[162] | 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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[295] | 8 | #include "Polygon3.h"
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[162] | 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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[295] | 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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[162] | 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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[312] | 130 | // returns the vertex indices in the range <0..7>, v = 4.x + 2.y + z, where
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| 131 | // x,y,z are either 0 or 1; (0 .. min coordinate, 1 .. max coordinate)
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[162] | 132 | void
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[312] | 133 | AxisAlignedBox3::GetEdge(const int edge, int &aIdx, int &bIdx) const
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| 134 | {
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| 135 | switch(edge) {
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| 136 | case 0: aIdx = 0; bIdx = 1; break;
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| 137 | case 1: aIdx = 0; bIdx = 2; break;
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| 138 | case 2: aIdx = 0; bIdx = 4; break;
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| 139 | case 3: aIdx = 7; bIdx = 6; break;
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| 140 | case 4: aIdx = 7; bIdx = 5; break;
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| 141 | case 5: aIdx = 7; bIdx = 3; break;
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| 142 | case 6: aIdx = 1; bIdx = 3; break;
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| 143 | case 7: aIdx = 1; bIdx = 5; break;
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| 144 | case 8: aIdx = 2; bIdx = 3; break;
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| 145 | case 9: aIdx = 2; bIdx = 6; break;
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| 146 | case 10: aIdx = 4; bIdx = 6; break;
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| 147 | case 11: aIdx = 4; bIdx = 5; break;
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| 148 | }
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| 149 | }
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| 150 |
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| 151 | void
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[162] | 152 | AxisAlignedBox3::Include(const int &axis, const float &newBound)
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| 153 | {
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| 154 | switch (axis) {
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| 155 | case 0: { // x-axis
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| 156 | if (mMin.x > newBound)
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| 157 | mMin.x = newBound;
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| 158 | if (mMax.x < newBound)
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| 159 | mMax.x = newBound;
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| 160 | break;
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| 161 | }
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| 162 | case 1: { // y-axis
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| 163 | if (mMin.y > newBound)
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| 164 | mMin.y = newBound;
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| 165 | if (mMax.y < newBound)
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| 166 | mMax.y = newBound;
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| 167 | break;
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| 168 | }
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| 169 | case 2: { // z-axis
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| 170 | if (mMin.z > newBound)
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| 171 | mMin.z = newBound;
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| 172 | if (mMax.z < newBound)
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| 173 | mMax.z = newBound;
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| 174 | break;
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| 175 | }
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| 176 | }
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| 177 | }
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| 178 |
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| 179 | #if 0
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| 180 | // ComputeMinMaxT computes the minimum and maximum signed distances
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| 181 | // of intersection with the ray; it returns 1 if the ray hits
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| 182 | // the bounding box and 0 if it does not.
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| 183 | int
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| 184 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
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| 185 | float *tmin,
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| 186 | float *tmax) const
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| 187 | {
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| 188 | float minx, maxx, miny, maxy, minz, maxz;
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| 189 |
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| 190 | if (fabs(ray.dir.x) < 0.001) {
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| 191 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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| 192 | minx = -MAXFLOAT;
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| 193 | maxx = MAXFLOAT;
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| 194 | }
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| 195 | else
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| 196 | return 0;
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| 197 | }
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| 198 | else {
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| 199 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
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| 200 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
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| 201 | if (t1 < t2) {
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| 202 | minx = t1;
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| 203 | maxx = t2;
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| 204 | }
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| 205 | else {
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| 206 | minx = t2;
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| 207 | maxx = t1;
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| 208 | }
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| 209 | if (maxx < 0)
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| 210 | return 0;
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| 211 | }
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| 212 |
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| 213 | if (fabs(ray.dir.y) < 0.001) {
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| 214 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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| 215 | miny = -MAXFLOAT;
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| 216 | maxy = MAXFLOAT;
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| 217 | }
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| 218 | else
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| 219 | return 0;
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| 220 | }
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| 221 | else {
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| 222 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
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| 223 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
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| 224 | if (t1 < t2) {
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| 225 | miny = t1;
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| 226 | maxy = t2;
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| 227 | }
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| 228 | else {
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| 229 | miny = t2;
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| 230 | maxy = t1;
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| 231 | }
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| 232 | if (maxy < 0.0)
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| 233 | return 0;
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| 234 | }
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| 235 |
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| 236 | if (fabs(ray.dir.z) < 0.001) {
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| 237 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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| 238 | minz = -MAXFLOAT;
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| 239 | maxz = MAXFLOAT;
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| 240 | }
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| 241 | else
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| 242 | return 0;
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| 243 | }
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| 244 | else {
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| 245 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
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| 246 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
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| 247 | if (t1 < t2) {
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| 248 | minz = t1;
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| 249 | maxz = t2;
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| 250 | }
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| 251 | else {
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| 252 | minz = t2;
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| 253 | maxz = t1;
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| 254 | }
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| 255 | if (maxz < 0.0)
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| 256 | return 0;
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| 257 | }
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| 258 |
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| 259 | *tmin = minx;
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| 260 | if (miny > *tmin)
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| 261 | *tmin = miny;
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| 262 | if (minz > *tmin)
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| 263 | *tmin = minz;
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| 264 |
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| 265 | *tmax = maxx;
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| 266 | if (maxy < *tmax)
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| 267 | *tmax = maxy;
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| 268 | if (maxz < *tmax)
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| 269 | *tmax = maxz;
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| 270 |
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| 271 | return 1; // yes, intersection was found
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| 272 | }
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| 273 | #else
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| 274 | // another variant of the same, with less variables
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| 275 | int
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| 276 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
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| 277 | float *tmin,
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| 278 | float *tmax) const
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| 279 | {
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| 280 | register float minx, maxx;
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| 281 | ray.ComputeInvertedDir();
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| 282 |
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| 283 | if (fabs(ray.dir.x) < 0.001) {
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| 284 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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| 285 | minx = -MAXFLOAT;
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| 286 | maxx = MAXFLOAT;
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| 287 | }
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| 288 | else
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| 289 | return 0;
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| 290 | }
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| 291 | else {
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| 292 | float t1 = (mMin.x - ray.loc.x) * ray.invDir.x;
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| 293 | float t2 = (mMax.x - ray.loc.x) * ray.invDir.x;
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| 294 | if (t1 < t2) {
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| 295 | minx = t1;
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| 296 | maxx = t2;
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| 297 | }
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| 298 | else {
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| 299 | minx = t2;
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| 300 | maxx = t1;
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| 301 | }
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| 302 | if (maxx < 0.0)
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| 303 | return 0;
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| 304 | }
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| 305 |
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| 306 | *tmin = minx;
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| 307 | *tmax = maxx;
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| 308 |
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| 309 | if (fabs(ray.dir.y) < 0.001) {
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| 310 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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| 311 | minx = -MAXFLOAT;
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| 312 | maxx = MAXFLOAT;
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| 313 | }
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| 314 | else
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| 315 | return 0;
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| 316 | }
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| 317 | else {
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| 318 | float t1 = (mMin.y - ray.loc.y) * ray.invDir.y;
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| 319 | float t2 = (mMax.y - ray.loc.y) * ray.invDir.y;
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| 320 | if (t1 < t2) {
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| 321 | minx = t1;
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| 322 | maxx = t2;
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| 323 | }
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| 324 | else {
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| 325 | minx = t2;
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| 326 | maxx = t1;
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| 327 | }
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| 328 | if (maxx < 0.0)
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| 329 | return 0;
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| 330 | }
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| 331 |
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| 332 | if (minx > *tmin)
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| 333 | *tmin = minx;
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| 334 | if (maxx < *tmax)
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| 335 | *tmax = maxx;
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| 336 |
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| 337 | if (fabs(ray.dir.z) < 0.001) {
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| 338 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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| 339 | minx = -MAXFLOAT;
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| 340 | maxx = MAXFLOAT;
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| 341 | }
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| 342 | else
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| 343 | return 0;
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| 344 | }
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| 345 | else {
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| 346 | float t1 = (mMin.z - ray.loc.z) * ray.invDir.z;
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| 347 | float t2 = (mMax.z - ray.loc.z) * ray.invDir.z;
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| 348 | if (t1 < t2) {
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| 349 | minx = t1;
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| 350 | maxx = t2;
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| 351 | }
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| 352 | else {
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| 353 | minx = t2;
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| 354 | maxx = t1;
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| 355 | }
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| 356 | if (maxx < 0.0)
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| 357 | return 0;
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| 358 | }
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| 359 |
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| 360 | if (minx > *tmin)
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| 361 | *tmin = minx;
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| 362 | if (maxx < *tmax)
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| 363 | *tmax = maxx;
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| 364 |
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| 365 | return 1; // yes, intersection was found
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| 366 | }
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| 367 | #endif
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| 368 |
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| 369 | // ComputeMinMaxT computes the minimum and maximum parameters
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| 370 | // of intersection with the ray; it returns 1 if the ray hits
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| 371 | // the bounding box and 0 if it does not.
