boundingBox, 0);
|
---|
778 | traverseStack = new TraverseStack[depth];
|
---|
779 |
|
---|
780 | // get rid of garbage
|
---|
781 | // decrease cache line memory pool to fit actual memory need
|
---|
782 | realloc(poolNodeTable, (nCacheLines + 1) * nCacheLineBytes);
|
---|
783 |
|
---|
784 | delete freeNodes;
|
---|
785 | }
|
---|
786 |
|
---|
787 | unsigned int* KDTree::findBound(unsigned int *extremeArrayStart, unsigned int nBounds, float loc, unsigned char axis)
|
---|
788 | {
|
---|
789 | while(nBounds > 1)
|
---|
790 | {
|
---|
791 | unsigned int wBounds = nBounds >> 1;
|
---|
792 | if(getBoundValue(extremeArrayStart+wBounds, axis) < loc)
|
---|
793 | {
|
---|
794 | extremeArrayStart += wBounds;
|
---|
795 | nBounds -= wBounds;
|
---|
796 | }
|
---|
797 | else
|
---|
798 | nBounds = wBounds;
|
---|
799 | }
|
---|
800 | return extremeArrayStart;
|
---|
801 |
|
---|
802 | }
|
---|
803 |
|
---|
804 | /*!this is more complicated then one would predict. rules are:
|
---|
805 | - if values are significantly different, no problem
|
---|
806 | - the minimum of a patch is smaller than its maximum
|
---|
807 | - if a maximum and a minimum are near, the other extrema of the patches decide
|
---|
808 | - if all four extrema are near, the 2 ends of a patch have to be simultaneusly
|
---|
809 | smaller or bigger than the other two ends
|
---|
810 | */
|
---|
811 | bool KDTree::compare(unsigned int aIndex, unsigned int bIndex, unsigned char axis)
|
---|
812 | {
|
---|
813 | unsigned int caIndex = aIndex & 0x7fffffff;
|
---|
814 | float aBegin = objects[caIndex]->bbox.minPoint[axis];
|
---|
815 | float aEnd = objects[caIndex]->bbox.maxPoint[axis];
|
---|
816 | unsigned int cbIndex = bIndex & 0x7fffffff;
|
---|
817 | float bBegin = objects[cbIndex]->bbox.minPoint[axis];
|
---|
818 | float bEnd = objects[cbIndex]->bbox.maxPoint[axis];
|
---|
819 |
|
---|
820 | if(aIndex & 0x80000000)
|
---|
821 | if(bIndex & 0x80000000)
|
---|
822 | {
|
---|
823 | if(caIndex == cbIndex)
|
---|
824 | return false;
|
---|
825 | if(aEnd + epsilon < bEnd)
|
---|
826 | return true;
|
---|
827 | if(bEnd + epsilon < aEnd)
|
---|
828 | return false;
|
---|
829 | if(aBegin + epsilon < bBegin)
|
---|
830 | return true;
|
---|
831 | if(bBegin + epsilon < aBegin)
|
---|
832 | return false;
|
---|
833 | return caIndex < cbIndex;
|
---|
834 | }
|
---|
835 | else
|
---|
836 | {
|
---|
837 | if(caIndex == cbIndex)
|
---|
838 | return false;
|
---|
839 | if(aEnd + epsilon < bBegin)
|
---|
840 | return true;
|
---|
841 | if(bBegin + epsilon < aEnd)
|
---|
842 | return false;
|
---|
843 | if(aBegin + epsilon < bEnd)
|
---|
844 | return true;
|
---|
845 | return caIndex < cbIndex;
|
---|
846 |
|
---|
847 | }
|
---|
848 | else
|
---|
849 | if(bIndex & 0x80000000)
|
---|
850 | {
|
---|
851 | if(caIndex == cbIndex)
|
---|
852 | return true;
|
---|
853 | if(bEnd + epsilon < aBegin)
|
---|
854 | return false;
|
---|
855 | if(aBegin + epsilon < bEnd)
|
---|
856 | return true;
|
---|
857 | if(bBegin + epsilon < aEnd)
|
---|
858 | return false;
|
---|
859 | return caIndex + epsilon < cbIndex;
|
---|
860 | }
|
---|
861 | else
|
---|
862 | {
|
---|
863 | if(caIndex == cbIndex)
|
---|
864 | return false;
|
---|
865 | if(aBegin + epsilon < bBegin)
|
---|
866 | return true;
|
---|
867 | if(bBegin + epsilon < aBegin)
|
---|
868 | return false;
|
---|
869 | if(aEnd + epsilon < bEnd)
|
---|
870 | return true;
|
---|
871 | if(bEnd + epsilon < aEnd)
|
---|
872 | return false;
|
---|
873 | return caIndex < cbIndex;
|
---|
874 |
|
---|
875 | }
|
---|
876 | }
|
---|
877 |
|
---|
878 | inline unsigned int KDTree::makePointer(unsigned int originalNode)
|
---|
879 | {
|
---|
880 | unsigned int subPos = originalNode & nCacheLineNodes; // position within cache line
|
---|
881 | unsigned int supPos = originalNode & ~nCacheLineNodes; // index of cache line
|
---|
882 | subPos = (subPos << 1) + 1; // child position
|
---|
883 | if(subPos < nCacheLineNodes) // within cache line
|
---|
884 | {
|
---|
885 | return originalNode;
|
---|
886 | }
|
---|
887 | else // find free node
|
---|
888 | {
|
---|
889 | unsigned int emptyNode;
|
---|
890 | if(!freeNodes->isEmpty())
|
---|
891 | {
|
---|
892 | emptyNode = freeNodes->removeMin();
|
---|
893 | }
|
---|
894 | else
|
---|
895 | {
|
---|
896 | //allocate a new cache line
|
---|
897 | emptyNode = nCacheLines * (nCacheLineNodes + 1); // root of new cache line
|
---|
898 | nCacheLines++;
|
---|
899 | if(nCacheLines > maxNCacheLines)
|
---|
900 | {
|
---|
901 | maxNCacheLines *= 1.1;
|
---|
902 | float * largerPoolNodeTable = (float*)malloc(
|
---|
903 | sizeof(float) * ( maxNCacheLines * (nCacheLineNodes + 1) + nCacheLineNodes + 1 ));
|
---|
904 | float* largerNodeTable = (float*)(((unsigned int)largerPoolNodeTable / nCacheLineBytes + 1) * nCacheLineBytes);
|
---|
905 | memcpy(largerNodeTable, nodeTable, nCacheLines * nCacheLineBytes);
|
---|
906 | nodeTable = largerNodeTable;
|
---|
907 | free(poolNodeTable);
|
---|
908 | poolNodeTable = largerPoolNodeTable;
|
---|
909 | }
|
---|
910 | }
|
---|
911 | // mark as non-leaf (being last-row and non-leaf means pointer node)
|
---|
912 | *(unsigned int*)&nodeTable[originalNode | nCacheLineNodes] &= ~(0x1 << (originalNode & nCacheLineNodes));
|
---|
913 | // insert index of empty node
|
---|
914 | ((unsigned int*)nodeTable)[originalNode] = emptyNode;
|
---|
915 | return emptyNode;
|
---|
916 | }
|
---|
917 | }
|
---|