1 |
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2 | // GOLEM library
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3 | #include <assert.h>
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4 | #include <iostream>
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5 | using namespace std;
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6 | #include "AxisAlignedBox3.h"
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7 | #include "Ray.h"
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8 | #include "Polygon3.h"
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9 |
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10 | #define FATAL Debug
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11 | #define FATAL_ABORT exit(1)
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12 |
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13 |
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14 | // AxisAlignedBox3 implementations
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15 |
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16 | // Overload << operator for C++-style output
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17 | ostream&
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18 | operator<< (ostream &s, const AxisAlignedBox3 &A)
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19 | {
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20 | return s << '[' << A.mMin.x << ", " << A.mMin.y << ", " << A.mMin.z << "]["
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21 | << A.mMax.x << ", " << A.mMax.y << ", " << A.mMax.z << ']';
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22 | }
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23 |
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24 | // Overload >> operator for C++-style input
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25 | istream&
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26 | operator>> (istream &s, AxisAlignedBox3 &A)
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27 | {
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28 | char a;
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29 | // read "[min.x, min.y, min.z][mMax.x, mMax.y, mMax.z]"
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30 | return s >> a >> A.mMin.x >> a >> A.mMin.y >> a >> A.mMin.z >> a >> a
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31 | >> A.mMax.x >> a >> A.mMax.y >> a >> A.mMax.z >> a;
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32 | }
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33 |
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34 | bool
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35 | AxisAlignedBox3::Unbounded() const
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36 | {
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37 | return (mMin == Vector3(-MAXFLOAT)) ||
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38 | (mMax == Vector3(-MAXFLOAT));
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39 | }
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40 |
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41 | void
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42 | AxisAlignedBox3::Include(const Vector3 &newpt)
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43 | {
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44 | Minimize(mMin, newpt);
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45 | Maximize(mMax, newpt);
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46 | }
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47 |
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48 | void
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49 | AxisAlignedBox3::Include(const Polygon3 &newpoly)
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50 | {
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51 | VertexContainer::const_iterator it, it_end = newpoly.mVertices.end();
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52 |
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53 | for (it = newpoly.mVertices.begin(); it != it_end; ++ it)
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54 | Include(*it);
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55 | }
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56 |
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57 | void
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58 | AxisAlignedBox3::Include(const AxisAlignedBox3 &bbox)
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59 | {
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60 | Minimize(mMin, bbox.mMin);
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61 | Maximize(mMax, bbox.mMax);
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62 | }
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63 |
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64 | bool
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65 | AxisAlignedBox3::IsCorrect()
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66 | {
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67 | if ( (mMin.x > mMax.x) ||
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68 | (mMin.y > mMax.y) ||
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69 | (mMin.z > mMax.z) )
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70 | return false; // box is not formed
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71 | return true;
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72 | }
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73 |
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74 | void
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75 | AxisAlignedBox3::GetEdge(const int edge, Vector3 *a, Vector3 *b) const
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76 | {
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77 | switch(edge) {
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78 | case 0:
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79 | a->SetValue(mMin.x, mMin.y, mMin.z);
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80 | b->SetValue(mMin.x, mMin.y, mMax.z);
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81 | break;
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82 | case 1:
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83 | a->SetValue(mMin.x, mMin.y, mMin.z);
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84 | b->SetValue(mMin.x, mMax.y, mMin.z);
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85 | break;
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86 | case 2:
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87 | a->SetValue(mMin.x, mMin.y, mMin.z);
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88 | b->SetValue(mMax.x, mMin.y, mMin.z);
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89 | break;
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90 | case 3:
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91 | a->SetValue(mMax.x, mMax.y, mMax.z);
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92 | b->SetValue(mMax.x, mMax.y, mMin.z);
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93 | break;
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94 | case 4:
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95 | a->SetValue(mMax.x, mMax.y, mMax.z);
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96 | b->SetValue(mMax.x, mMin.y, mMax.z);
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97 | break;
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98 | case 5:
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99 | a->SetValue(mMax.x, mMax.y, mMax.z);
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100 | b->SetValue(mMin.x, mMax.y, mMax.z);
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101 | break;
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102 |
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103 | case 6:
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104 | a->SetValue(mMin.x, mMin.y, mMax.z);
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105 | b->SetValue(mMin.x, mMax.y, mMax.z);
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106 | break;
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107 | case 7:
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108 | a->SetValue(mMin.x, mMin.y, mMax.z);
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109 | b->SetValue(mMax.x, mMin.y, mMax.z);
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110 | break;
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111 | case 8:
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112 | a->SetValue(mMin.x, mMax.y, mMin.z);
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113 | b->SetValue(mMin.x, mMax.y, mMax.z);
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114 | break;
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115 | case 9:
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116 | a->SetValue(mMin.x, mMax.y, mMin.z);
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117 | b->SetValue(mMax.x, mMax.y, mMin.z);
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118 | break;
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119 | case 10:
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120 | a->SetValue(mMax.x, mMin.y, mMin.z);
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121 | b->SetValue(mMax.x, mMax.y, mMin.z);
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122 | break;
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123 | case 11:
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124 | a->SetValue(mMax.x, mMin.y, mMin.z);
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125 | b->SetValue(mMax.x, mMin.y, mMax.z);
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126 | break;
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127 | }
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128 | }
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129 |
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130 | void
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131 | AxisAlignedBox3::Include(const int &axis, const float &newBound)
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132 | {
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133 | switch (axis) {
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134 | case 0: { // x-axis
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135 | if (mMin.x > newBound)
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136 | mMin.x = newBound;
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137 | if (mMax.x < newBound)
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138 | mMax.x = newBound;
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139 | break;
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140 | }
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141 | case 1: { // y-axis
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142 | if (mMin.y > newBound)
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143 | mMin.y = newBound;
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144 | if (mMax.y < newBound)
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145 | mMax.y = newBound;
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146 | break;
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147 | }
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148 | case 2: { // z-axis
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149 | if (mMin.z > newBound)
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150 | mMin.z = newBound;
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151 | if (mMax.z < newBound)
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152 | mMax.z = newBound;
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153 | break;
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154 | }
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155 | }
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156 | }
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157 |
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158 | #if 0
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159 | // ComputeMinMaxT computes the minimum and maximum signed distances
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160 | // of intersection with the ray; it returns 1 if the ray hits
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161 | // the bounding box and 0 if it does not.