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| 372 | int
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| 373 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax,
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| 374 | EFaces &entryFace, EFaces &exitFace) const
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| 375 | {
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| 376 | float minx, maxx, miny, maxy, minz, maxz;
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| 377 | int swapped[3];
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| 378 |
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| 379 | if (fabs(ray.dir.x) < 0.001) {
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| 380 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
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| 381 | minx = -MAXFLOAT;
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| 382 | maxx = MAXFLOAT;
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| 383 | }
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| 384 | else
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| 385 | return 0;
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| 386 | }
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| 387 | else {
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| 388 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
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| 389 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
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| 390 | if (t1 < t2) {
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| 391 | minx = t1;
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| 392 | maxx = t2;
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| 393 | swapped[0] = 0;
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| 394 | }
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| 395 | else {
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| 396 | minx = t2;
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| 397 | maxx = t1;
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| 398 | swapped[0] = 1;
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| 399 | }
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| 400 | if (maxx < 0)
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| 401 | return 0;
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| 402 | }
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| 403 |
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| 404 | if (fabs(ray.dir.y) < 0.001) {
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| 405 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
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| 406 | miny = -MAXFLOAT;
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| 407 | maxy = MAXFLOAT;
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| 408 | }
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| 409 | else
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| 410 | return 0;
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| 411 | }
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| 412 | else {
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| 413 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
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| 414 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
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| 415 | if (t1 < t2) {
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| 416 | miny = t1;
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| 417 | maxy = t2;
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| 418 | swapped[1] = 0;
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| 419 | }
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| 420 | else {
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| 421 | miny = t2;
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| 422 | maxy = t1;
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| 423 | swapped[1] = 1;
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| 424 | }
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| 425 | if (maxy < 0.0)
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| 426 | return 0;
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| 427 | }
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| 428 |
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| 429 | if (fabs(ray.dir.z) < 0.001) {
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| 430 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
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| 431 | minz = -MAXFLOAT;
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| 432 | maxz = MAXFLOAT;
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| 433 | }
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| 434 | else
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| 435 | return 0;
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| 436 | }
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| 437 | else {
|
---|
| 438 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
|
---|
| 439 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
|
---|
| 440 | if (t1 < t2) {
|
---|
| 441 | minz = t1;
|
---|
| 442 | maxz = t2;
|
---|
| 443 | swapped[2] = 0;
|
---|
| 444 | }
|
---|
| 445 | else {
|
---|
| 446 | minz = t2;
|
---|
| 447 | maxz = t1;
|
---|
| 448 | swapped[2] = 1;
|
---|
| 449 | }
|
---|
| 450 | if (maxz < 0.0)
|
---|
| 451 | return 0;
|
---|
| 452 | }
|
---|
| 453 |
|
---|
| 454 | *tmin = minx;
|
---|
| 455 | entryFace = ID_Back;
|
---|
| 456 | if (miny > *tmin) {
|
---|
| 457 | *tmin = miny;
|
---|
| 458 | entryFace = ID_Left;
|
---|
| 459 | }
|
---|
| 460 | if (minz > *tmin) {
|
---|
| 461 | *tmin = minz;
|
---|
| 462 | entryFace = ID_Bottom;
|
---|
| 463 | }
|
---|
| 464 |
|
---|
| 465 | *tmax = maxx;
|
---|
| 466 | exitFace = ID_Back;
|
---|
| 467 | if (maxy < *tmax) {
|
---|
| 468 | *tmax = maxy;
|
---|
| 469 | exitFace = ID_Left;
|
---|
| 470 | }
|
---|
| 471 | if (maxz < *tmax) {
|
---|
| 472 | *tmax = maxz;
|
---|
| 473 | exitFace = ID_Bottom;
|
---|
| 474 | }
|
---|
| 475 |
|
---|
| 476 | if (swapped[entryFace])
|
---|
| 477 | entryFace = (EFaces)(entryFace + 3);
|
---|
| 478 |
|
---|
| 479 | if (!swapped[exitFace])
|
---|
| 480 | exitFace = (EFaces)(exitFace + 3);
|
---|
| 481 |
|
---|
| 482 | return 1; // yes, intersection was found
|
---|
| 483 | }
|
---|
| 484 |
|
---|
| 485 | void
|
---|
| 486 | AxisAlignedBox3::Describe(ostream &app, int ind) const
|
---|
| 487 | {
|
---|
| 488 | indent(app, ind);
|
---|
| 489 | app << "AxisAlignedBox3: min at(" << mMin << "), max at(" << mMax << ")\n";
|
---|
| 490 | }
|
---|
| 491 |
|
---|
| 492 | // computes the passing through parameters for case tmin<tmax and tmax>0
|
---|
| 493 | int
|
---|
| 494 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax) const
|
---|
| 495 | {
|
---|
| 496 | if (!ComputeMinMaxT(ray, tmin, tmax))
|
---|
| 497 | return 0;
|
---|
| 498 | if ( *tmax < *tmin)
|
---|
| 499 | return 0; // the ray passes outside the box
|
---|
| 500 |
|
---|
| 501 | if ( *tmax < 0.0)
|
---|
| 502 | return 0; // the intersection is not on the positive halfline
|
---|
| 503 |
|
---|
| 504 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
| 505 | }
|
---|
| 506 |
|
---|
| 507 | // computes the signed distances for case tmin<tmax and tmax>0
|
---|
| 508 | int
|
---|
| 509 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax,
|
---|
| 510 | EFaces &entryFace, EFaces &exitFace) const
|
---|
| 511 | {
|
---|
| 512 | if (!ComputeMinMaxT(ray, tmin, tmax, entryFace, exitFace))
|
---|
| 513 | return 0;
|
---|
| 514 | if ( *tmax < *tmin)
|
---|
| 515 | return 0; // the ray passes outside the box
|
---|
| 516 |
|
---|
| 517 | if ( *tmax < 0.0)
|
---|
| 518 | return 0; // the intersection is not on the positive halfline
|
---|
| 519 |
|
---|
| 520 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
| 521 | }
|
---|
| 522 |
|
---|
| 523 | #if 0
|
---|
| 524 | int
|
---|
| 525 | AxisAlignedBox3::IsInside(const Vector3 &point) const
|
---|
| 526 | {
|
---|
| 527 | return (point.x >= mMin.x) && (point.x <= mMax.x) &&
|
---|
| 528 | (point.y >= mMin.y) && (point.y <= mMax.y) &&
|
---|
| 529 | (point.z >= mMin.z) && (point.z <= mMax.z);
|
---|
| 530 | }
|
---|
| 531 | #else
|
---|
| 532 | int
|
---|
| 533 | AxisAlignedBox3::IsInside(const Vector3 &v) const
|
---|
| 534 | {
|
---|
| 535 | return ! (v.x < mMin.x ||
|
---|
| 536 | v.x > mMax.x ||
|
---|
| 537 | v.y < mMin.y ||
|
---|
| 538 | v.y > mMax.y ||
|
---|
| 539 | v.z < mMin.z ||
|
---|
| 540 | v.z > mMax.z);
|
---|
| 541 | }
|
---|
| 542 | #endif
|
---|
| 543 |
|
---|
| 544 | bool
|
---|
| 545 | AxisAlignedBox3::Includes(const AxisAlignedBox3 &b) const
|
---|
| 546 | {
|
---|
| 547 | return (b.mMin.x >= mMin.x &&
|
---|
| 548 | b.mMin.y >= mMin.y &&
|
---|
| 549 | b.mMin.z >= mMin.z &&
|
---|
| 550 | b.mMax.x <= mMax.x &&
|
---|
| 551 | b.mMax.y <= mMax.y &&
|
---|
| 552 | b.mMax.z <= mMax.z);
|
---|
| 553 |
|
---|
| 554 | }
|
---|
| 555 |
|
---|
| 556 |
|
---|
| 557 | // compute the coordinates of one vertex of the box
|
---|
| 558 | Vector3
|
---|
| 559 | AxisAlignedBox3::GetVertex(int xAxis, int yAxis, int zAxis) const
|
---|
| 560 | {
|
---|
| 561 | Vector3 p;
|
---|
| 562 | if (xAxis)
|
---|
| 563 | p.x = mMax.x;
|
---|
| 564 | else
|
---|
| 565 | p.x = mMin.x;
|
---|
| 566 |
|
---|
