[162] | 1 | #ifndef _AxisAlignedBox3_H__ |
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| 2 | #define _AxisAlignedBox3_H__ |
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| 3 | |
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| 4 | |
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| 5 | #include "Matrix4x4.h" |
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| 6 | #include "Vector3.h" |
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| 7 | #include "Plane3.h" |
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| 8 | |
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| 9 | class Plane3; |
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| 10 | class Ray; |
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| 11 | |
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| 12 | |
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| 13 | // -------------------------------------------------------- |
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| 14 | // CAABox class. |
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| 15 | // This is a box in 3-space, defined by min and max |
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| 16 | // corner vectors. Many useful operations are defined |
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| 17 | // on this |
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| 18 | // -------------------------------------------------------- |
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| 19 | class AxisAlignedBox3 |
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| 20 | { |
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| 21 | protected: |
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| 22 | Vector3 mMin, mMax; |
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| 23 | public: |
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| 24 | // Constructors. |
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| 25 | AxisAlignedBox3() { } |
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| 26 | AxisAlignedBox3(const Vector3 &nMin, const Vector3 &nMax) |
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| 27 | { |
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| 28 | mMin = nMin; mMax = nMax; |
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| 29 | } |
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| 30 | |
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| 31 | // AxisAlignedBox3(const Vector3 ¢er, const float radius):min(center - Vector3(radius)), |
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| 32 | // max(center + Vector3(radius)) {} |
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| 33 | |
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| 34 | // initialization to the non existing bounding box |
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| 35 | void Initialize() { |
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| 36 | mMin = Vector3(MAXFLOAT); |
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| 37 | mMax = Vector3(-MAXFLOAT); |
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| 38 | } |
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| 39 | |
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| 40 | // The center of the box |
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| 41 | Vector3 Center() const { return 0.5 * (mMin + mMax); } |
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| 42 | |
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| 43 | // The diagonal of the box |
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| 44 | Vector3 Diagonal() const { return (mMax -mMin); } |
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| 45 | |
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| 46 | float Center(const int axis) const { |
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| 47 | return 0.5 * (mMin[axis] + mMax[axis]); |
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| 48 | } |
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| 49 | |
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| 50 | float Min(const int axis) const { |
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| 51 | return mMin[axis]; |
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| 52 | } |
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| 53 | |
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| 54 | float Max(const int axis) const { |
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| 55 | return mMax[axis]; |
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| 56 | } |
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| 57 | |
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| 58 | // Read-only const access tomMin and max vectors using references |
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| 59 | const Vector3& Min() const { return mMin;} |
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| 60 | const Vector3& Max() const { return mMax;} |
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| 61 | |
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| 62 | void Enlarge (const Vector3 &v) { |
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| 63 | mMax += v; |
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| 64 | mMin -= v; |
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| 65 | } |
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| 66 | |
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| 67 | void SetMin(int axis, const float value) { |
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| 68 | mMin[axis] = value; |
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| 69 | } |
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| 70 | |
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| 71 | void SetMax(int axis, const float value) { |
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| 72 | mMax[axis] = value; |
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| 73 | } |
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| 74 | |
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| 75 | // Decrease box by given splitting plane |
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| 76 | void Reduce(int axis, int right, float value) { |
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| 77 | if ( (value >=mMin[axis]) && (value <= mMax[axis]) ) |
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| 78 | if (right) |
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| 79 | mMin[axis] = value; |
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| 80 | else |
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| 81 | mMax[axis] = value; |
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| 82 | } |
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| 83 | |
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| 84 | // the size of the box along all the axes |
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| 85 | Vector3 Size() const { return mMax -mMin; } |
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| 86 | |
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| 87 | // Return whether the box is unbounded. Unbounded boxes appear |
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| 88 | // when unbounded objects such as quadric surfaces are included. |
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| 89 | bool Unbounded() const; |
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| 90 | |
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| 91 | // Expand the axis-aligned box to include the given object. |
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| 92 | void Include(const Vector3 &newpt); |
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| 93 | void Include(const AxisAlignedBox3 &bbox); |
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| 94 | // Expand the axis-aligned box to include given values in particular axis |
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| 95 | void Include(const int &axis, const float &newBound); |
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| 96 | |
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| 97 | |
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| 98 | |
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| 99 | // Overlap returns 1 if the two axis-aligned boxes overlap .. even weakly |
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| 100 | friend inline bool Overlap(const AxisAlignedBox3 &, const AxisAlignedBox3 &); |
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| 101 | |