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162 | int
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163 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
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164 | float *tmin,
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165 | float *tmax) const
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166 | {
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167 | float minx, maxx, miny, maxy, minz, maxz;
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168 |
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169 | if (fabs(ray.dir.x) < 0.001) {
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170 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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171 | minx = -MAXFLOAT;
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172 | maxx = MAXFLOAT;
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173 | }
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174 | else
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175 | return 0;
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176 | }
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177 | else {
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178 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
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179 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
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180 | if (t1 < t2) {
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181 | minx = t1;
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182 | maxx = t2;
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183 | }
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184 | else {
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185 | minx = t2;
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186 | maxx = t1;
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187 | }
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188 | if (maxx < 0)
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189 | return 0;
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190 | }
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191 |
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192 | if (fabs(ray.dir.y) < 0.001) {
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193 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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194 | miny = -MAXFLOAT;
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195 | maxy = MAXFLOAT;
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196 | }
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197 | else
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198 | return 0;
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199 | }
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200 | else {
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201 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
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202 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
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203 | if (t1 < t2) {
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204 | miny = t1;
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205 | maxy = t2;
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206 | }
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207 | else {
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208 | miny = t2;
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209 | maxy = t1;
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210 | }
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211 | if (maxy < 0.0)
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212 | return 0;
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213 | }
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214 |
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215 | if (fabs(ray.dir.z) < 0.001) {
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216 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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217 | minz = -MAXFLOAT;
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218 | maxz = MAXFLOAT;
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219 | }
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220 | else
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221 | return 0;
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222 | }
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223 | else {
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224 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
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225 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
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226 | if (t1 < t2) {
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227 | minz = t1;
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228 | maxz = t2;
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229 | }
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230 | else {
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231 | minz = t2;
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232 | maxz = t1;
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233 | }
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234 | if (maxz < 0.0)
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235 | return 0;
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236 | }
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237 |
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238 | *tmin = minx;
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239 | if (miny > *tmin)
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240 | *tmin = miny;
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241 | if (minz > *tmin)
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242 | *tmin = minz;
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243 |
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244 | *tmax = maxx;
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245 | if (maxy < *tmax)
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246 | *tmax = maxy;
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247 | if (maxz < *tmax)
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248 | *tmax = maxz;
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249 |
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250 | return 1; // yes, intersection was found
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251 | }
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252 | #else
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253 | // another variant of the same, with less variables
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254 | int
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255 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
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256 | float *tmin,
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257 | float *tmax) const
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258 | {
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259 | register float minx, maxx;
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260 | ray.ComputeInvertedDir();
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261 |
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262 | if (fabs(ray.dir.x) < 0.001) {
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263 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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264 | minx = -MAXFLOAT;
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265 | maxx = MAXFLOAT;
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266 | }
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267 | else
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268 | return 0;
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269 | }
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270 | else {
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271 | float t1 = (mMin.x - ray.loc.x) * ray.invDir.x;
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272 | float t2 = (mMax.x - ray.loc.x) * ray.invDir.x;
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273 | if (t1 < t2) {
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274 | minx = t1;
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275 | maxx = t2;
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276 | }
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277 | else {
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278 | minx = t2;
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279 | maxx = t1;
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280 | }
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281 | if (maxx < 0.0)
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282 | return 0;
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283 | }
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284 |
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285 | *tmin = minx;
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286 | *tmax = maxx;
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287 |
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288 | if (fabs(ray.dir.y) < 0.001) {
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289 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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290 | minx = -MAXFLOAT;
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291 | maxx = MAXFLOAT;
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292 | }
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293 | else
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294 | return 0;
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295 | }
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296 | else {
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297 | float t1 = (mMin.y - ray.loc.y) * ray.invDir.y;
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298 | float t2 = (mMax.y - ray.loc.y) * ray.invDir.y;
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299 | if (t1 < t2) {
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300 | minx = t1;
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301 | maxx = t2;
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302 | }
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303 | else {
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304 | minx = t2;
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305 | maxx = t1;
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306 | }
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307 | if (maxx < 0.0)
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308 | return 0;
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309 | }
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310 |
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311 | if (minx > *tmin)
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312 | *tmin = minx;
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313 | if (maxx < *tmax)
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314 | *tmax = maxx;
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315 |
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316 | if (fabs(ray.dir.z) < 0.001) {
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317 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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318 | minx = -MAXFLOAT;
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319 | maxx = MAXFLOAT;
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320 | }
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321 | else
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322 | return 0;
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323 | }
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324 | else {
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325 | float t1 = (mMin.z - ray.loc.z) * ray.invDir.z;
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326 | float t2 = (mMax.z - ray.loc.z) * ray.invDir.z;
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327 | if (t1 < t2) {