| 567 | if (yAxis)
|
---|
| 568 | p.y = mMax.y;
|
---|
| 569 | else
|
---|
| 570 | p.y = mMin.y;
|
---|
| 571 |
|
---|
| 572 | if (zAxis)
|
---|
| 573 | p.z = mMax.z;
|
---|
| 574 | else
|
---|
| 575 | p.z = mMin.z;
|
---|
| 576 | return p;
|
---|
| 577 | }
|
---|
| 578 |
|
---|
| 579 | // compute the vertex for number N = <0..7>, N = 4.x + 2.y + z, where
|
---|
| 580 | // x,y,z are either 0 or 1; (0 .. min coordinate, 1 .. max coordinate)
|
---|
| 581 | void
|
---|
[191] | 582 | AxisAlignedBox3::GetVertex(const int N, Vector3 &vertex) const
|
---|
[162] | 583 | {
|
---|
| 584 | switch (N) {
|
---|
| 585 | case 0: vertex = mMin; break;
|
---|
| 586 | case 1: vertex.SetValue(mMin.x, mMin.y, mMax.z); break;
|
---|
| 587 | case 2: vertex.SetValue(mMin.x, mMax.y, mMin.z); break;
|
---|
| 588 | case 3: vertex.SetValue(mMin.x, mMax.y, mMax.z); break;
|
---|
| 589 | case 4: vertex.SetValue(mMax.x, mMin.y, mMin.z); break;
|
---|
| 590 | case 5: vertex.SetValue(mMax.x, mMin.y, mMax.z); break;
|
---|
| 591 | case 6: vertex.SetValue(mMax.x, mMax.y, mMin.z); break;
|
---|
| 592 | case 7: vertex = mMax; break;
|
---|
| 593 | default: {
|
---|
| 594 | FATAL << "ERROR in AxisAlignedBox3::GetVertex N=" << N << "\n";
|
---|
| 595 | FATAL_ABORT;
|
---|
| 596 | }
|
---|
| 597 | }
|
---|
| 598 | }
|
---|
| 599 |
|
---|
| 600 | // Returns region 0 .. 26 ; R = 9*x + 3*y + z ; (x,y,z) \in {0,1,2}
|
---|
| 601 | int
|
---|
| 602 | AxisAlignedBox3::GetRegionID(const Vector3 &point) const
|
---|
| 603 | {
|
---|
| 604 | int ID = 0;
|
---|
| 605 |
|
---|
| 606 | if (point.z >= mMin.z) {
|
---|
| 607 | if (point.z <= mMax.z)
|
---|
| 608 | ID += 1; // inside the two boundary planes
|
---|
| 609 | else
|
---|
| 610 | ID += 2; // outside
|
---|
| 611 | }
|
---|
| 612 |
|
---|
| 613 | if (point.y >= mMin.y) {
|
---|
| 614 | if (point.y <= mMax.y)
|
---|
| 615 | ID += 3; // inside the two boundary planes
|
---|
| 616 | else
|
---|
| 617 | ID += 6; // outside
|
---|
| 618 | }
|
---|
| 619 |
|
---|
| 620 | if (point.x >= mMin.x) {
|
---|
| 621 | if (point.x <= mMax.x)
|
---|
| 622 | ID += 9; // inside the two boundary planes
|
---|
| 623 | else
|
---|
| 624 | ID += 18; // outside
|
---|
| 625 | }
|
---|
| 626 | return ID;
|
---|
| 627 | }
|
---|
| 628 |
|
---|
| 629 |
|
---|
| 630 |
|
---|
| 631 | // computes if a given box (smaller) lies at least in one
|
---|
| 632 | // projection whole in the box (larger) = this encompasses given
|
---|
| 633 | // ;-----;
|
---|
| 634 | // | ;-; |
|
---|
| 635 | // | '-' |
|
---|
| 636 | // '-----'
|
---|
| 637 | int
|
---|
| 638 | AxisAlignedBox3::IsPiercedByBox(const AxisAlignedBox3 &box, int &axis) const
|
---|
| 639 | {
|
---|
| 640 | // test on x-axis
|
---|
| 641 | if ( (mMax.x < box.mMin.x) ||
|
---|
| 642 | (mMin.x > box.mMax.x) )
|
---|
| 643 | return 0; // the boxes do not overlap at all at x-axis
|
---|
| 644 | if ( (box.mMin.y > mMin.y) &&
|
---|
| 645 | (box.mMax.y < mMax.y) &&
|
---|
| 646 | (box.mMin.z > mMin.z) &&
|
---|
| 647 | (box.mMax.z < mMax.z) ) {
|
---|
| 648 | axis = 0;
|
---|
| 649 | return 1; // the boxes overlap in x-axis
|
---|
| 650 | }
|
---|
| 651 | // test on y-axis
|
---|
| 652 | if ( (mMax.y < box.mMin.y) ||
|
---|
| 653 | (mMin.y > box.mMax.y) )
|
---|
| 654 | return 0; // the boxes do not overlap at all at y-axis
|
---|
| 655 | if ( (box.mMin.x > mMin.x) &&
|
---|
| 656 | (box.mMax.x < mMax.x) &&
|
---|
| 657 | (box.mMin.z > mMin.z) &&
|
---|
| 658 | (box.mMax.z < mMax.z) ) {
|
---|
| 659 | axis = 1;
|
---|
| 660 | return 1; // the boxes overlap in y-axis
|
---|
| 661 | }
|
---|
| 662 | // test on z-axis
|
---|
| 663 | if ( (mMax.z < box.mMin.z) ||
|
---|
| 664 | (mMin.z > box.mMax.z) )
|
---|
| 665 | return 0; // the boxes do not overlap at all at y-axis
|
---|
| 666 | if ( (box.mMin.x > mMin.x) &&
|
---|
| 667 | (box.mMax.x < mMax.x) &&
|
---|
| 668 | (box.mMin.y > mMin.y) &&
|
---|
| 669 | (box.mMax.y < mMax.y) ) {
|
---|
| 670 | axis = 2;
|
---|
| 671 | return 1; // the boxes overlap in z-axis
|
---|
| 672 | }
|
---|
| 673 | return 0;
|
---|
| 674 | }
|
---|
| 675 |
|
---|
| 676 | float
|
---|
| 677 | AxisAlignedBox3::SurfaceArea() const
|
---|
| 678 | {
|
---|
| 679 | Vector3 ext = mMax - mMin;
|
---|
[302] | 680 |
|
---|
[162] | 681 | return 2.0 * (ext.x * ext.y +
|
---|
| 682 | ext.x * ext.z +
|
---|
| 683 | ext.y * ext.z);
|
---|
| 684 | }
|
---|
| 685 |
|
---|
| 686 | const int AxisAlignedBox3::bvertices[27][9] =
|
---|
| 687 | { // region number.. position
|
---|
| 688 | {5,1,3,2,6,4,-1,-1,-1}, // 0 .. x=0 y=0 z=0
|
---|
| 689 | {4,5,1,3,2,0,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
| 690 | {4,5,7,3,2,0,-1,-1,-1}, // 2 .. x=0 y=0 z=2
|
---|
| 691 |
|
---|
| 692 | {0,1,3,2,6,4,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
| 693 | {0,1,3,2,-1,-1,-1,-1,-1}, // 4 .. x=0 y=1 z=1
|
---|
| 694 | {1,5,7,3,2,0,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
| 695 |
|
---|
| 696 | {0,1,3,7,6,4,-1,-1,-1}, // 6 .. x=0 y=2 z=0
|
---|
| 697 | {0,1,3,7,6,2,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
| 698 | {1,5,7,6,2,0,-1,-1,-1}, // 8 .. x=0 y=2 z=2
|
---|
| 699 |
|
---|
| 700 | // the regions number <9,17>
|
---|
| 701 | {5,1,0,2,6,4,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
| 702 | {5,1,0,4,-1,-1,-1,-1,-1}, // 10 .. x=1 y=0 z=1
|
---|
| 703 | {7,3,1,0,4,5,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
| 704 |
|
---|
| 705 | {4,0,2,6,-1,-1,-1,-1,-1}, // 12 .. x=1 y=1 z=0
|
---|
| 706 | {0,2,3,1,5,4,6,7,-1}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 707 | {1,5,7,3,-1,-1,-1,-1,-1}, // 14 .. x=1 y=1 z=2
|
---|
| 708 |
|
---|
| 709 | {4,0,2,3,7,6,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
| 710 | {6,2,3,7,-1,-1,-1,-1,-1}, // 16 .. x=1 y=2 z=1
|
---|
| 711 | {1,5,7,6,2,3,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
| 712 |
|
---|
| 713 | // the regions number <18,26>
|
---|
| 714 | {1,0,2,6,7,5,-1,-1,-1}, // 18 .. x=2 y=0 z=0
|
---|
| 715 | {1,0,4,6,7,5,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
| 716 | {0,4,6,7,3,1,-1,-1,-1}, // 20 .. x=2 y=0 z=2
|
---|
| 717 |
|
---|
| 718 | {4,0,2,6,7,5,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
| 719 | {5,4,6,7,-1,-1,-1,-1,-1}, // 22 .. x=2 y=1 z=1
|
---|
| 720 | {5,4,6,7,3,1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
| 721 |
|
---|
| 722 | {4,0,2,3,7,5,-1,-1,-1}, // 24 .. x=2 y=2 z=0
|
---|
| 723 | {5,4,6,2,3,7,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
| 724 | {5,4,6,2,3,1,-1,-1,-1}, // 26 .. x=2 y=2 z=2
|
---|
| 725 | };
|
---|
| 726 |
|
---|
| 727 | // the visibility of boundary faces from a given region
|
---|
| 728 | // one to three triples: (axis, min_vertex, max_vertex), axis==-1(terminator)
|
---|
| 729 | const int AxisAlignedBox3::bfaces[27][10] =
|
---|
| 730 | { // region number .. position
|
---|
| 731 | {0,0,3,1,0,5,2,0,6,-1}, // 0 .. x=0 y=0 z=0
|
---|
| 732 | {0,0,3,1,0,5,-1,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
| 733 | {0,0,3,1,0,5,2,1,7,-1}, // 2 .. x=0 y=0 z=2
|
---|
| 734 |
|
---|
| 735 | {0,0,3,2,0,6,-1,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
| 736 | {0,0,3,-1,-1,-1,-1,-1,-1,-1},// 4 .. x=0 y=1 z=1
|
---|
| 737 | {0,0,3,2,1,7,-1,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
| 738 |
|
---|
| 739 | {0,0,3,1,2,7,2,0,6,-1}, // 6 .. x=0 y=2 z=0
|
---|
| 740 | {0,0,3,1,2,7,-1,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
| 741 | {0,0,3,1,2,7,2,1,7,-1}, // 8 .. x=0 y=2 z=2
|
---|
| 742 |
|
---|
| 743 | // the regions number <9,17>
|
---|
| 744 | {1,0,5,2,0,6,-1,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
| 745 | {1,0,5,-1,-1,-1,-1,-1,-1,-1},// 10 .. x=1 y=0 z=1
|
---|
| 746 | {1,0,5,2,1,7,-1,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
| 747 |
|
---|
| 748 | {2,0,6,-1,-1,-1,-1,-1,-1,-1},// 12 .. x=1 y=1 z=0
|
---|
| 749 | {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1},// 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 750 | {2,1,7,-1,-1,-1,-1,-1,-1,-1},// 14 .. x=1 y=1 z=2
|
---|
| 751 |
|
---|
| 752 | {1,2,7,2,0,6,-1,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
| 753 | {1,2,7,-1,-1,-1,-1,-1,-1,-1},// 16 .. x=1 y=2 z=1
|
---|
| 754 | {1,2,7,2,1,7,-1,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
| 755 |
|
---|
| 756 | // the region number <18,26>
|
---|
| 757 | {0,4,7,1,0,5,2,0,6,-1}, // 18 .. x=2 y=0 z=0
|
---|
| 758 | {0,4,7,1,0,5,-1,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
| 759 | {0,4,7,1,0,5,2,1,7,-1}, // 20 .. x=2 y=0 z=2
|
---|
| 760 |
|
---|
| 761 | {0,4,7,2,0,6,-1,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
| 762 | {0,4,7,-1,-1,-1,-1,-1,-1,-1},// 22 .. x=2 y=1 z=1
|
---|
| 763 | {0,4,7,2,1,7,-1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
| 764 |
|
---|
| 765 | {0,4,7,1,2,7,2,0,6,-1}, // 24 .. x=2 y=2 z=0
|
---|
| 766 | {0,4,7,1,2,7,-1,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
| 767 | {0,4,7,1,2,7,2,1,7,-1}, // 26 .. x=2 y=2 z=2
|
---|
| 768 | };
|
---|
| 769 |
|
---|
| 770 | // the correct corners indexing from entry face to exit face
|
---|
| 771 | // first index determines entry face, second index exit face, and
|
---|
| 772 | // the two numbers (indx, inc) determines: ind = the index on the exit
|
---|
| 773 | // face, when starting from the vertex 0 on entry face, 'inc' is
|
---|
| 774 | // the increment when we go on entry face in order 0,1,2,3 to create
|
---|
| 775 | // convex shaft with the rectangle on exit face. That is, inc = -1 or 1.