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| 102 | // Overlap returns 1 if the two axis-aligned boxes overlap .. only strongly |
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| 103 | friend inline bool OverlapS(const AxisAlignedBox3 &,const AxisAlignedBox3 &); |
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| 104 | |
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| 105 | // Overlap returns 1 if the two axis-aligned boxes overlap for a given |
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| 106 | // epsilon. If eps > 0.0, then the boxes has to have the real intersection |
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| 107 | // box, if eps < 0.0, then the boxes need not intersect really, they |
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| 108 | // can be at eps distance in the projection |
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| 109 | friend inline bool Overlap(const AxisAlignedBox3 &, |
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| 110 | const AxisAlignedBox3 &, |
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| 111 | float eps); |
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| 112 | |
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| 113 | // Includes returns true if a includes b (completely |
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| 114 | bool Includes(const AxisAlignedBox3 &b) const; |
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| 115 | |
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| 116 | virtual int IsInside(const Vector3 &v) const; |
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| 117 | |
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| 118 | // Test if the box is really sensefull |
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| 119 | virtual bool IsCorrect(); |
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| 120 | |
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| 121 | // To answer true requires the box of real volume of non-zero value |
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| 122 | bool IsSingularOrIncorrect() const; |
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| 123 | |
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| 124 | // When the box is not of non-zero or negative surface area |
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| 125 | bool IsCorrectAndNotPoint() const; |
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| 126 | |
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| 127 | // Returns true when the box degenerates to a point |
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| 128 | bool IsPoint() const; |
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| 129 | |
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| 130 | void |
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| 131 | GetSqrDistances(const Vector3 &point, |
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| 132 | float &minDistance, |
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| 133 | float &maxDistance |
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| 134 | ) const; |
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| 135 | |
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| 136 | // returns true, when the sphere specified by the origin and radius |
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| 137 | // fully contains the box |
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| 138 | bool IsFullyContainedInSphere(const Vector3 ¢er, float radius) const; |
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| 139 | |
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| 140 | // returns true, when the volume of the sphere and volume of the |
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| 141 | // axis aligned box has no intersection |
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| 142 | bool HasNoIntersectionWithSphere(const Vector3 ¢er, |
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| 143 | float radius) const; |
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| 144 | |
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| 145 | |
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| 146 | // Given a sphere described by the center and radius, |
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| 147 | // the fullowing function returns: |
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| 148 | // -1 ... the sphere and the box are completely separate |
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| 149 | // 0 ... the sphere and the box only partially overlap |
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| 150 | // 1 ... the sphere contains fully the box |
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| 151 | // Note: the case when box fully contains the sphere is not reported |
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| 152 | // since it was not required. |
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| 153 | int MutualPositionWithSphere(const Vector3 ¢er, float radius) const; |
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| 154 | |
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| 155 | // Given a cube described by the center and half-size (radius), |
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| 156 | // the following function returns: |
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| 157 | // -1 ... the cube and the box are completely separate |
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| 158 | // 0 ... the cube and the box only partially overlap |
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| 159 | // 1 ... the cube contains fully the box |
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| 160 | int MutualPositionWithCube(const Vector3 ¢er, float halfSize) const; |
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| 161 | |
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| 162 | // Returns the smallest axis-aligned box that includes all points |
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| 163 | // inside the two given boxes. |
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| 164 | friend inline AxisAlignedBox3 Union(const AxisAlignedBox3 &x, |
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| 165 | const AxisAlignedBox3 &y); |
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| 166 | |
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| 167 | // Returns the intersection of two axis-aligned boxes. |
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| 168 | friend inline AxisAlignedBox3 Intersect(const AxisAlignedBox3 &x, |
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| 169 | const AxisAlignedBox3 &y); |
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| 170 | |
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| 171 | // Given 4x4 matrix, transform the current box to new one. |
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| 172 | friend inline AxisAlignedBox3 Transform(const AxisAlignedBox3 &box, |
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| 173 | const Matrix4x4 &tform); |
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| 174 | |
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| 175 | // returns true when two boxes are completely equal |
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| 176 | friend inline int operator== (const AxisAlignedBox3 &A, const AxisAlignedBox3 &B); |
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| 177 | |
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| 178 | virtual float SurfaceArea() const; |
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| 179 | virtual float GetVolume() const { |
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| 180 | return (mMax.x -mMin.x) * (mMax.y -mMin.y) * (mMax.z - mMin.z); |
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| 181 | } |
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| 182 | |
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| 183 | // Six faces are distuinguished by their name. |
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| 184 | enum EFaces { ID_Back = 0, ID_Left = 1, ID_Bottom = 2, ID_Front = 3, |
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| 185 | ID_Right = 4, ID_Top = 5}; |
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| 186 | |
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| 187 | // Compute tmin and tmax for a ray, whenever required .. need not pierce box |