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328 | minx = t1;
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329 | maxx = t2;
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330 | }
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331 | else {
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332 | minx = t2;
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333 | maxx = t1;
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334 | }
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335 | if (maxx < 0.0)
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336 | return 0;
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337 | }
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338 |
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339 | if (minx > *tmin)
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340 | *tmin = minx;
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341 | if (maxx < *tmax)
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342 | *tmax = maxx;
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343 |
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344 | return 1; // yes, intersection was found
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345 | }
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346 | #endif
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347 |
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348 | // ComputeMinMaxT computes the minimum and maximum parameters
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349 | // of intersection with the ray; it returns 1 if the ray hits
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350 | // the bounding box and 0 if it does not.
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351 | int
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352 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax,
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353 | EFaces &entryFace, EFaces &exitFace) const
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354 | {
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355 | float minx, maxx, miny, maxy, minz, maxz;
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356 | int swapped[3];
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357 |
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358 | if (fabs(ray.dir.x) < 0.001) {
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359 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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360 | minx = -MAXFLOAT;
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361 | maxx = MAXFLOAT;
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362 | }
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363 | else
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364 | return 0;
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365 | }
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366 | else {
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367 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
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368 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
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369 | if (t1 < t2) {
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370 | minx = t1;
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371 | maxx = t2;
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372 | swapped[0] = 0;
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373 | }
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374 | else {
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375 | minx = t2;
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376 | maxx = t1;
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377 | swapped[0] = 1;
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378 | }
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379 | if (maxx < 0)
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380 | return 0;
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381 | }
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382 |
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383 | if (fabs(ray.dir.y) < 0.001) {
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384 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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385 | miny = -MAXFLOAT;
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386 | maxy = MAXFLOAT;
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387 | }
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388 | else
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389 | return 0;
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390 | }
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391 | else {
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392 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
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393 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
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394 | if (t1 < t2) {
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395 | miny = t1;
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396 | maxy = t2;
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397 | swapped[1] = 0;
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398 | }
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399 | else {
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400 | miny = t2;
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401 | maxy = t1;
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402 | swapped[1] = 1;
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403 | }
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404 | if (maxy < 0.0)
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405 | return 0;
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406 | }
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407 |
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408 | if (fabs(ray.dir.z) < 0.001) {
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409 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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410 | minz = -MAXFLOAT;
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411 | maxz = MAXFLOAT;
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412 | }
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413 | else
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414 | return 0;
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415 | }
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416 | else {
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417 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
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418 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
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419 | if (t1 < t2) {
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420 | minz = t1;
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421 | maxz = t2;
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422 | swapped[2] = 0;
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423 | }
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424 | else {
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425 | minz = t2;
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426 | maxz = t1;
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427 | swapped[2] = 1;
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428 | }
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429 | if (maxz < 0.0)
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430 | return 0;
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431 | }
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432 |
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433 | *tmin = minx;
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434 | entryFace = ID_Back;
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435 | if (miny > *tmin) {
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436 | *tmin = miny;
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437 | entryFace = ID_Left;
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438 | }
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439 | if (minz > *tmin) {
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440 | *tmin = minz;
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441 | entryFace = ID_Bottom;
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442 | }
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443 |
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444 | *tmax = maxx;
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445 | exitFace = ID_Back;
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446 | if (maxy < *tmax) {
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447 | *tmax = maxy;
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448 | exitFace = ID_Left;
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449 | }
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450 | if (maxz < *tmax) {
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451 | *tmax = maxz;
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452 | exitFace = ID_Bottom;
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453 | }
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454 |
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455 | if (swapped[entryFace])
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456 | entryFace = (EFaces)(entryFace + 3);
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457 |
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458 | if (!swapped[exitFace])
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459 | exitFace = (EFaces)(exitFace + 3);
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460 |
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461 | return 1; // yes, intersection was found
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462 | }
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463 |
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464 | void
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465 | AxisAlignedBox3::Describe(ostream &app, int ind) const
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466 | {
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467 | indent(app, ind);
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468 | app << "AxisAlignedBox3: min at(" << mMin << "), max at(" << mMax << ")\n";
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469 | }
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470 |
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471 | // computes the passing through parameters for case tmin<tmax and tmax>0
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472 | int
|
---|
473 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax) const
|
---|
474 | {
|
---|
475 | if (!ComputeMinMaxT(ray, tmin, tmax))
|
---|
476 | return 0;
|
---|
477 | if ( *tmax < *tmin)
|
---|
478 | return 0; // the ray passes outside the box
|
---|
479 |
|
---|
480 | if ( *tmax < 0.0)
|
---|
481 | return 0; // the intersection is not on the positive halfline
|
---|
482 |
|
---|
483 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
484 | }
|
---|
485 |
|
---|
486 | // computes the signed distances for case tmin<tmax and tmax>0
|
---|
487 | int
|
---|
488 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax,
|
---|
489 | EFaces &entryFace, EFaces &exitFace) const
|
---|
490 | {
|
---|
491 | if (!ComputeMinMaxT(ray, tmin, tmax, entryFace, exitFace))
|
---|
492 | return 0;
|
---|
493 | if ( *tmax < *tmin)
|
---|
494 | return 0; // the ray passes outside the box
|
---|
495 |
|
---|
496 | if ( *tmax < 0.0)
|
---|
497 | return 0; // the intersection is not on the positive halfline
|
---|
498 |
|
---|
499 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
500 | }
|
---|
501 |
|
---|
502 | #if 0
|
---|
503 | int
|
---|
504 | AxisAlignedBox3::IsInside(const Vector3 &point) const
|
---|
505 | {
|
---|
506 | return (point.x >= mMin.x) && (point.x <= mMax.x) &&
|
---|
507 | (point.y >= mMin.y) && (point.y <= mMax.y) &&
|
---|
508 | (point.z >= mMin.z) && (point.z <= mMax.z);
|
---|
509 | }
|
---|
510 | #else
|
---|
511 | int
|
---|
512 | AxisAlignedBox3::IsInside(const Vector3 &v) const
|
---|
513 | {