|
---|
| 776 | const int AxisAlignedBox3::pairFaceRects[6][6][2] = {
|
---|
| 777 | { // entry face = 0
|
---|
| 778 | {-1,0}, // exit face 0 .. no meaning
|
---|
| 779 | {0,-1}, // 1
|
---|
| 780 | {0,-1}, // 2
|
---|
| 781 | {0,1}, // 3 .. opposite face
|
---|
| 782 | {3,1}, // 4
|
---|
| 783 | {1,1} // 5
|
---|
| 784 | },
|
---|
| 785 | { // entry face = 1
|
---|
| 786 | {0,-1}, // exit face 0
|
---|
| 787 | {-1,0}, // 1 .. no meaning
|
---|
| 788 | {0,-1}, // 2
|
---|
| 789 | {1,1}, // 3
|
---|
| 790 | {0,1}, // 4 .. opposite face
|
---|
| 791 | {3,1} // 5
|
---|
| 792 | },
|
---|
| 793 | { // entry face = 2
|
---|
| 794 | {0,-1}, // 0
|
---|
| 795 | {0,-1}, // 1
|
---|
| 796 | {-1,0}, // 2 .. no meaning
|
---|
| 797 | {3,1}, // 3
|
---|
| 798 | {1,1}, // 4
|
---|
| 799 | {0,1} // 5 .. opposite face
|
---|
| 800 | },
|
---|
| 801 | { // entry face = 3
|
---|
| 802 | {0,1}, // 0 .. opposite face
|
---|
| 803 | {3,-1}, // 1
|
---|
| 804 | {1,1}, // 2
|
---|
| 805 | {-1,0}, // 3 .. no meaning
|
---|
| 806 | {0,-1}, // 4
|
---|
| 807 | {0,-1} // 5
|
---|
| 808 | },
|
---|
| 809 | { // entry face = 4
|
---|
| 810 | {1,1}, // 0
|
---|
| 811 | {0,1}, // 1 .. opposite face
|
---|
| 812 | {3,1}, // 2
|
---|
| 813 | {0,-1}, // 3
|
---|
| 814 | {-1,0}, // 4 .. no meaning
|
---|
| 815 | {0,-1} // 5
|
---|
| 816 | },
|
---|
| 817 | { // entry face = 5
|
---|
| 818 | {3,-1}, // 0
|
---|
| 819 | {1,1}, // 1
|
---|
| 820 | {0,1}, // 2 .. opposite face
|
---|
| 821 | {0,-1}, // 3
|
---|
| 822 | {0,-1}, // 4
|
---|
| 823 | {-1,0} // 5 .. no meaning
|
---|
| 824 | }
|
---|
| 825 | };
|
---|
| 826 |
|
---|
| 827 |
|
---|
| 828 | // ------------------------------------------------------------
|
---|
| 829 | // The vertices that form CLOSEST points with respect to the region
|
---|
| 830 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
| 831 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
| 832 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
| 833 | // at most 8 points, at least 1 point.
|
---|
| 834 | // The table includes the closest 1/2/4/8 points, followed possibly
|
---|
| 835 | // by the set of coordinates that should be used for testing for
|
---|
| 836 | // the proximity queries. The coordinates to be tested are described by
|
---|
| 837 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
| 838 | // when a=1, we want to test max vector of the box
|
---|
| 839 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
| 840 | // The sequence is ended by 15, number -1 is used as the separator
|
---|
| 841 | // between the vertices and coordinates.
|
---|
| 842 | const int
|
---|
| 843 | AxisAlignedBox3::cvertices[27][9] =
|
---|
| 844 | { // region number.. position
|
---|
| 845 | {0,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D one vertex
|
---|
| 846 | {0,1,-1,0,0,0,1,15,15}, // 1 .. x=0 y=0 z=1 D two vertices foll. by 2
|
---|
| 847 | {1,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D one vertex
|
---|
| 848 |
|
---|
| 849 | {0,2,-1,0,0,0,2,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
| 850 | {0,1,3,2,-1,0,0,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
| 851 | {1,3,-1,0,0,1,2,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
| 852 |
|
---|
| 853 | {2,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
| 854 | {2,3,-1,0,0,1,1,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
| 855 | {3,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
| 856 |
|
---|
| 857 | // the regions number <9,17>
|
---|
| 858 | {0,4,-1,0,1,0,2,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
| 859 | {5,1,0,4,-1,0,1,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
| 860 | {1,5,-1,0,1,1,2,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
| 861 |
|
---|
| 862 | {4,0,2,6,-1,0,2,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
| 863 | {0,2,3,1,5,4,6,7,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 864 | {1,5,7,3,-1,1,2,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
| 865 |
|
---|
| 866 | {6,2,-1,0,2,1,1,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
| 867 | {6,2,3,7,-1,1,1,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
| 868 | {3,7,-1,1,1,1,2,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
| 869 |
|
---|
| 870 | // the regions number <18,26>
|
---|
| 871 | {4,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
| 872 | {4,5,-1,0,1,1,0,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
| 873 | {5,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
| 874 |
|
---|
| 875 | {4,6,-1,0,2,1,0,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
| 876 | {5,4,6,7,-1,1,0,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
| 877 | {7,5,-1,1,0,1,2,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
| 878 |
|
---|
| 879 | {6,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
| 880 | {6,7,-1,1,0,1,1,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
| 881 | {7,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
| 882 | };
|
---|
| 883 |
|
---|
| 884 | // Table for Sphere-AABB intersection based on the region knowledge
|
---|
| 885 | // Similar array to previous cvertices, but we omit the surfaces
|
---|
| 886 | // which are not necessary for testing. First are vertices,
|
---|
| 887 | // they are finished with -1. Second, there are indexes in
|
---|
| 888 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
| 889 | // when a=1, we want to test max vector of the box
|
---|
| 890 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
| 891 | //
|
---|
| 892 | // So either we check the vertices or only the distance in specified
|
---|
| 893 | // dimensions. There are at all four possible cases:
|
---|
| 894 | //
|
---|
| 895 | // 1) we check one vertex - then sequence start with non-negative index
|
---|
| 896 | // and is finished with 15
|
---|
| 897 | // 2) we check two coordinates of min/max vector describe by the pair
|
---|
| 898 | // (a,b) .. a=min/max(0/1) b=x/y/z (0/1/2), sequence starts with 8
|
---|
| 899 | // and finishes with 15
|
---|
| 900 | // 3) we check only one coordinate of min/max, as for 2), sequence start
|
---|
| 901 | // with 9 and ends with 15
|
---|
| 902 | // 4) Position 13 - sphere is inside the box, intersection always exist
|
---|
| 903 | // the sequence start with 15 .. no further testing is necessary
|
---|
| 904 | // in this case
|
---|
| 905 | const int
|
---|
| 906 | AxisAlignedBox3::csvertices[27][6] =
|
---|
| 907 | { // region number.. position
|
---|
| 908 | {0,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D vertex only
|
---|
| 909 | {8,0,0,0,1,15}, // 1 .. x=0 y=0 z=1 D two coords.
|
---|
| 910 | {1,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D vertex only
|
---|
| 911 |
|
---|
| 912 | {8,0,0,0,2,15}, // 3 .. x=0 y=1 z=0 D two coords
|
---|
| 913 | {9,0,0,15,15,15}, // 4 .. x=0 y=1 z=1 D one coord
|
---|
| 914 | {8,0,0,1,2,15}, // 5 .. x=0 y=1 z=2 D two coords.
|
---|
| 915 |
|
---|
| 916 | {2,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D one vertex
|
---|
| 917 | {8,0,0,1,1,15}, // 7 .. x=0 y=2 z=1 D two coords
|
---|
| 918 | {3,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D one vertex
|
---|
| 919 |
|
---|
| 920 | // the regions number <9,17>
|
---|
| 921 | {8,0,1,0,2,15}, // 9 .. x=1 y=0 z=0 D two coords
|
---|
| 922 | {9,0,1,15,15,15}, // 10 .. x=1 y=0 z=1 D one coord
|
---|
| 923 | {8,0,1,1,2,15}, // 11 .. x=1 y=0 z=2 D two coords
|
---|
| 924 |
|
---|
| 925 | {9,0,2,15,15,15}, // 12 .. x=1 y=1 z=0 D one coord
|
---|
| 926 | {15,15,15,15,15,15}, // 13 .. x=1 y=1 z=1 inside the box, special case/value
|
---|
| 927 | {9,1,2,15,15,15}, // 14 .. x=1 y=1 z=2 D one corrd
|
---|
| 928 |
|
---|
| 929 | {8,0,2,1,1,15}, // 15 .. x=1 y=2 z=0 D two coords
|
---|
| 930 | {9,1,1,15,15}, // 16 .. x=1 y=2 z=1 D one coord
|
---|
| 931 | {8,1,1,1,2,15}, // 17 .. x=1 y=2 z=2 D two coords
|
---|
| 932 |
|
---|
| 933 | // the regions number <18,26>
|
---|
| 934 | {4,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D one vertex
|
---|
| 935 | {8,0,1,1,0,15}, // 19 .. x=2 y=0 z=1 D two coords
|
---|
| 936 | {5,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D one vertex
|
---|
| 937 |
|
---|
| 938 | {8,0,2,1,0,15}, // 21 .. x=2 y=1 z=0 D two coords
|
---|
| 939 | {9,1,0,15,15,15}, // 22 .. x=2 y=1 z=1 D one coord
|
---|
| 940 | {8,1,0,1,2,15}, // 23 .. x=2 y=1 z=2 D two coords
|
---|
| 941 |
|
---|
| 942 | {6,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D one vertex
|
---|
| 943 | {8,1,0,1,1,15}, // 25 .. x=2 y=2 z=1 D two coords
|
---|
| 944 | {7,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D one vertex
|
---|
| 945 | };
|
---|
| 946 |
|
---|
| 947 |
|
---|
| 948 | // The vertices that form all FARTHEST points with respect to the region
|
---|
| 949 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
| 950 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
| 951 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
| 952 | // at most 8 points, at least 1 point.