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| 188 | int ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax) const; |
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| 189 | |
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| 190 | // Compute tmin and tmax for a ray, whenever required .. need not pierce box |
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| 191 | int ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax, |
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| 192 | EFaces &entryFace, EFaces &exitFace) const; |
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| 193 | |
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| 194 | // If a ray pierces the box .. returns 1, otherwise 0. |
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| 195 | // Computes the signed distances for case: tmin < tmax and tmax > 0 |
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| 196 | int GetMinMaxT(const Ray &ray, float *tmin, float *tmax) const; |
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| 197 | // computes the signed distances for case: tmin < tmax and tmax > 0 |
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| 198 | int GetMinMaxT(const Ray &ray, float *tmin, float *tmax, |
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| 199 | EFaces &entryFace, EFaces &exitFace) const; |
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| 200 | |
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| 201 | // Writes a brief description of the object, indenting by the given |
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| 202 | // number of spaces first. |
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| 203 | virtual void Describe(ostream& app, int ind) const; |
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| 204 | |
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| 205 | // For edge .. number <0..11> returns two incident vertices |
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| 206 | void GetEdge(const int edge, Vector3 *a, Vector3 *b) const; |
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| 207 | |
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| 208 | // Compute the coordinates of one vertex of the box for 0/1 in each axis |
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| 209 | // 0 .. smaller coordinates, 1 .. large coordinates |
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| 210 | Vector3 GetVertex(int xAxis, int yAxis, int zAxis) const; |
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| 211 | |
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| 212 | // Compute the vertex for number N=<0..7>, N = 4*x + 2*y + z, where |
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| 213 | // x,y,z are either 0 or 1; (0 .. lower coordinate, 1 .. large coordinate) |
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| 214 | // (xmin,ymin, zmin) .. N = 0, (xmax, ymax, zmax) .. N= 7 |
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| 215 | void GetVertex(int N, Vector3 &vertex) const; |
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| 216 | |
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| 217 | // Returns 1, if the box includes on arbitrary face a given box |
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| 218 | int IsPiercedByBox(const AxisAlignedBox3 &box, int &axis) const; |
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| 219 | |
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| 220 | // For a given point returns the region, where the point is located |
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| 221 | // there are 27 regions (0..26) .. determined by the planes embedding in the |
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| 222 | // sides of the bounding box (0 .. lower the position of the box, |
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| 223 | // 1 .. inside the box, 2 .. greater than box). The region number is given as |
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| 224 | // R = 9*x + 3*y + z ; e.g. region .. inside the box is 13. |
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| 225 | int GetRegionID(const Vector3 &point) const; |
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| 226 | |
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| 227 | // Set the corner point of rectangle on the face of bounding box |
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| 228 | // given by the index number and the rectangle lying on this face |
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| 229 | // void GetFaceRectCorner(const CRectLeaf2D *rect, EFaces faceIndx, |
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| 230 | // const int &cornerIndx, Vector3 &cornerPoint); |
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| 231 | |
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| 232 | // Project the box to a plane given a normal vector of this plane. Computes |
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| 233 | // the surface area of projected silhouettes for parallel projection. |
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| 234 | float ProjectToPlaneSA(const Vector3 &normal) const; |
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| 235 | |
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| 236 | // Computes projected surface area of the box to a given viewing plane |
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| 237 | // given a viewpoint. This corresponds the probability, the box will |
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| 238 | // be hit by the ray .. moreover returns .. the region number (0-26). |
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| 239 | // the function supposes all the points lie of the box lies in the viewing |
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| 240 | // frustrum !!! The positive halfspace of viewplane has to contain |
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| 241 | // viewpoint. "projectionType" == 0 .. perspective projection, |
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| 242 | // == 1 .. parallel projection. |
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| 243 | float ProjectToPlaneSA(const Plane3 &viewplane, |
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| 244 | const Vector3 &viewpoint, |
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| 245 | int *tcase, |
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| 246 | const float &maxSA, |
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| 247 | int projectionType) const; |
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| 248 | |
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| 249 | // Computes projected surface area of the box to a given viewing plane |
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| 250 | // and viewpoint. It clipps the area by all the planes given .. they should |
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| 251 | // define the viewing frustrum. Variable tclip defines, which planes are |
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| 252 | // used for clipping, parameter 31 is the most general, clip all the plane. |
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| 253 | // 1 .. clip left, 2 .. clip top, 4 .. clip right, 8 .. clip bottom, |
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| 254 | // 16 .. clip supporting plane(its normal towards the viewing frustrum). |
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| 255 | // "typeProjection" == 0 .. perspective projection, |
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| 256 | // == 1 .. parallel projection |
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| 257 | float ProjectToPlaneSA(const Plane3 &viewplane, |
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| 258 | const Vector3 &viewpoint, |
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| 259 | int *tcase, int &tclip, |
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| 260 | const Plane3 &leftPlane, |
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| 261 | const Plane3 &topPlane, |
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| 262 | const Plane3 &rightPlane, |
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| 263 | const Plane3 &bottomPlane, |
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| 264 | const Plane3 &suppPlane, |
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| 265 | const float &maxSA, |
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| 266 | int typeProjection) const; |