|
---|
514 | return ! (v.x < mMin.x ||
|
---|
515 | v.x > mMax.x ||
|
---|
516 | v.y < mMin.y ||
|
---|
517 | v.y > mMax.y ||
|
---|
518 | v.z < mMin.z ||
|
---|
519 | v.z > mMax.z);
|
---|
520 | }
|
---|
521 | #endif
|
---|
522 |
|
---|
523 | bool
|
---|
524 | AxisAlignedBox3::Includes(const AxisAlignedBox3 &b) const
|
---|
525 | {
|
---|
526 | return (b.mMin.x >= mMin.x &&
|
---|
527 | b.mMin.y >= mMin.y &&
|
---|
528 | b.mMin.z >= mMin.z &&
|
---|
529 | b.mMax.x <= mMax.x &&
|
---|
530 | b.mMax.y <= mMax.y &&
|
---|
531 | b.mMax.z <= mMax.z);
|
---|
532 |
|
---|
533 | }
|
---|
534 |
|
---|
535 |
|
---|
536 | // compute the coordinates of one vertex of the box
|
---|
537 | Vector3
|
---|
538 | AxisAlignedBox3::GetVertex(int xAxis, int yAxis, int zAxis) const
|
---|
539 | {
|
---|
540 | Vector3 p;
|
---|
541 | if (xAxis)
|
---|
542 | p.x = mMax.x;
|
---|
543 | else
|
---|
544 | p.x = mMin.x;
|
---|
545 |
|
---|
546 | if (yAxis)
|
---|
547 | p.y = mMax.y;
|
---|
548 | else
|
---|
549 | p.y = mMin.y;
|
---|
550 |
|
---|
551 | if (zAxis)
|
---|
552 | p.z = mMax.z;
|
---|
553 | else
|
---|
554 | p.z = mMin.z;
|
---|
555 | return p;
|
---|
556 | }
|
---|
557 |
|
---|
558 | // compute the vertex for number N = <0..7>, N = 4.x + 2.y + z, where
|
---|
559 | // x,y,z are either 0 or 1; (0 .. min coordinate, 1 .. max coordinate)
|
---|
560 | void
|
---|
561 | AxisAlignedBox3::GetVertex(const int N, Vector3 &vertex) const
|
---|
562 | {
|
---|
563 | switch (N) {
|
---|
564 | case 0: vertex = mMin; break;
|
---|
565 | case 1: vertex.SetValue(mMin.x, mMin.y, mMax.z); break;
|
---|
566 | case 2: vertex.SetValue(mMin.x, mMax.y, mMin.z); break;
|
---|
567 | case 3: vertex.SetValue(mMin.x, mMax.y, mMax.z); break;
|
---|
568 | case 4: vertex.SetValue(mMax.x, mMin.y, mMin.z); break;
|
---|
569 | case 5: vertex.SetValue(mMax.x, mMin.y, mMax.z); break;
|
---|
570 | case 6: vertex.SetValue(mMax.x, mMax.y, mMin.z); break;
|
---|
571 | case 7: vertex = mMax; break;
|
---|
572 | default: {
|
---|
573 | FATAL << "ERROR in AxisAlignedBox3::GetVertex N=" << N << "\n";
|
---|
574 | FATAL_ABORT;
|
---|
575 | }
|
---|
576 | }
|
---|
577 | }
|
---|
578 |
|
---|
579 | // Returns region 0 .. 26 ; R = 9*x + 3*y + z ; (x,y,z) \in {0,1,2}
|
---|
580 | int
|
---|
581 | AxisAlignedBox3::GetRegionID(const Vector3 &point) const
|
---|
582 | {
|
---|
583 | int ID = 0;
|
---|
584 |
|
---|
585 | if (point.z >= mMin.z) {
|
---|
586 | if (point.z <= mMax.z)
|
---|
587 | ID += 1; // inside the two boundary planes
|
---|
588 | else
|
---|
589 | ID += 2; // outside
|
---|
590 | }
|
---|
591 |
|
---|
592 | if (point.y >= mMin.y) {
|
---|
593 | if (point.y <= mMax.y)
|
---|
594 | ID += 3; // inside the two boundary planes
|
---|
595 | else
|
---|
596 | ID += 6; // outside
|
---|
597 | }
|
---|
598 |
|
---|
599 | if (point.x >= mMin.x) {
|
---|
600 | if (point.x <= mMax.x)
|
---|
601 | ID += 9; // inside the two boundary planes
|
---|
602 | else
|
---|
603 | ID += 18; // outside
|
---|
604 | }
|
---|
605 | return ID;
|
---|
606 | }
|
---|
607 |
|
---|
608 |
|
---|
609 |
|
---|
610 | // computes if a given box (smaller) lies at least in one
|
---|
611 | // projection whole in the box (larger) = this encompasses given
|
---|
612 | // ;-----;
|
---|
613 | // | ;-; |
|
---|
614 | // | '-' |
|
---|
615 | // '-----'
|
---|
616 | int
|
---|
617 | AxisAlignedBox3::IsPiercedByBox(const AxisAlignedBox3 &box, int &axis) const
|
---|
618 | {
|
---|
619 | // test on x-axis
|
---|
620 | if ( (mMax.x < box.mMin.x) ||
|
---|
621 | (mMin.x > box.mMax.x) )
|
---|
622 | return 0; // the boxes do not overlap at all at x-axis
|
---|
623 | if ( (box.mMin.y > mMin.y) &&
|
---|
624 | (box.mMax.y < mMax.y) &&
|
---|
625 | (box.mMin.z > mMin.z) &&
|
---|
626 | (box.mMax.z < mMax.z) ) {
|
---|
627 | axis = 0;
|
---|
628 | return 1; // the boxes overlap in x-axis
|
---|
629 | }
|
---|
630 | // test on y-axis
|
---|
631 | if ( (mMax.y < box.mMin.y) ||
|
---|
632 | (mMin.y > box.mMax.y) )
|
---|
633 | return 0; // the boxes do not overlap at all at y-axis
|
---|
634 | if ( (box.mMin.x > mMin.x) &&
|
---|
635 | (box.mMax.x < mMax.x) &&
|
---|
636 | (box.mMin.z > mMin.z) &&
|
---|
637 | (box.mMax.z < mMax.z) ) {
|
---|
638 | axis = 1;
|
---|
639 | return 1; // the boxes overlap in y-axis
|
---|
640 | }
|
---|
641 | // test on z-axis
|
---|
642 | if ( (mMax.z < box.mMin.z) ||
|
---|
643 | (mMin.z > box.mMax.z) )
|
---|
644 | return 0; // the boxes do not overlap at all at y-axis
|
---|
645 | if ( (box.mMin.x > mMin.x) &&
|
---|
646 | (box.mMax.x < mMax.x) &&
|
---|
647 | (box.mMin.y > mMin.y) &&
|
---|
648 | (box.mMax.y < mMax.y) ) {
|
---|
649 | axis = 2;
|
---|
650 | return 1; // the boxes overlap in z-axis
|
---|
651 | }
|
---|
652 | return 0;
|
---|
653 | }
|
---|
654 |
|
---|
655 | float
|
---|
656 | AxisAlignedBox3::SurfaceArea() const
|
---|
657 | {
|
---|
658 | Vector3 ext = mMax - mMin;
|
---|
659 | return 2.0 * (ext.x * ext.y +
|
---|
660 | ext.x * ext.z +
|
---|
661 | ext.y * ext.z);
|
---|
662 | }
|
---|
663 |
|
---|
664 | const int AxisAlignedBox3::bvertices[27][9] =
|
---|
665 | { // region number.. position
|
---|
666 | {5,1,3,2,6,4,-1,-1,-1}, // 0 .. x=0 y=0 z=0
|
---|
667 | {4,5,1,3,2,0,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
668 | {4,5,7,3,2,0,-1,-1,-1}, // 2 .. x=0 y=0 z=2
|
---|
669 |
|
---|
670 | {0,1,3,2,6,4,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
671 | {0,1,3,2,-1,-1,-1,-1,-1}, // 4 .. x=0 y=1 z=1
|
---|
672 | {1,5,7,3,2,0,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
673 |
|
---|
674 | {0,1,3,7,6,4,-1,-1,-1}, // 6 .. x=0 y=2 z=0
|
---|
675 | {0,1,3,7,6,2,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
676 | {1,5,7,6,2,0,-1,-1,-1}, // 8 .. x=0 y=2 z=2
|
---|
677 |
|
---|
678 | // the regions number <9,17>
|
---|
679 | {5,1,0,2,6,4,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
680 | {5,1,0,4,-1,-1,-1,-1,-1}, // 10 .. x=1 y=0 z=1
|
---|
681 | {7,3,1,0,4,5,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
682 |
|
---|
683 | {4,0,2,6,-1,-1,-1,-1,-1}, // 12 .. x=1 y=1 z=0
|
---|
684 | {0,2,3,1,5,4,6,7,-1}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
685 | {1,5,7,3,-1,-1,-1,-1,-1}, // 14 .. x=1 y=1 z=2
|
---|
686 |
|
---|
687 | {4,0,2,3,7,6,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
688 | {6,2,3,7,-1,-1,-1,-1,-1}, // 16 .. x=1 y=2 z=1
|
---|
689 | {1,5,7,6,2,3,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
690 |
|
---|
691 | // the regions number <18,26>
|
---|
692 | {1,0,2,6,7,5,-1,-1,-1}, // 18 .. x=2 y=0 z=0
|
---|
693 | {1,0,4,6,7,5,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
694 | {0,4,6,7,3,1,-1,-1,-1}, // 20 .. x=2 y=0 z=2
|
---|
695 |
|
---|
696 | {4,0,2,6,7,5,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
697 | {5,4,6,7,-1,-1,-1,-1,-1}, // 22 .. x=2 y=1 z=1
|
---|
698 | {5,4,6,7,3,1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
699 |
|
---|
700 | {4,0,2,3,7,5,-1,-1,-1}, // 24 .. x=2 y=2 z=0
|
---|
701 | {5,4,6,2,3,7,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
702 | {5,4,6,2,3,1,-1,-1,-1}, // 26 .. x=2 y=2 z=2
|
---|
703 | };
|
---|
704 |
|
---|
705 | // the visibility of boundary faces from a given region
|
---|
706 | // one to three triples: (axis, min_vertex, max_vertex), axis==-1(terminator)
|
---|
707 | const int AxisAlignedBox3::bfaces[27][10] =
|
---|
708 | { // region number .. position
|
---|
709 | {0,0,3,1,0,5,2,0,6,-1}, // 0 .. x=0 y=0 z=0
|
---|
710 | {0,0,3,1,0,5,-1,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
711 | {0,0,3,1,0,5,2,1,7,-1}, // 2 .. x=0 y=0 z=2
|
---|
712 |
|
---|
713 | {0,0,3,2,0,6,-1,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
714 | {0,0,3,-1,-1,-1,-1,-1,-1,-1},// 4 .. x=0 y=1 z=1
|
---|
715 | {0,0,3,2,1,7,-1,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
716 |
|
---|
717 | {0,0,3,1,2,7,2,0,6,-1}, // 6 .. x=0 y=2 z=0
|
---|
718 | {0,0,3,1,2,7,-1,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
719 | {0,0,3,1,2,7,2,1,7,-1}, // 8 .. x=0 y=2 z=2
|
---|
720 |
|
---|
721 | // the regions number <9,17>
|
---|
722 | {1,0,5,2,0,6,-1,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
723 | {1,0,5,-1,-1,-1,-1,-1,-1,-1},// 10 .. x=1 y=0 z=1
|
---|
724 | {1,0,5,2,1,7,-1,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
725 |
|
---|
726 | {2,0,6,-1,-1,-1,-1,-1,-1,-1},// 12 .. x=1 y=1 z=0
|
---|
727 | {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1},// 13 .. x=1 y=1 z=1 .. inside the box
|
---|
728 | {2,1,7,-1,-1,-1,-1,-1,-1,-1},// 14 .. x=1 y=1 z=2
|
---|
729 |
|
---|
730 | {1,2,7,2,0,6,-1,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
731 | {1,2,7,-1,-1,-1,-1,-1,-1,-1},// 16 .. x=1 y=2 z=1
|
---|
732 | {1,2,7,2,1,7,-1,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
733 |
|
---|
734 | // the region number <18,26>
|
---|
735 | {0,4,7,1,0,5,2,0,6,-1}, // 18 .. x=2 y=0 z=0
|
---|
736 | {0,4,7,1,0,5,-1,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
737 | {0,4,7,1,0,5,2,1,7,-1}, // 20 .. x=2 y=0 z=2
|
---|
738 |
|
---|
739 | {0,4,7,2,0,6,-1,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
740 | {0,4,7,-1,-1,-1,-1,-1,-1,-1},// 22 .. x=2 y=1 z=1
|
---|
741 | {0,4,7,2,1,7,-1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
742 |
|
---|
743 | {0,4,7,1,2,7,2,0,6,-1}, // 24 .. x=2 y=2 z=0
|
---|
744 | {0,4,7,1,2,7,-1,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
745 | {0,4,7,1,2,7,2,1,7,-1}, // 26 .. x=2 y=2 z=2
|
---|
746 | };
|
---|
747 |
|
---|
748 | // the correct corners indexing from entry face to exit face
|
---|
749 | // first index determines entry face, second index exit face, and
|
---|
750 | // the two numbers (indx, inc) determines: ind = the index on the exit
|
---|
751 | // face, when starting from the vertex 0 on entry face, 'inc' is
|
---|
752 | // the increment when we go on entry face in order 0,1,2,3 to create
|
---|
753 | // convex shaft with the rectangle on exit face. That is, inc = -1 or 1.
|
---|
754 | const int AxisAlignedBox3::pairFaceRects[6][6][2] = {
|
---|
755 | { // entry face = 0
|
---|
756 | {-1,0}, // exit face 0 .. no meaning
|
---|
757 | {0,-1}, // 1
|
---|
758 | {0,-1}, // 2
|
---|
759 | {0,1}, // 3 .. opposite face
|
---|
760 | {3,1}, // 4
|
---|
761 | {1,1} // 5
|
---|
762 | },
|
---|
763 | { // entry face = 1
|
---|
764 | {0,-1}, // exit face 0
|
---|
765 | {-1,0}, // 1 .. no meaning
|
---|
766 | {0,-1}, // 2
|
---|
767 | {1,1}, // 3
|
---|
768 | {0,1}, // 4 .. opposite face
|
---|
769 | {3,1} // 5
|
---|
770 | },
|
---|
771 | { // entry face = 2
|
---|
772 | {0,-1}, // 0
|
---|
773 | {0,-1}, // 1
|
---|
774 | {-1,0}, // 2 .. no meaning
|
---|
775 | {3,1}, // 3
|
---|
776 | {1,1}, // 4
|
---|
777 | {0,1} // 5 .. opposite face
|
---|
778 | },
|
---|
779 | { // entry face = 3
|
---|
780 | {0,1}, // 0 .. opposite face
|
---|
781 | {3,-1}, // 1
|
---|
782 | {1,1}, // 2
|
---|
783 | {-1,0}, // 3 .. no meaning
|
---|
784 | {0,-1}, // 4
|
---|
785 | {0,-1} // 5
|
---|
786 | },
|
---|
787 | { // entry face = 4
|
---|
788 | {1,1}, // 0
|
---|
789 | {0,1}, // 1 .. opposite face
|
---|
790 | {3,1}, // 2
|
---|
791 | {0,-1}, // 3
|
---|
792 | {-1,0}, // 4 .. no meaning
|
---|
793 | {0,-1} // 5
|
---|
794 | },
|
---|
795 | { // entry face = 5
|
---|
796 | {3,-1}, // 0
|
---|
797 | {1,1}, // 1
|
---|
798 | {0,1}, // 2 .. opposite face
|
---|
799 | {0,-1}, // 3
|
---|
800 | {0,-1}, // 4
|
---|
801 | {-1,0} // 5 .. no meaning
|
---|
802 | }
|
---|
803 | };
|
---|
804 |
|
---|
805 |
|
---|
806 | // ------------------------------------------------------------
|
---|
807 | // The vertices that form CLOSEST points with respect to the region
|
---|
808 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
809 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
810 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
811 | // at most 8 points, at least 1 point.
|
---|
812 | // The table includes the closest 1/2/4/8 points, followed possibly
|
---|
813 | // by the set of coordinates that should be used for testing for
|
---|
814 | // the proximity queries. The coordinates to be tested are described by
|
---|
815 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
816 | // when a=1, we want to test max vector of the box
|
---|
817 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
818 | // The sequence is ended by 15, number -1 is used as the separator
|
---|
819 | // between the vertices and coordinates.