|
---|
| 953 | // For testing, if the AABB is whole in the sphere, it is enough
|
---|
| 954 | // to test only vertices, either 1,2,4, or 8.
|
---|
| 955 | const int
|
---|
| 956 | AxisAlignedBox3::fvertices[27][9] =
|
---|
| 957 | { // region number.. position
|
---|
| 958 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D
|
---|
| 959 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D
|
---|
| 960 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D
|
---|
| 961 |
|
---|
| 962 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
| 963 | {4,5,7,6,15,15,15,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
| 964 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
| 965 |
|
---|
| 966 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
| 967 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
| 968 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
| 969 |
|
---|
| 970 | // the regions number <9,17>
|
---|
| 971 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
| 972 | {7,3,2,6,15,15,15,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
| 973 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
| 974 |
|
---|
| 975 | {5,1,3,7,15,15,15,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
| 976 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 977 | {0,4,6,2,15,15,15,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
| 978 |
|
---|
| 979 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
| 980 | {4,0,1,5,15,15,15,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
| 981 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
| 982 |
|
---|
| 983 | // the regions number <18,26>
|
---|
| 984 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
| 985 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
| 986 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
| 987 |
|
---|
| 988 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
| 989 | {1,0,2,3,15,15,15,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
| 990 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
| 991 |
|
---|
| 992 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
| 993 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
| 994 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
| 995 | };
|
---|
| 996 |
|
---|
| 997 | // Similar table as above, farthest points, but only the ones
|
---|
| 998 | // necessary for testing the intersection problem. If we do
|
---|
| 999 | // not consider the case 13, center of the sphere is inside the
|
---|
| 1000 | // box, then we can always test at most 2 box vertices to say whether
|
---|
| 1001 | // the whole box is inside the sphere.
|
---|
| 1002 | // The number of vertices is minimized using some assumptions
|
---|
| 1003 | // about the ortogonality of vertices and sphere properties.
|
---|
| 1004 | const int
|
---|
| 1005 | AxisAlignedBox3::fsvertices[27][9] =
|
---|
| 1006 | { // region number.. position
|
---|
| 1007 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D 1 vertex
|
---|
| 1008 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D 2 vertices
|
---|
| 1009 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D 1 vertex
|
---|
| 1010 |
|
---|
| 1011 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D 2 vertices
|
---|
| 1012 | {4,7,15,5,6,15,15,15,15}, // 4 .. x=0 y=1 z=1 D 4/2 vertices
|
---|
| 1013 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D 2 vertices
|
---|
| 1014 |
|
---|
| 1015 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D 1 vertex
|
---|
| 1016 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D 2 vertices
|
---|
| 1017 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D 1 vertex
|
---|
| 1018 |
|
---|
| 1019 | // the regions number <9,17>
|
---|
| 1020 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D 2 vertices
|
---|
| 1021 | {7,2,15,3,6,15,15,15,15}, // 10 .. x=1 y=0 z=1 D 4/2 vertices
|
---|
| 1022 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D 2 vertices
|
---|
| 1023 |
|
---|
| 1024 | {5,3,15,1,7,15,15,15,15}, // 12 .. x=1 y=1 z=0 D 4/2 vertices
|
---|
| 1025 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 1026 | {0,6,15,4,2,15,15,15,15}, // 14 .. x=1 y=1 z=2 D 4/2 vertices
|
---|
| 1027 |
|
---|
| 1028 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D 2 vertices
|
---|
| 1029 | {4,1,15,0,5,15,15,15,15}, // 16 .. x=1 y=2 z=1 D 4/2 vertices
|
---|
| 1030 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D 2 vertices
|
---|
| 1031 |
|
---|
| 1032 | // the regions number <18,26>
|
---|
| 1033 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D 1 vertex
|
---|
| 1034 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D 2 vertices
|
---|
| 1035 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D 1 vertex
|
---|
| 1036 |
|
---|
| 1037 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D 2 vertices
|
---|
| 1038 | {1,2,15,0,3,15,15,15,15}, // 22 .. x=2 y=1 z=1 D 4/2 vertices
|
---|
| 1039 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D 2 vertices
|
---|
| 1040 |
|
---|
| 1041 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D 1 vertex
|
---|
| 1042 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D 2 vertices
|
---|
| 1043 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D 1 vertex
|
---|
| 1044 | };
|
---|
| 1045 |
|
---|
[312] | 1046 |
|
---|
[162] | 1047 | // The fast computation of arctangent .. the maximal error is less
|
---|
| 1048 | // than 4.1 degrees, according to Graphics GEMSII, 1991, pages 389--391
|
---|
| 1049 | // Ron Capelli: "Fast approximation to the arctangent"
|
---|
| 1050 | float
|
---|
| 1051 | atan22(const float& y)
|
---|
| 1052 | {
|
---|
| 1053 | const float x = 1.0;
|
---|
| 1054 | const float c = (float)(M_PI * 0.25);
|
---|
| 1055 |
|
---|
| 1056 | if (y < 0.0) {
|
---|
| 1057 | if (y < -1.0)
|
---|
| 1058 | return c * (-2.0 + x / y); // for angle in <-PI/2, -PI/4)
|
---|
| 1059 | else
|
---|
| 1060 | return c * (y / x); // for angle in <-PI/4 , 0>
|
---|
| 1061 | }
|
---|
| 1062 | else {
|
---|
| 1063 | if (y > 1.0)
|
---|
| 1064 | return c * (2.0 - x / y); // for angle in <PI/4, PI/2>
|
---|
| 1065 | else
|
---|
| 1066 | return c * (y / x); // for angle in <0, PI/2>
|
---|
| 1067 | }
|
---|
| 1068 | }
|
---|
| 1069 |
|
---|
| 1070 |
|
---|
| 1071 | float
|
---|
| 1072 | AxisAlignedBox3::ProjectToSphereSA(const Vector3 &viewpoint, int *tcase) const
|
---|
| 1073 | {
|
---|
| 1074 | int id = GetRegionID(viewpoint);
|
---|
| 1075 | *tcase = id;
|
---|
| 1076 |
|
---|
| 1077 | // spherical projection .. SA represents solid angle
|
---|
| 1078 | if (id == 13) // .. inside the box
|
---|
| 1079 | return (float)(4.0*M_PI); // the whole sphere
|
---|
| 1080 | float SA = 0.0; // inital value
|
---|
| 1081 |
|
---|
| 1082 | int i = 0; // the pointer in the array of vertices
|
---|
| 1083 | while (bfaces[id][i] >= 0) {
|
---|
| 1084 | int axisO = bfaces[id][i++];
|
---|
| 1085 | int minvIdx = bfaces[id][i++];
|
---|
| 1086 | int maxvIdx = bfaces[id][i++];
|
---|
| 1087 | Vector3 vmin, vmax;
|
---|
| 1088 | GetVertex(minvIdx, vmin);
|
---|
| 1089 | GetVertex(maxvIdx, vmax);
|
---|
| 1090 | float h = fabs(vmin[axisO] - viewpoint[axisO]);
|
---|
| 1091 | int axis = (axisO + 1) % 3; // next axis
|
---|
| 1092 | float a = (vmin[axis] - viewpoint[axis]) / h; // minimum for v-range
|
---|
| 1093 | float b = (vmax[axis] - viewpoint[axis]) / h; // maximum for v-range
|
---|
| 1094 | //if (a > b) {
|
---|
| 1095 | // FATAL << "ProjectToSphereSA::Error a > b\n";
|
---|
| 1096 | // FATAL_ABORT;
|
---|
| 1097 | //}
|
---|
| 1098 | //if (vmin[axisO] != vmax[axisO]) {
|
---|
| 1099 | // FATAL << "ProjectToSphereSA::Error a-axis != b-axis\n";
|
---|
| 1100 | // FATAL_ABORT;
|
---|
| 1101 | //}
|
---|
| 1102 | axis = (axisO + 2) % 3; // next second axis
|
---|
| 1103 | float c = (vmin[axis] - viewpoint[axis]) / h; // minimum for u-range
|
---|
| 1104 | float d = (vmax[axis] - viewpoint[axis]) / h; // maximum for u-range
|
---|
| 1105 | //if (c > d) {
|
---|
| 1106 | // FATAL << "ProjectToSphereSA::Error c > d\n";
|
---|
| 1107 | // FATAL_ABORT;
|
---|
| 1108 | //}
|
---|
| 1109 | SA +=atan22(d*b/sqrt(b*b + d*d + 1.0)) - atan22(b*c/sqrt(b*b + c*c + 1.0))
|
---|
| 1110 | - atan22(d*a/sqrt(a*a + d*d + 1.0)) + atan22(a*c/sqrt(a*a + c*c + 1.0));
|
---|
| 1111 | }
|
---|
| 1112 |
|
---|
| 1113 | #if 0
|
---|
| 1114 | if ((SA > 2.0*M_PI) ||
|
---|
| 1115 | (SA < 0.0)) {
|
---|
| 1116 | FATAL << "The solid angle has strange value: ";
|
---|
| 1117 | FATAL << "SA = "<< SA << endl;
|
---|
| 1118 | FATAL_ABORT;
|
---|
| 1119 | }
|
---|
| 1120 | #endif
|
---|
| 1121 |
|
---|
| 1122 | return SA;
|
---|
| 1123 | }
|
---|
| 1124 |
|
---|
| 1125 | // Projects the box to a plane given a normal vector only and
|
---|
| 1126 | // computes the surface area of the projected silhouette
|
---|
| 1127 | // no clipping of the box is performed.
|
---|
| 1128 | float
|
---|
| 1129 | AxisAlignedBox3::ProjectToPlaneSA(const Vector3 &normal) const
|
---|
| 1130 | {
|
---|
| 1131 | Vector3 size = Size();
|
---|
| 1132 |
|
---|
| 1133 | // the surface area of the box to a yz-plane - perpendicular to x-axis
|
---|
| 1134 | float sax = size.y * size.z;
|
---|
| 1135 |
|
---|
| 1136 | // the surface area of the box to a zx-plane - perpendicular to y-axis
|
---|
| 1137 | float say = size.z * size.x;
|
---|
| 1138 |
|
---|
| 1139 | // the surface area of the box to a xy-plane - perpendicular to z-axis
|
---|
| 1140 | float saz = size.x * size.y;
|
---|
| 1141 |
|
---|
| 1142 | return sax * fabs(normal.x) + say * fabs(normal.y) + saz * fabs(normal.z);
|
---|
| 1143 | }
|
---|
| 1144 |
|
---|
| 1145 |
|
---|
| 1146 |
|
---|
| 1147 | // This definition allows to be a point when answering true
|
---|
| 1148 | bool
|
---|
| 1149 | AxisAlignedBox3::IsCorrectAndNotPoint() const
|
---|
| 1150 | {
|
---|
| 1151 | if ( (mMin.x > mMax.x) ||
|
---|
| 1152 | (mMin.y > mMax.y) ||
|
---|
| 1153 | (mMin.z > mMax.z) )
|
---|
| 1154 | return false; // box is not formed
|
---|
| 1155 |
|
---|
| 1156 | if ( (mMin.x == mMax.x) &&
|
---|
| 1157 | (mMin.y == mMax.y) &&
|
---|
| 1158 | (mMin.z == mMax.z) )
|
---|
| 1159 | return false; // degenerates to a point
|
---|
| 1160 |
|
---|
| 1161 | return true;
|
---|
| 1162 | }
|
---|
| 1163 |
|
---|
| 1164 | // This definition allows to be a point when answering true
|
---|
| 1165 | bool
|
---|
| 1166 | AxisAlignedBox3::IsPoint() const
|
---|
| 1167 | {
|
---|
| 1168 | if ( (mMin.x == mMax.x) &&
|
---|
| 1169 | (mMin.y == mMax.y) &&
|
---|
| 1170 | (mMin.z == mMax.z) )
|
---|
| 1171 | return true; // degenerates to a point
|
---|
| 1172 |
|
---|
| 1173 | return false;
|
---|
| 1174 | }
|
---|
| 1175 |
|
---|
| 1176 | // This definition requires shape of non-zero volume
|
---|
| 1177 | bool
|
---|
| 1178 | AxisAlignedBox3::IsSingularOrIncorrect() const
|
---|
| 1179 | {
|
---|
| 1180 | if ( (mMin.x >= mMax.x) ||
|
---|
| 1181 | (mMin.y >= mMax.y) ||
|
---|
| 1182 | (mMin.z >= mMax.z) )
|
---|
| 1183 | return true; // box is not formed
|
---|
| 1184 |
|
---|
| 1185 | return false; // has non-zero volume
|
---|
| 1186 | }
|
---|
| 1187 |
|
---|
| 1188 | // returns true, when the sphere specified by the origin and radius
|
---|
| 1189 | // fully contains the box
|
---|
| 1190 | bool
|
---|
| 1191 | AxisAlignedBox3::IsFullyContainedInSphere(const Vector3 ¢er, float rad) const
|
---|
| 1192 | {
|
---|
| 1193 | int region = GetRegionID(center);
|
---|
| 1194 | float rad2 = rad*rad;
|
---|
| 1195 |
|
---|
| 1196 | // vertex of the box
|
---|
| 1197 | Vector3 vertex;
|
---|
| 1198 |
|
---|
| 1199 | int i = 0;
|
---|
| 1200 | for (i = 0 ; ; i++) {
|
---|
| 1201 | int a = fsvertices[region][i];
|
---|
| 1202 | if (a == 15)
|
---|
| 1203 | return true; // if was not false untill now, it must be contained
|
---|
| 1204 |
|
---|
| 1205 | assert( (a>=0) && (a<8) );
|
---|
| 1206 |
|
---|
| 1207 | // normal vertex
|
---|
| 1208 | GetVertex(a, vertex);
|
---|
| 1209 |
|
---|
| 1210 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1211 | return false;
|
---|
| 1212 | } // for
|
---|
| 1213 |
|
---|
| 1214 | }
|
---|
| 1215 |
|
---|
| 1216 | // returns true, when the volume of the sphere and volume of the
|
---|
| 1217 | // axis aligned box has no intersection
|
---|
| 1218 | bool
|
---|
| 1219 | AxisAlignedBox3::HasNoIntersectionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1220 | {
|
---|
| 1221 | int region = GetRegionID(center);
|
---|
| 1222 | float rad2 = rad*rad;
|
---|
| 1223 |
|
---|
| 1224 | // vertex of the box
|
---|
| 1225 | Vector3 vertex;
|
---|
| 1226 |
|
---|
| 1227 | switch (csvertices[region][0]) {
|
---|
| 1228 | case 8: {
|
---|
| 1229 | // test two coordinates described within the field
|
---|
| 1230 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1231 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
| 1232 | dist *= dist;
|
---|
| 1233 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
| 1234 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
| 1235 | dist += (dist2 * dist2);
|
---|
| 1236 | if (dist > rad2)
|
---|
| 1237 | return true; // no intersection is possible
|
---|
| 1238 | }
|
---|
| 1239 | case 9: {
|
---|
| 1240 | // test one coordinate described within the field
|
---|
| 1241 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1242 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
| 1243 | if (dist > rad)
|
---|
| 1244 | return true; // no intersection is possible
|
---|
| 1245 | }
|
---|
| 1246 | case 15:
|
---|
| 1247 | return false; // box and sphere surely has intersection
|
---|
| 1248 | default: {
|
---|
| 1249 | // test using normal vertices
|
---|
| 1250 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
| 1251 |
|
---|
| 1252 | // normal vertex
|
---|
| 1253 | GetVertex(csvertices[region][0], vertex);
|
---|
| 1254 |
|
---|
| 1255 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1256 | return true; // no intersectino is possible
|
---|
| 1257 | }
|
---|
| 1258 | } // switch
|
---|
| 1259 |
|
---|
| 1260 | return false; // partial or full containtment
|
---|
| 1261 | }
|
---|
| 1262 |
|
---|
| 1263 | #if 0
|
---|
| 1264 | // Given the sphere, determine the mutual position between the
|
---|
| 1265 | // sphere and box
|
---|
| 1266 |
|
---|
| 1267 | // SOME BUG IS INSIDE !!!! V.H. 25/4/2001
|
---|
| 1268 | int
|
---|
| 1269 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1270 | {
|
---|
| 1271 | int region = GetRegionID(center);
|
---|
| 1272 | float rad2 = rad*rad;
|
---|
| 1273 |
|
---|
| 1274 | // vertex of the box
|
---|
| 1275 | Vector3 vertex;
|
---|
| 1276 |
|
---|
| 1277 | // first testing for full containtment - whether sphere fully
|
---|
| 1278 | // contains the box
|
---|
| 1279 | int countInside = 0; // how many points were found inside
|
---|
| 1280 |
|
---|
| 1281 | int i = 0;
|
---|
| 1282 | for (i = 0 ; ; i++) {
|
---|
| 1283 | int a = fsvertices[region][i];
|
---|
| 1284 | if (a == 15)
|
---|
| 1285 | return 1; // the sphere fully contain the box
|
---|
| 1286 |
|
---|
| 1287 | assert( (a>=0) && (a<8) );
|
---|
| 1288 |
|
---|
| 1289 | // normal vertex
|
---|
| 1290 | GetVertex(a, vertex);
|
---|
| 1291 |
|
---|
| 1292 | if (SqrMagnitude(vertex - center) <= rad2)
|
---|
| 1293 | countInside++; // the number of vertices inside the sphere
|
---|
| 1294 | else {
|
---|
| 1295 | if (countInside)
|
---|
| 1296 | return 0; // partiall overlap has been found
|
---|
| 1297 | // the sphere does not fully contain the box .. only way to break
|
---|
| 1298 | // this loop and go for other testing
|
---|
| 1299 | break;
|
---|
| 1300 | }
|
---|
| 1301 | } // for
|
---|
| 1302 |
|
---|
| 1303 | // now only box and sphere can partially overlap or no intersection
|
---|
| 1304 | switch (csvertices[region][0]) {
|
---|
| 1305 | case 8: {
|
---|
| 1306 | // test two coordinates described within the field
|
---|
| 1307 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1308 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
| 1309 | dist *= dist;
|
---|
| 1310 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
| 1311 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
| 1312 | dist += (dist2 * dist2);
|
---|
| 1313 | if (dist > rad2 )
|
---|
| 1314 | return -1; // no intersection is possible
|
---|
| 1315 | }
|
---|
| 1316 | case 9: {
|
---|
| 1317 | // test one coordinate described within the field
|
---|
| 1318 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1319 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
| 1320 | if (dist > rad)
|
---|
| 1321 | return -1; // no intersection is possible
|
---|
| 1322 | }
|
---|
| 1323 | case 15:
|
---|
| 1324 | return 0 ; // partial overlap is now guaranteed
|
---|
| 1325 | default: {
|
---|
| 1326 | // test using normal vertices
|
---|
| 1327 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
| 1328 |
|
---|
| 1329 | // normal vertex
|
---|
| 1330 | GetVertex(csvertices[region][0], vertex);
|
---|
| 1331 |
|
---|
| 1332 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1333 | return -1; // no intersection is possible
|
---|
| 1334 | }
|
---|
| 1335 | } // switch
|
---|
| 1336 |
|
---|
| 1337 | return 0; // partial intersection is guaranteed
|
---|
| 1338 | }
|
---|
| 1339 | #else
|
---|
| 1340 |
|
---|
| 1341 | // Some maybe smarter version, extendible easily to d-dimensional
|
---|
| 1342 | // space!