|
---|
820 | const int
|
---|
821 | AxisAlignedBox3::cvertices[27][9] =
|
---|
822 | { // region number.. position
|
---|
823 | {0,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D one vertex
|
---|
824 | {0,1,-1,0,0,0,1,15,15}, // 1 .. x=0 y=0 z=1 D two vertices foll. by 2
|
---|
825 | {1,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D one vertex
|
---|
826 |
|
---|
827 | {0,2,-1,0,0,0,2,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
828 | {0,1,3,2,-1,0,0,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
829 | {1,3,-1,0,0,1,2,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
830 |
|
---|
831 | {2,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
832 | {2,3,-1,0,0,1,1,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
833 | {3,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
834 |
|
---|
835 | // the regions number <9,17>
|
---|
836 | {0,4,-1,0,1,0,2,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
837 | {5,1,0,4,-1,0,1,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
838 | {1,5,-1,0,1,1,2,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
839 |
|
---|
840 | {4,0,2,6,-1,0,2,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
841 | {0,2,3,1,5,4,6,7,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
842 | {1,5,7,3,-1,1,2,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
843 |
|
---|
844 | {6,2,-1,0,2,1,1,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
845 | {6,2,3,7,-1,1,1,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
846 | {3,7,-1,1,1,1,2,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
847 |
|
---|
848 | // the regions number <18,26>
|
---|
849 | {4,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
850 | {4,5,-1,0,1,1,0,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
851 | {5,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
852 |
|
---|
853 | {4,6,-1,0,2,1,0,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
854 | {5,4,6,7,-1,1,0,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
855 | {7,5,-1,1,0,1,2,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
856 |
|
---|
857 | {6,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
858 | {6,7,-1,1,0,1,1,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
859 | {7,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
860 | };
|
---|
861 |
|
---|
862 | // Table for Sphere-AABB intersection based on the region knowledge
|
---|
863 | // Similar array to previous cvertices, but we omit the surfaces
|
---|
864 | // which are not necessary for testing. First are vertices,
|
---|
865 | // they are finished with -1. Second, there are indexes in
|
---|
866 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
867 | // when a=1, we want to test max vector of the box
|
---|
868 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
869 | //
|
---|
870 | // So either we check the vertices or only the distance in specified
|
---|
871 | // dimensions. There are at all four possible cases:
|
---|
872 | //
|
---|
873 | // 1) we check one vertex - then sequence start with non-negative index
|
---|
874 | // and is finished with 15
|
---|
875 | // 2) we check two coordinates of min/max vector describe by the pair
|
---|
876 | // (a,b) .. a=min/max(0/1) b=x/y/z (0/1/2), sequence starts with 8
|
---|
877 | // and finishes with 15
|
---|
878 | // 3) we check only one coordinate of min/max, as for 2), sequence start
|
---|
879 | // with 9 and ends with 15
|
---|
880 | // 4) Position 13 - sphere is inside the box, intersection always exist
|
---|
881 | // the sequence start with 15 .. no further testing is necessary
|
---|
882 | // in this case
|
---|
883 | const int
|
---|
884 | AxisAlignedBox3::csvertices[27][6] =
|
---|
885 | { // region number.. position
|
---|
886 | {0,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D vertex only
|
---|
887 | {8,0,0,0,1,15}, // 1 .. x=0 y=0 z=1 D two coords.
|
---|
888 | {1,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D vertex only
|
---|
889 |
|
---|
890 | {8,0,0,0,2,15}, // 3 .. x=0 y=1 z=0 D two coords
|
---|
891 | {9,0,0,15,15,15}, // 4 .. x=0 y=1 z=1 D one coord
|
---|
892 | {8,0,0,1,2,15}, // 5 .. x=0 y=1 z=2 D two coords.
|
---|
893 |
|
---|
894 | {2,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D one vertex
|
---|
895 | {8,0,0,1,1,15}, // 7 .. x=0 y=2 z=1 D two coords
|
---|
896 | {3,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D one vertex
|
---|
897 |
|
---|
898 | // the regions number <9,17>
|
---|
899 | {8,0,1,0,2,15}, // 9 .. x=1 y=0 z=0 D two coords
|
---|
900 | {9,0,1,15,15,15}, // 10 .. x=1 y=0 z=1 D one coord
|
---|
901 | {8,0,1,1,2,15}, // 11 .. x=1 y=0 z=2 D two coords
|
---|
902 |
|
---|
903 | {9,0,2,15,15,15}, // 12 .. x=1 y=1 z=0 D one coord
|
---|
904 | {15,15,15,15,15,15}, // 13 .. x=1 y=1 z=1 inside the box, special case/value
|
---|
905 | {9,1,2,15,15,15}, // 14 .. x=1 y=1 z=2 D one corrd
|
---|
906 |
|
---|
907 | {8,0,2,1,1,15}, // 15 .. x=1 y=2 z=0 D two coords
|
---|
908 | {9,1,1,15,15}, // 16 .. x=1 y=2 z=1 D one coord
|
---|
909 | {8,1,1,1,2,15}, // 17 .. x=1 y=2 z=2 D two coords
|
---|
910 |
|
---|
911 | // the regions number <18,26>
|
---|
912 | {4,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D one vertex
|
---|
913 | {8,0,1,1,0,15}, // 19 .. x=2 y=0 z=1 D two coords
|
---|
914 | {5,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D one vertex
|
---|
915 |
|
---|
916 | {8,0,2,1,0,15}, // 21 .. x=2 y=1 z=0 D two coords
|
---|
917 | {9,1,0,15,15,15}, // 22 .. x=2 y=1 z=1 D one coord
|
---|
918 | {8,1,0,1,2,15}, // 23 .. x=2 y=1 z=2 D two coords
|
---|
919 |
|
---|
920 | {6,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D one vertex
|
---|
921 | {8,1,0,1,1,15}, // 25 .. x=2 y=2 z=1 D two coords
|
---|
922 | {7,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D one vertex
|
---|
923 | };
|
---|
924 |
|
---|
925 |
|
---|
926 | // The vertices that form all FARTHEST points with respect to the region
|
---|
927 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
928 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
929 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
930 | // at most 8 points, at least 1 point.
|
---|
931 | // For testing, if the AABB is whole in the sphere, it is enough
|
---|
932 | // to test only vertices, either 1,2,4, or 8.
|
---|
933 | const int
|
---|
934 | AxisAlignedBox3::fvertices[27][9] =
|
---|
935 | { // region number.. position
|
---|
936 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D
|
---|
937 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D
|
---|
938 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D
|
---|
939 |
|
---|
940 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
941 | {4,5,7,6,15,15,15,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
942 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
943 |
|
---|
944 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
945 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
946 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
947 |
|
---|
948 | // the regions number <9,17>
|
---|
949 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
950 | {7,3,2,6,15,15,15,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
951 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
952 |
|
---|
953 | {5,1,3,7,15,15,15,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
954 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
955 | {0,4,6,2,15,15,15,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
956 |
|
---|
957 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
958 | {4,0,1,5,15,15,15,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
959 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
960 |
|
---|
961 | // the regions number <18,26>
|
---|
962 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
963 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
964 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
965 |
|
---|
966 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
967 | {1,0,2,3,15,15,15,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
968 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
969 |
|
---|
970 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
971 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
972 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
973 | };
|
---|
974 |
|
---|
975 | // Similar table as above, farthest points, but only the ones
|
---|
976 | // necessary for testing the intersection problem. If we do
|
---|
977 | // not consider the case 13, center of the sphere is inside the
|
---|
978 | // box, then we can always test at most 2 box vertices to say whether
|
---|
979 | // the whole box is inside the sphere.
|
---|
980 | // The number of vertices is minimized using some assumptions
|
---|
981 | // about the ortogonality of vertices and sphere properties.