|
---|
| 1343 | // Given a sphere described by the center and radius,
|
---|
| 1344 | // the fullowing function returns:
|
---|
| 1345 | // -1 ... the sphere and the box are completely separate
|
---|
| 1346 | // 0 ... the sphere and the box only partially overlap
|
---|
| 1347 | // 1 ... the sphere contains fully the box
|
---|
| 1348 | // Note: the case when box fully contains the sphere is not reported
|
---|
| 1349 | // since it was not required.
|
---|
| 1350 | int
|
---|
| 1351 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1352 | {
|
---|
| 1353 | //#define SPEED_UP
|
---|
| 1354 |
|
---|
| 1355 | #ifndef SPEED_UP
|
---|
| 1356 | // slow version, instructively written
|
---|
| 1357 | #if 0
|
---|
| 1358 | // does it make sense to test
|
---|
| 1359 | // checking the sides of the box for possible non-intersection
|
---|
| 1360 | if ( ((center.x + rad) < mMin.x) ||
|
---|
| 1361 | ((center.x - rad) > mMax.x) ||
|
---|
| 1362 | ((center.y + rad) < mMin.y) ||
|
---|
| 1363 | ((center.y - rad) > mMax.y) ||
|
---|
| 1364 | ((center.z + rad) < mMin.z) ||
|
---|
| 1365 | ((center.z - rad) > mMax.z) ) {
|
---|
| 1366 | // cout << "r ";
|
---|
| 1367 | return -1; // no overlap is possible
|
---|
| 1368 | }
|
---|
| 1369 | #endif
|
---|
| 1370 |
|
---|
| 1371 | // someoverlap is possible, check the distance of vertices
|
---|
| 1372 | rad = rad*rad;
|
---|
| 1373 | float sumMin = 0;
|
---|
| 1374 | // Try to minimize the function of a distance
|
---|
| 1375 | // from the sphere center
|
---|
| 1376 |
|
---|
| 1377 | // for x-axis
|
---|
| 1378 | float minSqrX = sqr(mMin.x - center.x);
|
---|
| 1379 | float maxSqrX = sqr(mMax.x - center.x);
|
---|
| 1380 | if (center.x < mMin.x)
|
---|
| 1381 | sumMin = minSqrX;
|
---|
| 1382 | else
|
---|
| 1383 | if (center.x > mMax.x)
|
---|
| 1384 | sumMin = maxSqrX;
|
---|
| 1385 |
|
---|
| 1386 | // for y-axis
|
---|
| 1387 | float minSqrY = sqr(mMin.y - center.y);
|
---|
| 1388 | float maxSqrY = sqr(mMax.y - center.y);
|
---|
| 1389 | if (center.y < mMin.y)
|
---|
| 1390 | sumMin += minSqrY;
|
---|
| 1391 | else
|
---|
| 1392 | if (center.y > mMax.y)
|
---|
| 1393 | sumMin += maxSqrY;
|
---|
| 1394 |
|
---|
| 1395 | // for z-axis
|
---|
| 1396 | float minSqrZ = sqr(mMin.z - center.z);
|
---|
| 1397 | float maxSqrZ = sqr(mMax.z - center.z);
|
---|
| 1398 | if (center.z < mMin.z)
|
---|
| 1399 | sumMin += minSqrZ;
|
---|
| 1400 | else
|
---|
| 1401 | if (center.z > mMax.z)
|
---|
| 1402 | sumMin += maxSqrZ;
|
---|
| 1403 |
|
---|
| 1404 | if (sumMin > rad)
|
---|
| 1405 | return -1; // no intersection between sphere and box
|
---|
| 1406 |
|
---|
| 1407 | // try to find out the maximum distance between the
|
---|
| 1408 | // sphere center and vertices
|
---|
| 1409 | float sumMax = 0;
|
---|
| 1410 |
|
---|
| 1411 | if (minSqrX > maxSqrX)
|
---|
| 1412 | sumMax = minSqrX;
|
---|
| 1413 | else
|
---|
| 1414 | sumMax = maxSqrX;
|
---|
| 1415 |
|
---|
| 1416 | if (minSqrY > maxSqrY)
|
---|
| 1417 | sumMax += minSqrY;
|
---|
| 1418 | else
|
---|
| 1419 | sumMax += maxSqrY;
|
---|
| 1420 |
|
---|
| 1421 | if (minSqrZ > maxSqrZ)
|
---|
| 1422 | sumMax += minSqrZ;
|
---|
| 1423 | else
|
---|
| 1424 | sumMax += maxSqrZ;
|
---|
| 1425 |
|
---|
| 1426 | // sumMin < rad
|
---|
| 1427 | if (sumMax < rad)
|
---|
| 1428 | return 1; // the sphere contains the box completely
|
---|
| 1429 |
|
---|
| 1430 | // partial intersection, part of the box is outside the sphere
|
---|
| 1431 | return 0;
|
---|
| 1432 | #else
|
---|
| 1433 |
|
---|
| 1434 | // Optimized version of the test
|
---|
| 1435 |
|
---|
| 1436 | #ifndef __VECTOR_HACK
|
---|
| 1437 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
| 1438 | #endif
|
---|
| 1439 |
|
---|
| 1440 | // some overlap is possible, check the distance of vertices
|
---|
| 1441 | rad = rad*rad;
|
---|
| 1442 | float sumMin = 0;
|
---|
| 1443 | float sumMax = 0;
|
---|
| 1444 | // Try to minimize the function of a distance
|
---|
| 1445 | // from the sphere center
|
---|
| 1446 |
|
---|
| 1447 | const float *minp = &(min[0]);
|
---|
| 1448 | const float *maxp = &(max[0]);
|
---|
| 1449 | const float *pcenter = &(center[0]);
|
---|
| 1450 |
|
---|
| 1451 | // for x-axis
|
---|
| 1452 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
| 1453 | float minsqr = sqr(*minp - *pcenter);
|
---|
| 1454 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
| 1455 | if (*pcenter < *minp)
|
---|
| 1456 | sumMin += minsqr;
|
---|
| 1457 | else
|
---|
| 1458 | if (*pcenter > *maxp)
|
---|
| 1459 | sumMin += maxsqr;
|
---|
| 1460 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
| 1461 | }
|
---|
| 1462 |
|
---|
| 1463 | if (sumMin > rad)
|
---|
| 1464 | return -1; // no intersection between sphere and box
|
---|
| 1465 |
|
---|
| 1466 | // sumMin < rad
|
---|
| 1467 | if (sumMax < rad)
|
---|
| 1468 | return 1; // the sphere contains the box completely
|
---|
| 1469 |
|
---|
| 1470 | // partial intersection, part of the box is outside the sphere
|
---|
| 1471 | return 0;
|
---|
| 1472 | #endif
|
---|
| 1473 | }
|
---|
| 1474 | #endif
|
---|
| 1475 |
|
---|
| 1476 | // Given the cube describe by the center and the half-sie,
|
---|
| 1477 | // determine the mutual position between the cube and the box
|
---|
| 1478 | int
|
---|
| 1479 | AxisAlignedBox3::MutualPositionWithCube(const Vector3 ¢er, float radius) const
|
---|
| 1480 | {
|
---|
| 1481 | // the cube is described by the center and the distance to the any face
|
---|
| 1482 | // along the axes
|
---|
| 1483 |
|
---|
| 1484 | // Note on efficiency!