|
---|
982 | const int
|
---|
983 | AxisAlignedBox3::fsvertices[27][9] =
|
---|
984 | { // region number.. position
|
---|
985 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D 1 vertex
|
---|
986 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D 2 vertices
|
---|
987 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D 1 vertex
|
---|
988 |
|
---|
989 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D 2 vertices
|
---|
990 | {4,7,15,5,6,15,15,15,15}, // 4 .. x=0 y=1 z=1 D 4/2 vertices
|
---|
991 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D 2 vertices
|
---|
992 |
|
---|
993 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D 1 vertex
|
---|
994 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D 2 vertices
|
---|
995 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D 1 vertex
|
---|
996 |
|
---|
997 | // the regions number <9,17>
|
---|
998 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D 2 vertices
|
---|
999 | {7,2,15,3,6,15,15,15,15}, // 10 .. x=1 y=0 z=1 D 4/2 vertices
|
---|
1000 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D 2 vertices
|
---|
1001 |
|
---|
1002 | {5,3,15,1,7,15,15,15,15}, // 12 .. x=1 y=1 z=0 D 4/2 vertices
|
---|
1003 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
1004 | {0,6,15,4,2,15,15,15,15}, // 14 .. x=1 y=1 z=2 D 4/2 vertices
|
---|
1005 |
|
---|
1006 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D 2 vertices
|
---|
1007 | {4,1,15,0,5,15,15,15,15}, // 16 .. x=1 y=2 z=1 D 4/2 vertices
|
---|
1008 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D 2 vertices
|
---|
1009 |
|
---|
1010 | // the regions number <18,26>
|
---|
1011 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D 1 vertex
|
---|
1012 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D 2 vertices
|
---|
1013 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D 1 vertex
|
---|
1014 |
|
---|
1015 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D 2 vertices
|
---|
1016 | {1,2,15,0,3,15,15,15,15}, // 22 .. x=2 y=1 z=1 D 4/2 vertices
|
---|
1017 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D 2 vertices
|
---|
1018 |
|
---|
1019 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D 1 vertex
|
---|
1020 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D 2 vertices
|
---|
1021 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D 1 vertex
|
---|
1022 | };
|
---|
1023 |
|
---|
1024 | // The fast computation of arctangent .. the maximal error is less
|
---|
1025 | // than 4.1 degrees, according to Graphics GEMSII, 1991, pages 389--391
|
---|
1026 | // Ron Capelli: "Fast approximation to the arctangent"
|
---|
1027 | float
|
---|
1028 | atan22(const float& y)
|
---|
1029 | {
|
---|
1030 | const float x = 1.0;
|
---|
1031 | const float c = (float)(M_PI * 0.25);
|
---|
1032 |
|
---|
1033 | if (y < 0.0) {
|
---|
1034 | if (y < -1.0)
|
---|
1035 | return c * (-2.0 + x / y); // for angle in <-PI/2, -PI/4)
|
---|
1036 | else
|
---|
1037 | return c * (y / x); // for angle in <-PI/4 , 0>
|
---|
1038 | }
|
---|
1039 | else {
|
---|
1040 | if (y > 1.0)
|
---|
1041 | return c * (2.0 - x / y); // for angle in <PI/4, PI/2>
|
---|
1042 | else
|
---|
1043 | return c * (y / x); // for angle in <0, PI/2>
|
---|
1044 | }
|
---|
1045 | }
|
---|
1046 |
|
---|
1047 |
|
---|
1048 | float
|
---|
1049 | AxisAlignedBox3::ProjectToSphereSA(const Vector3 &viewpoint, int *tcase) const
|
---|
1050 | {
|
---|
1051 | int id = GetRegionID(viewpoint);
|
---|
1052 | *tcase = id;
|
---|
1053 |
|
---|
1054 | // spherical projection .. SA represents solid angle
|
---|
1055 | if (id == 13) // .. inside the box
|
---|
1056 | return (float)(4.0*M_PI); // the whole sphere
|
---|
1057 | float SA = 0.0; // inital value
|
---|
1058 |
|
---|
1059 | int i = 0; // the pointer in the array of vertices
|
---|
1060 | while (bfaces[id][i] >= 0) {
|
---|
1061 | int axisO = bfaces[id][i++];
|
---|
1062 | int minvIdx = bfaces[id][i++];
|
---|
1063 | int maxvIdx = bfaces[id][i++];
|
---|
1064 | Vector3 vmin, vmax;
|
---|
1065 | GetVertex(minvIdx, vmin);
|
---|
1066 | GetVertex(maxvIdx, vmax);
|
---|
1067 | float h = fabs(vmin[axisO] - viewpoint[axisO]);
|
---|
1068 | int axis = (axisO + 1) % 3; // next axis
|
---|
1069 | float a = (vmin[axis] - viewpoint[axis]) / h; // minimum for v-range
|
---|
1070 | float b = (vmax[axis] - viewpoint[axis]) / h; // maximum for v-range
|
---|
1071 | //if (a > b) {
|
---|
1072 | // FATAL << "ProjectToSphereSA::Error a > b\n";
|
---|
1073 | // FATAL_ABORT;
|
---|
1074 | //}
|
---|
1075 | //if (vmin[axisO] != vmax[axisO]) {
|
---|
1076 | // FATAL << "ProjectToSphereSA::Error a-axis != b-axis\n";
|
---|
1077 | // FATAL_ABORT;
|
---|
1078 | //}
|
---|
1079 | axis = (axisO + 2) % 3; // next second axis
|
---|
1080 | float c = (vmin[axis] - viewpoint[axis]) / h; // minimum for u-range
|
---|
1081 | float d = (vmax[axis] - viewpoint[axis]) / h; // maximum for u-range
|
---|
1082 | //if (c > d) {
|
---|
1083 | // FATAL << "ProjectToSphereSA::Error c > d\n";
|
---|
1084 | // FATAL_ABORT;
|
---|
1085 | //}
|
---|
1086 | SA +=atan22(d*b/sqrt(b*b + d*d + 1.0)) - atan22(b*c/sqrt(b*b + c*c + 1.0))
|
---|
1087 | - atan22(d*a/sqrt(a*a + d*d + 1.0)) + atan22(a*c/sqrt(a*a + c*c + 1.0));
|
---|
1088 | }
|
---|
1089 |
|
---|
1090 | #if 0
|
---|
1091 | if ((SA > 2.0*M_PI) ||
|
---|
1092 | (SA < 0.0)) {
|
---|
1093 | FATAL << "The solid angle has strange value: ";
|
---|
1094 | FATAL << "SA = "<< SA << endl;
|
---|
1095 | FATAL_ABORT;
|
---|
1096 | }
|
---|
1097 | #endif
|
---|
1098 |
|
---|
1099 | return SA;
|
---|
1100 | }
|
---|
1101 |
|
---|
1102 | // Projects the box to a plane given a normal vector only and
|
---|
1103 | // computes the surface area of the projected silhouette
|
---|
1104 | // no clipping of the box is performed.
|
---|
1105 | float
|
---|
1106 | AxisAlignedBox3::ProjectToPlaneSA(const Vector3 &normal) const
|
---|
1107 | {
|
---|
1108 | Vector3 size = Size();
|
---|
1109 |
|
---|
1110 | // the surface area of the box to a yz-plane - perpendicular to x-axis
|
---|
1111 | float sax = size.y * size.z;
|
---|
1112 |
|
---|
1113 | // the surface area of the box to a zx-plane - perpendicular to y-axis
|
---|
1114 | float say = size.z * size.x;
|
---|
1115 |
|
---|
1116 | // the surface area of the box to a xy-plane - perpendicular to z-axis
|
---|
1117 | float saz = size.x * size.y;
|
---|
1118 |
|
---|
1119 | return sax * fabs(normal.x) + say * fabs(normal.y) + saz * fabs(normal.z);
|
---|
1120 | }
|
---|
1121 |
|
---|
1122 |
|
---|
1123 |
|
---|
1124 | // This definition allows to be a point when answering true
|
---|
1125 | bool
|
---|
1126 | AxisAlignedBox3::IsCorrectAndNotPoint() const
|
---|
1127 | {
|
---|
1128 | if ( (mMin.x > mMax.x) ||
|
---|
1129 | (mMin.y > mMax.y) ||
|
---|
1130 | (mMin.z > mMax.z) )
|
---|
1131 | return false; // box is not formed
|
---|
1132 |
|
---|
1133 | if ( (mMin.x == mMax.x) &&
|
---|
1134 | (mMin.y == mMax.y) &&
|
---|
1135 | (mMin.z == mMax.z) )
|
---|
1136 | return false; // degenerates to a point
|
---|
1137 |
|
---|
1138 | return true;
|
---|
1139 | }
|
---|
1140 |
|
---|
1141 | // This definition allows to be a point when answering true
|
---|
1142 | bool
|
---|
1143 | AxisAlignedBox3::IsPoint() const
|
---|
1144 | {
|
---|
1145 | if ( (mMin.x == mMax.x) &&
|
---|
1146 | (mMin.y == mMax.y) &&
|
---|
1147 | (mMin.z == mMax.z) )
|
---|
1148 | return true; // degenerates to a point
|
---|
1149 |
|
---|
1150 | return false;
|
---|
1151 | }
|
---|
1152 |
|
---|
1153 | // This definition requires shape of non-zero volume
|
---|
1154 | bool
|
---|
1155 | AxisAlignedBox3::IsSingularOrIncorrect() const
|
---|
1156 | {
|
---|
1157 | if ( (mMin.x >= mMax.x) ||
|
---|
1158 | (mMin.y >= mMax.y) ||
|
---|
1159 | (mMin.z >= mMax.z) )
|
---|
1160 | return true; // box is not formed
|
---|
1161 |
|
---|
1162 | return false; // has non-zero volume
|
---|
1163 | }
|
---|
1164 |
|
---|
1165 | // returns true, when the sphere specified by the origin and radius
|
---|
1166 | // fully contains the box
|
---|
1167 | bool
|
---|
1168 | AxisAlignedBox3::IsFullyContainedInSphere(const Vector3 ¢er, float rad) const
|
---|
1169 | {
|
---|
1170 | int region = GetRegionID(center);
|
---|
1171 | float rad2 = rad*rad;
|
---|
1172 |
|
---|
1173 | // vertex of the box
|
---|
1174 | Vector3 vertex;
|
---|
1175 |
|
---|
1176 | int i = 0;
|
---|
1177 | for (i = 0 ; ; i++) {
|
---|
1178 | int a = fsvertices[region][i];
|
---|
1179 | if (a == 15)
|
---|
1180 | return true; // if was not false untill now, it must be contained
|
---|
1181 |
|
---|
1182 | assert( (a>=0) && (a<8) );
|
---|
1183 |
|
---|
1184 | // normal vertex
|
---|
1185 | GetVertex(a, vertex);
|
---|
1186 |
|
---|
1187 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
1188 | return false;
|
---|
1189 | } // for
|
---|
1190 |
|
---|
1191 | }
|
---|
1192 |
|
---|
1193 | // returns true, when the volume of the sphere and volume of the
|
---|
1194 | // axis aligned box has no intersection
|
---|
1195 | bool
|
---|
1196 | AxisAlignedBox3::HasNoIntersectionWithSphere(const Vector3 ¢er, float rad) const
|
---|
1197 | {
|
---|
1198 | int region = GetRegionID(center);
|
---|
1199 | float rad2 = rad*rad;
|
---|
1200 |
|
---|
1201 | // vertex of the box
|
---|
1202 | Vector3 vertex;
|
---|
1203 |
|
---|
1204 | switch (csvertices[region][0]) {
|
---|
1205 | case 8: {
|
---|
1206 | // test two coordinates described within the field
|
---|
1207 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
1208 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
1209 | dist *= dist;
|
---|
1210 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
1211 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
1212 | dist += (dist2 * dist2);
|
---|
1213 | if (dist > rad2)
|
---|
1214 | return true; // no intersection is possible
|
---|
1215 | }
|
---|
1216 | case 9: {
|
---|
1217 | // test one coordinate described within the field
|
---|
1218 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
1219 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
1220 | if (dist > rad)
|
---|
1221 | return true; // no intersection is possible
|
---|
1222 | }
|
---|
1223 | case 15:
|
---|
1224 | return false; // box and sphere surely has intersection
|
---|
1225 | default: {
|
---|
1226 | // test using normal vertices
|
---|
1227 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
1228 |
|
---|
1229 | // normal vertex
|
---|
1230 | GetVertex(csvertices[region][0], vertex);
|
---|
1231 |
|
---|
1232 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
1233 | return true; // no intersectino is possible
|
---|
1234 | }
|
---|
1235 | } // switch
|
---|
1236 |
|
---|
1237 | return false; // partial or full containtment
|
---|
1238 | }
|
---|
1239 |
|
---|
1240 | #if 0
|
---|
1241 | // Given the sphere, determine the mutual position between the
|
---|
1242 | // sphere and box
|
---|
1243 |
|
---|
1244 | // SOME BUG IS INSIDE !!!! V.H. 25/4/2001
|
---|
1245 | int
|
---|
1246 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
1247 | {
|
---|
1248 | int region = GetRegionID(center);
|
---|
1249 | float rad2 = rad*rad;
|
---|
1250 |
|
---|
1251 | // vertex of the box
|
---|
1252 | Vector3 vertex;
|
---|
1253 |
|
---|
1254 | // first testing for full containtment - whether sphere fully
|
---|
1255 | // contains the box
|
---|
1256 | int countInside = 0; // how many points were found inside
|
---|
1257 |
|
---|
1258 | int i = 0;
|
---|
1259 | for (i = 0 ; ; i++) {
|
---|
1260 | int a = fsvertices[region][i];
|
---|
1261 | if (a == 15)
|
---|
1262 | return 1; // the sphere fully contain the box
|
---|
1263 |
|
---|
1264 | assert( (a>=0) && (a<8) );
|
---|
1265 |
|
---|
1266 | // normal vertex
|
---|
1267 | GetVertex(a, vertex);
|
---|
1268 |
|
---|
1269 | if (SqrMagnitude(vertex - center) <= rad2)
|
---|
1270 | countInside++; // the number of vertices inside the sphere
|
---|
1271 | else {
|
---|
1272 | if (countInside)
|
---|
1273 | return 0; // partiall overlap has been found
|
---|
1274 | // the sphere does not fully contain the box .. only way to break
|
---|
1275 | // this loop and go for other testing
|
---|
1276 | break;
|
---|
1277 | }
|
---|
1278 | } // for
|
---|
1279 |
|
---|
1280 | // now only box and sphere can partially overlap or no intersection
|
---|
1281 | switch (csvertices[region][0]) {
|
---|
1282 | case 8: {
|
---|
1283 | // test two coordinates described within the field
|
---|
1284 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
1285 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
1286 | dist *= dist;
|
---|
1287 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
1288 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
1289 | dist += (dist2 * dist2);
|
---|
1290 | if (dist > rad2 )
|
---|
1291 | return -1; // no intersection is possible
|
---|
1292 | }
|
---|
1293 | case 9: {
|
---|
1294 | // test one coordinate described within the field
|
---|
1295 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
1296 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
1297 | if (dist > rad)
|
---|
1298 | return -1; // no intersection is possible
|
---|
1299 | }
|
---|
1300 | case 15:
|
---|
1301 | return 0 ; // partial overlap is now guaranteed
|
---|
1302 | default: {
|
---|
1303 | // test using normal vertices
|
---|
1304 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
1305 |
|
---|
1306 | // normal vertex
|
---|
1307 | GetVertex(csvertices[region][0], vertex);
|
---|
1308 |
|
---|
1309 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
1310 | return -1; // no intersection is possible
|
---|
1311 | }
|
---|
1312 | } // switch
|
---|
1313 |
|
---|
1314 | return 0; // partial intersection is guaranteed
|
---|
1315 | }
|
---|
1316 | #else
|
---|
1317 |
|
---|
1318 | // Some maybe smarter version, extendible easily to d-dimensional
|
---|
1319 | // space!
|
---|
1320 | // Given a sphere described by the center and radius,
|
---|
1321 | // the fullowing function returns:
|
---|
1322 | // -1 ... the sphere and the box are completely separate
|
---|
1323 | // 0 ... the sphere and the box only partially overlap
|
---|
1324 | // 1 ... the sphere contains fully the box
|
---|
1325 | // Note: the case when box fully contains the sphere is not reported
|
---|
1326 | // since it was not required.
|
---|
1327 | int
|
---|
1328 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
1329 | {
|
---|
1330 | //#define SPEED_UP
|
---|
1331 |
|
---|
1332 | #ifndef SPEED_UP
|
---|
1333 | // slow version, instructively written
|
---|
1334 | #if 0
|
---|
1335 | // does it make sense to test
|
---|
1336 | // checking the sides of the box for possible non-intersection
|
---|
1337 | if ( ((center.x + rad) < mMin.x) ||
|
---|
1338 | ((center.x - rad) > mMax.x) ||
|
---|
1339 | ((center.y + rad) < mMin.y) ||
|
---|
1340 | ((center.y - rad) > mMax.y) ||
|
---|
1341 | ((center.z + rad) < mMin.z) ||
|
---|
1342 | ((center.z - rad) > mMax.z) ) {
|
---|
1343 | // cout << "r ";
|
---|
1344 | return -1; // no overlap is possible
|
---|
1345 | }
|
---|
1346 | #endif
|
---|
1347 |
|
---|
1348 | // someoverlap is possible, check the distance of vertices
|
---|
1349 | rad = rad*rad;
|
---|
1350 | float sumMin = 0;
|
---|
1351 | // Try to minimize the function of a distance
|
---|
1352 | // from the sphere center
|
---|
1353 |
|
---|
1354 | // for x-axis
|
---|
1355 | float minSqrX = sqr(mMin.x - center.x);
|
---|
1356 | float maxSqrX = sqr(mMax.x - center.x);
|
---|
1357 | if (center.x < mMin.x)
|
---|
1358 | sumMin = minSqrX;
|
---|
1359 | else
|
---|
1360 | if (center.x > mMax.x)
|
---|
1361 | sumMin = maxSqrX;
|
---|
1362 |
|
---|
1363 | // for y-axis
|
---|
1364 | float minSqrY = sqr(mMin.y - center.y);
|
---|
1365 | float maxSqrY = sqr(mMax.y - center.y);
|
---|
1366 | if (center.y < mMin.y)
|
---|
1367 | sumMin += minSqrY;
|
---|
1368 | else
|
---|
1369 | if (center.y > mMax.y)
|
---|
1370 | sumMin += maxSqrY;
|
---|
1371 |
|
---|
1372 | // for z-axis
|
---|
1373 | float minSqrZ = sqr(mMin.z - center.z);
|
---|
1374 | float maxSqrZ = sqr(mMax.z - center.z);
|
---|
1375 | if (center.z < mMin.z)
|
---|
1376 | sumMin += minSqrZ;
|
---|
1377 | else
|
---|
1378 | if (center.z > mMax.z)
|
---|
1379 | sumMin += maxSqrZ;
|
---|
1380 |
|
---|
1381 | if (sumMin > rad)
|
---|
1382 | return -1; // no intersection between sphere and box
|
---|
1383 |
|
---|
1384 | // try to find out the maximum distance between the
|
---|
1385 | // sphere center and vertices
|
---|
1386 | float sumMax = 0;
|
---|
1387 |
|
---|
1388 | if (minSqrX > maxSqrX)
|
---|
1389 | sumMax = minSqrX;
|
---|
1390 | else
|
---|
1391 | sumMax = maxSqrX;
|
---|
1392 |
|
---|
1393 | if (minSqrY > maxSqrY)
|
---|
1394 | sumMax += minSqrY;
|
---|
1395 | else
|
---|
1396 | sumMax += maxSqrY;
|
---|
1397 |
|
---|
1398 | if (minSqrZ > maxSqrZ)
|
---|
1399 | sumMax += minSqrZ;
|
---|
1400 | else
|
---|
1401 | sumMax += maxSqrZ;
|
---|
1402 |
|
---|
1403 | // sumMin < rad
|
---|
1404 | if (sumMax < rad)
|
---|
1405 | return 1; // the sphere contains the box completely
|
---|
1406 |
|
---|
1407 | // partial intersection, part of the box is outside the sphere
|
---|
1408 | return 0;
|
---|
1409 | #else
|
---|
1410 |
|
---|
1411 | // Optimized version of the test
|
---|
1412 |
|
---|
1413 | #ifndef __VECTOR_HACK
|
---|
1414 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
1415 | #endif
|
---|
1416 |
|
---|
1417 | // some overlap is possible, check the distance of vertices
|
---|
1418 | rad = rad*rad;
|
---|
1419 | float sumMin = 0;
|
---|
1420 | float sumMax = 0;
|
---|
1421 | // Try to minimize the function of a distance
|
---|
1422 | // from the sphere center
|
---|
1423 |
|
---|
1424 | const float *minp = &(min[0]);
|
---|
1425 | const float *maxp = &(max[0]);
|
---|
1426 | const float *pcenter = &(center[0]);
|
---|
1427 |
|
---|
1428 | // for x-axis
|
---|
1429 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
1430 | float minsqr = sqr(*minp - *pcenter);
|
---|
1431 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
1432 | if (*pcenter < *minp)
|
---|
1433 | sumMin += minsqr;
|
---|
1434 | else
|
---|
1435 | if (*pcenter > *maxp)
|
---|
1436 | sumMin += maxsqr;
|
---|
1437 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
1438 | }
|
---|
1439 |
|
---|
1440 | if (sumMin > rad)
|
---|
1441 | return -1; // no intersection between sphere and box
|
---|
1442 |
|
---|
1443 | // sumMin < rad
|
---|
1444 | if (sumMax < rad)
|
---|
1445 | return 1; // the sphere contains the box completely
|
---|
1446 |
|
---|
1447 | // partial intersection, part of the box is outside the sphere
|
---|
1448 | return 0;
|
---|
1449 | #endif
|
---|
1450 | }
|
---|
1451 | #endif
|
---|
1452 |
|
---|
1453 | // Given the cube describe by the center and the half-sie,
|
---|
1454 | // determine the mutual position between the cube and the box
|
---|
1455 | int
|
---|
1456 | AxisAlignedBox3::MutualPositionWithCube(const Vector3 ¢er, float radius) const
|
---|
1457 | {
|
---|
1458 | // the cube is described by the center and the distance to the any face
|
---|
1459 | // along the axes
|
---|
1460 |
|
---|
1461 | // Note on efficiency!