|
---|
| 1485 | // Can be quite optimized using tables, but I do not have time
|
---|
| 1486 | // V.H. 18/11/2001
|
---|
| 1487 |
|
---|
| 1488 | AxisAlignedBox3 a =
|
---|
| 1489 | AxisAlignedBox3(Vector3(center.x - radius, center.y - radius, center.z - radius),
|
---|
| 1490 | Vector3(center.x + radius, center.y + radius, center.z + radius));
|
---|
| 1491 |
|
---|
| 1492 | if (a.Includes(*this))
|
---|
| 1493 | return 1; // cube contains the box
|
---|
| 1494 |
|
---|
| 1495 | if (OverlapS(a,*this))
|
---|
| 1496 | return 0; // cube partially overlap the box
|
---|
| 1497 |
|
---|
| 1498 | return -1; // completely separate
|
---|
| 1499 | }
|
---|
| 1500 |
|
---|
| 1501 | void
|
---|
| 1502 | AxisAlignedBox3::GetSqrDistances(const Vector3 &point,
|
---|
| 1503 | float &minDistance,
|
---|
| 1504 | float &maxDistance
|
---|
[209] | 1505 | ) const
|
---|
[162] | 1506 | {
|
---|
| 1507 |
|
---|
| 1508 |
|
---|
| 1509 | #ifndef __VECTOR_HACK
|
---|
| 1510 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
| 1511 | #endif
|
---|
| 1512 |
|
---|
| 1513 | // some overlap is possible, check the distance of vertices
|
---|
| 1514 | float sumMin = 0;
|
---|
| 1515 | float sumMax = 0;
|
---|
| 1516 |
|
---|
| 1517 | // Try to minimize the function of a distance
|
---|
| 1518 | // from the sphere center
|
---|
| 1519 |
|
---|
| 1520 | const float *minp = &(mMin[0]);
|
---|
| 1521 | const float *maxp = &(mMax[0]);
|
---|
| 1522 | const float *pcenter = &(point[0]);
|
---|
| 1523 |
|
---|
| 1524 | // for x-axis
|
---|
| 1525 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
| 1526 | float minsqr = sqr(*minp - *pcenter);
|
---|
| 1527 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
| 1528 | if (*pcenter < *minp)
|
---|
| 1529 | sumMin += minsqr;
|
---|
| 1530 | else
|
---|
| 1531 | if (*pcenter > *maxp)
|
---|
| 1532 | sumMin += maxsqr;
|
---|
| 1533 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
| 1534 | }
|
---|
| 1535 |
|
---|
| 1536 | minDistance = sumMin;
|
---|
| 1537 | maxDistance = sumMax;
|
---|
| 1538 | }
|
---|
| 1539 |
|
---|
| 1540 |
|
---|
[177] | 1541 | int
|
---|
| 1542 | AxisAlignedBox3::Side(const Plane3 &plane) const
|
---|
| 1543 | {
|
---|
| 1544 | Vector3 v;
|
---|
| 1545 | int i, m=3, M=-3, s;
|
---|
| 1546 |
|
---|
| 1547 | for (i=0;i<8;i++) {
|
---|
| 1548 | GetVertex(i, v);
|
---|
| 1549 | if((s = plane.Side(v)) < m)
|
---|
| 1550 | m=s;
|
---|
| 1551 | if(s > M)
|
---|
| 1552 | M=s;
|
---|
| 1553 | if (m && m==-M)
|
---|
| 1554 | return 0;
|
---|
| 1555 | }
|
---|
| 1556 |
|
---|
| 1557 | return (m == M) ? m : m + M;
|
---|
| 1558 | }
|
---|
[191] | 1559 |
|
---|
| 1560 | int
|
---|
| 1561 | AxisAlignedBox3::GetFaceVisibilityMask(const Rectangle3 &rectangle) const
|
---|
| 1562 | {
|
---|
| 1563 | int mask = 0;
|
---|
| 1564 | for (int i=0; i < 4; i++)
|
---|
| 1565 | mask |= GetFaceVisibilityMask(rectangle.mVertices[i]);
|
---|
| 1566 | return mask;
|
---|
| 1567 | }
|
---|
| 1568 |
|
---|
| 1569 | int
|
---|
| 1570 | AxisAlignedBox3::GetFaceVisibilityMask(const Vector3 &position) const {
|
---|
| 1571 |
|
---|
| 1572 | // assume that we are not inside the box
|
---|
| 1573 | int c=0;
|
---|
| 1574 |
|
---|
| 1575 | if (position.x<(mMin.x-Limits::Small))
|
---|
| 1576 | c|=1;
|
---|
| 1577 | else
|
---|
| 1578 | if (position.x>(mMax.x+Limits::Small))
|
---|
| 1579 | c|=2;
|
---|
| 1580 |
|
---|
| 1581 | if (position.y<(mMin.y-Limits::Small))
|
---|
| 1582 | c|=4;
|
---|
| 1583 | else
|
---|
| 1584 | if (position.y>(mMax.y+Limits::Small))
|
---|
| 1585 | c|=8;
|
---|
| 1586 |
|
---|
| 1587 | if (position.z<(mMin.z-Limits::Small))
|
---|
| 1588 | c|=16;
|
---|
| 1589 | else
|
---|
| 1590 | if (position.z>(mMax.z+Limits::Small))
|
---|
| 1591 | c|=32;
|
---|
| 1592 |
|
---|
| 1593 | return c;
|
---|
| 1594 | }
|
---|
| 1595 |
|
---|
| 1596 |
|
---|
| 1597 | Rectangle3
|
---|
| 1598 | AxisAlignedBox3::GetFace(const int face) const
|
---|
| 1599 | {
|
---|
| 1600 | Vector3 v[4];
|
---|
| 1601 | switch (face) {
|
---|
| 1602 |
|
---|
| 1603 | case 0:
|
---|
| 1604 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1605 | v[2].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1606 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1607 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1608 | break;
|
---|
| 1609 |
|
---|
| 1610 | case 1:
|
---|
| 1611 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1612 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1613 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1614 | v[3].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1615 | break;
|
---|
| 1616 |
|
---|
| 1617 | case 2:
|
---|
| 1618 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1619 | v[2].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1620 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1621 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1622 | break;
|
---|
| 1623 |
|
---|
| 1624 | case 3:
|
---|
| 1625 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1626 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1627 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1628 | v[3].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1629 | break;
|
---|
| 1630 |
|
---|
| 1631 | case 4:
|
---|
| 1632 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1633 | v[2].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1634 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1635 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1636 | break;
|
---|
| 1637 |
|
---|
| 1638 | case 5:
|
---|
| 1639 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1640 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1641 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1642 | v[3].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1643 | break;
|
---|
| 1644 | }
|
---|
| 1645 |
|
---|
| 1646 | return Rectangle3(v[0], v[1], v[2], v[3]);
|
---|
| 1647 | }
|
---|
[313] | 1648 |
|
---|
[318] | 1649 | struct VertexData
|
---|
| 1650 | {
|
---|
| 1651 | Vector3 mVertex;
|
---|
| 1652 | float mAngle;
|
---|
| 1653 |
|
---|
| 1654 | VertexData(Vector3 vtx, float angle): mVertex(vtx), mAngle(angle)
|
---|
| 1655 | {}
|
---|
| 1656 |
|
---|
| 1657 | bool operator<(const VertexData &b) const
|
---|
| 1658 | { |
---|
[321] | 1659 | return mAngle > b.mAngle; |
---|
[318] | 1660 | }
|
---|
| 1661 | };
|
---|
| 1662 |
|
---|
[312] | 1663 | // TODO: use a table to avoid normal and distance computations
|
---|
[318] | 1664 | Polygon3 *AxisAlignedBox3::CrossSection(const Plane3 &plane) |
---|
[312] | 1665 | { |
---|
[318] | 1666 | Polygon3 *planePoly = new Polygon3(); |
---|
| 1667 | |
---|
[312] | 1668 | int side[8]; |
---|
[318] | 1669 | bool onFrontSide = false, onBackSide = false; |
---|
| 1670 | |
---|
[312] | 1671 | Vector3 vtx; |
---|
[318] | 1672 | //-- compute classification of vertices |
---|
[312] | 1673 | for (int i = 0; i < 8; ++i) |
---|
| 1674 | { |
---|
| 1675 | GetVertex(i, vtx); |
---|
[329] | 1676 | side[i] = plane.Side(vtx); |
---|
[312] | 1677 | if (side[i] > 0) |
---|
| 1678 | onFrontSide = true; |
---|
| 1679 | else if (side[i] < 0) |
---|
| 1680 | onBackSide = true; |
---|
| 1681 | else // vertex coincident => push_back |
---|
[318] | 1682 | planePoly->mVertices.push_back(vtx); |
---|
[312] | 1683 | } |
---|
| 1684 | |
---|
[318] | 1685 | //-- find intersections |
---|
| 1686 | if (onFrontSide && onBackSide) |
---|
[312] | 1687 | { |
---|
[318] | 1688 | Vector3 ptA, ptB; |
---|
| 1689 | for (int i = 0; i < 12; ++ i) |
---|
| 1690 | { |
---|
| 1691 | int aIdx, bIdx; |
---|
| 1692 | GetEdge(i, aIdx, bIdx); |
---|
[312] | 1693 | |
---|
[318] | 1694 | ptA = GetVertex(aIdx); |
---|
| 1695 | ptB = GetVertex(bIdx); |
---|
[312] | 1696 | |
---|
[318] | 1697 | int sideA = side[aIdx]; |
---|
| 1698 | int sideB = side[bIdx]; |
---|
[312] | 1699 | |
---|
[318] | 1700 | if (((sideA > 0) && (sideB < 0)) || (sideA < 0) && (sideB > 0)) |
---|
| 1701 | planePoly->mVertices.push_back(plane.FindIntersection(ptA, ptB)); |
---|
| 1702 | } |
---|
[312] | 1703 | } |
---|
| 1704 | |
---|
[318] | 1705 | // order intersectioins |
---|
| 1706 | if (planePoly->mVertices.size() > 3) |
---|
[312] | 1707 | { |
---|
[318] | 1708 | Vector3 centerOfMass(0); |
---|
[359] | 1709 | int i; |
---|
[318] | 1710 | // compute center of mass |
---|
[359] | 1711 | for (i = 0; i < (int)planePoly->mVertices.size(); ++ i) |
---|
[318] | 1712 | centerOfMass += planePoly->mVertices[i]; |
---|
| 1713 | |
---|
| 1714 | centerOfMass /= (float)planePoly->mVertices.size(); |
---|
| 1715 | |
---|
| 1716 | vector<VertexData> vertexData; |
---|
| 1717 | |
---|
| 1718 | Vector3 refVec = Normalize(centerOfMass - planePoly->mVertices[0]); |
---|
| 1719 | |
---|
| 1720 | // compute angle to reference point |
---|
[333] | 1721 | for (i = 1; i < (int)planePoly->mVertices.size(); ++ i) |
---|
[359] | 1722 | { |
---|
| 1723 | float angle = |
---|
| 1724 | Angle(refVec, centerOfMass - planePoly->mVertices[i], plane.mNormal); |
---|
| 1725 | |
---|
| 1726 | vertexData.push_back(VertexData(planePoly->mVertices[i], angle)); |
---|
| 1727 | } |
---|
[318] | 1728 | |
---|
| 1729 | std::stable_sort(vertexData.begin(), vertexData.end()); |
---|
[313] | 1730 | |
---|
[318] | 1731 | // update vertices |
---|
[333] | 1732 | for (i = 1; i < (int)planePoly->mVertices.size(); ++ i) |
---|
[318] | 1733 | planePoly->mVertices[i] = vertexData[i - 1].mVertex; |
---|
| 1734 | } |
---|
| 1735 | else if (planePoly->mVertices.size() == 3) |
---|
| 1736 | { |
---|
| 1737 | // fix orientation if needed |
---|
| 1738 | if (DotProd(planePoly->GetNormal(), plane.mNormal) < 0)
|
---|
| 1739 | {
|
---|
| 1740 | Vector3 v = planePoly->mVertices[1];
|
---|
| 1741 | planePoly->mVertices[1] = planePoly->mVertices[2];
|
---|
| 1742 | planePoly->mVertices[2] = v;
|
---|
[312] | 1743 | } |
---|
| 1744 | } |
---|
[313] | 1745 | |
---|
[312] | 1746 | return planePoly; |
---|
[333] | 1747 | } |
---|