|
---|
1462 | // Can be quite optimized using tables, but I do not have time
|
---|
1463 | // V.H. 18/11/2001
|
---|
1464 |
|
---|
1465 | AxisAlignedBox3 a =
|
---|
1466 | AxisAlignedBox3(Vector3(center.x - radius, center.y - radius, center.z - radius),
|
---|
1467 | Vector3(center.x + radius, center.y + radius, center.z + radius));
|
---|
1468 |
|
---|
1469 | if (a.Includes(*this))
|
---|
1470 | return 1; // cube contains the box
|
---|
1471 |
|
---|
1472 | if (OverlapS(a,*this))
|
---|
1473 | return 0; // cube partially overlap the box
|
---|
1474 |
|
---|
1475 | return -1; // completely separate
|
---|
1476 | }
|
---|
1477 |
|
---|
1478 | void
|
---|
1479 | AxisAlignedBox3::GetSqrDistances(const Vector3 &point,
|
---|
1480 | float &minDistance,
|
---|
1481 | float &maxDistance
|
---|
1482 | ) const
|
---|
1483 | {
|
---|
1484 |
|
---|
1485 |
|
---|
1486 | #ifndef __VECTOR_HACK
|
---|
1487 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
1488 | #endif
|
---|
1489 |
|
---|
1490 | // some overlap is possible, check the distance of vertices
|
---|
1491 | float sumMin = 0;
|
---|
1492 | float sumMax = 0;
|
---|
1493 |
|
---|
1494 | // Try to minimize the function of a distance
|
---|
1495 | // from the sphere center
|
---|
1496 |
|
---|
1497 | const float *minp = &(mMin[0]);
|
---|
1498 | const float *maxp = &(mMax[0]);
|
---|
1499 | const float *pcenter = &(point[0]);
|
---|
1500 |
|
---|
1501 | // for x-axis
|
---|
1502 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
1503 | float minsqr = sqr(*minp - *pcenter);
|
---|
1504 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
1505 | if (*pcenter < *minp)
|
---|
1506 | sumMin += minsqr;
|
---|
1507 | else
|
---|
1508 | if (*pcenter > *maxp)
|
---|
1509 | sumMin += maxsqr;
|
---|
1510 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
1511 | }
|
---|
1512 |
|
---|
1513 | minDistance = sumMin;
|
---|
1514 | maxDistance = sumMax;
|
---|
1515 | }
|
---|
1516 |
|
---|
1517 |
|
---|
1518 | int
|
---|
1519 | AxisAlignedBox3::Side(const Plane3 &plane) const
|
---|
1520 | {
|
---|
1521 | Vector3 v;
|
---|
1522 | int i, m=3, M=-3, s;
|
---|
1523 |
|
---|
1524 | for (i=0;i<8;i++) {
|
---|
1525 | GetVertex(i, v);
|
---|
1526 | if((s = plane.Side(v)) < m)
|
---|
1527 | m=s;
|
---|
1528 | if(s > M)
|
---|
1529 | M=s;
|
---|
1530 | if (m && m==-M)
|
---|
1531 | return 0;
|
---|
1532 | }
|
---|
1533 |
|
---|
1534 | return (m == M) ? m : m + M;
|
---|
1535 | }
|
---|
1536 |
|
---|
1537 | int
|
---|
1538 | AxisAlignedBox3::GetFaceVisibilityMask(const Rectangle3 &rectangle) const
|
---|
1539 | {
|
---|
1540 | int mask = 0;
|
---|
1541 | for (int i=0; i < 4; i++)
|
---|
1542 | mask |= GetFaceVisibilityMask(rectangle.mVertices[i]);
|
---|
1543 | return mask;
|
---|
1544 | }
|
---|
1545 |
|
---|
1546 | int
|
---|
1547 | AxisAlignedBox3::GetFaceVisibilityMask(const Vector3 &position) const {
|
---|
1548 |
|
---|
1549 | // assume that we are not inside the box
|
---|
1550 | int c=0;
|
---|
1551 |
|
---|
1552 | if (position.x<(mMin.x-Limits::Small))
|
---|
1553 | c|=1;
|
---|
1554 | else
|
---|
1555 | if (position.x>(mMax.x+Limits::Small))
|
---|
1556 | c|=2;
|
---|
1557 |
|
---|
1558 | if (position.y<(mMin.y-Limits::Small))
|
---|
1559 | c|=4;
|
---|
1560 | else
|
---|
1561 | if (position.y>(mMax.y+Limits::Small))
|
---|
1562 | c|=8;
|
---|
1563 |
|
---|
1564 | if (position.z<(mMin.z-Limits::Small))
|
---|
1565 | c|=16;
|
---|
1566 | else
|
---|
1567 | if (position.z>(mMax.z+Limits::Small))
|
---|
1568 | c|=32;
|
---|
1569 |
|
---|
1570 | return c;
|
---|
1571 | }
|
---|
1572 |
|
---|
1573 |
|
---|
1574 | Rectangle3
|
---|
1575 | AxisAlignedBox3::GetFace(const int face) const
|
---|
1576 | {
|
---|
1577 | Vector3 v[4];
|
---|
1578 | switch (face) {
|
---|
1579 |
|
---|
1580 | case 0:
|
---|
1581 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
1582 | v[2].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
1583 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
1584 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
1585 | break;
|
---|
1586 |
|
---|
1587 | case 1:
|
---|
1588 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
1589 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
1590 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
1591 | v[3].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
1592 | break;
|
---|
1593 |
|
---|
1594 | case 2:
|
---|
1595 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
1596 | v[2].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
1597 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
1598 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
1599 | break;
|
---|
1600 |
|
---|
1601 | case 3:
|
---|
1602 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
1603 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
1604 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
1605 | v[3].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
1606 | break;
|
---|
1607 |
|
---|
1608 | case 4:
|
---|
1609 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
1610 | v[2].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
1611 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
1612 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
1613 | break;
|
---|
1614 |
|
---|
1615 | case 5:
|
---|
1616 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
1617 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
1618 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
1619 | v[3].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
1620 | break;
|
---|
1621 | }
|
---|
1622 |
|
---|
1623 | return Rectangle3(v[0], v[1], v[2], v[3]);
|
---|
1624 | }
|
---|