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| 267 | |
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| 268 | // Projects the box to a unit sphere enclosing a given viewpoint and |
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| 269 | // returns the solid angle of the box projected to a unit sphere |
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| 270 | float ProjectToSphereSA(const Vector3 &viewpoint, int *tcase) const; |
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| 271 | |
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| 272 | |
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| 273 | #define __EXTENT_HACK |
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| 274 | // get the extent of face |
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| 275 | float GetExtent(const int &face) const { |
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| 276 | #if defined(__EXTENT_HACK) && defined(__VECTOR_HACK) |
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| 277 | return mMin[face]; |
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| 278 | #else |
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| 279 | if (face < 3) |
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| 280 | return mMin[face]; |
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| 281 | else |
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| 282 | return mMax[face-3]; |
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| 283 | #endif |
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| 284 | } |
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| 285 | |
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| 286 | // The vertices that form boundaries of the projected bounding box |
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| 287 | // for all the regions possible, number of regions is 3^3 = 27, |
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| 288 | // since two parallel sides of bbox forms three disjoint spaces |
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| 289 | // the vertices are given in anti-clockwise order .. stopped by -1 elem. |
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| 290 | static const int bvertices[27][9]; |
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| 291 | |
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| 292 | // The list of all faces visible from a given region (except region 13) |
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| 293 | // the faces are identified by triple: (axis, min-vertex, max-vertex), |
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| 294 | // that is maximaly three triples are defined. axis = 0 (x-axis), |
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| 295 | // axis = 1 (y-axis), axis = 2 (z-axis), -1 .. terminator. Is is always |
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| 296 | // true that: min-vertex < max-vertex for all coordinates excluding axis |
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| 297 | static const int bfaces[27][10]; |
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| 298 | |
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| 299 | // The correct corners indexed starting from entry face to exit face |
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| 300 | // first index determines entry face, second index exit face, and |
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| 301 | // the two numbers (indx, inc) determines: ind = the index on the exit |
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| 302 | // face, when starting from the vertex 0 on entry face, 'inc' is |
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| 303 | // the increment when we go on entry face in order 0,1,2,3 to create |
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| 304 | // convex shaft with the rectangle on exit face. That is, inc = -1 or 1. |
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| 305 | static const int pairFaceRects[6][6][2]; |
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| 306 | |
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| 307 | // The vertices that form CLOSEST points with respect to the region |
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| 308 | // for all the regions possible, number of regions is 3^3 = 27, |
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| 309 | // since two parallel sides of bbox forms three disjoint spaces. |
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| 310 | // The vertices are given in anti-clockwise order, stopped by -1 elem, |
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| 311 | // at most 8 points, at least 1 point. |
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| 312 | static const int cvertices[27][9]; |
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| 313 | static const int csvertices[27][6]; |
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| 314 | |
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| 315 | // The vertices that form FARTHEST points with respect to the region |
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| 316 | // for all the regions possible, number of regions is 3^3 = 27, |
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| 317 | // since two parallel sides of bbox forms three disjoint spaces. |
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| 318 | // The vertices are given in anti-clockwise order, stopped by -1 elem, |
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| 319 | // at most 8 points, at least 1 point. |
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| 320 | static const int fvertices[27][9]; |
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| 321 | static const int fsvertices[27][9]; |
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| 322 | |
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| 323 | // input and output operator with stream |
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| 324 | friend ostream& operator<<(ostream &s, const AxisAlignedBox3 &A); |
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| 325 | friend istream& operator>>(istream &s, AxisAlignedBox3 &A); |
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| 326 | |
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| 327 | protected: |
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| 328 | // definition of friend functions |
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| 329 | friend class Ray; |
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| 330 | }; |
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| 331 | |
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| 332 | // -------------------------------------------------------------------------- |
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| 333 | // Implementation of inline (member) functions |
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| 334 | |
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| 335 | inline bool |
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| 336 | Overlap(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y) |
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| 337 | { |
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| 338 | if (x.mMax.x < y.mMin.x || |
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| 339 | x.mMin.x > y.mMax.x || |
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| 340 | x.mMax.y < y.mMin.y || |
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| 341 | x.mMin.y > y.mMax.y || |
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| 342 | x.mMax.z < y.mMin.z || |
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| 343 | x.mMin.z > y.mMax.z) { |
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| 344 | return false; |
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| 345 | } |
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| 346 | return true; |
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| 347 | } |
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| 348 | |
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| 349 | inline bool |
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| 350 | OverlapS(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y) |
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| 351 | { |
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| 352 | if (x.mMax.x <= y.mMin.x || |
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| 353 | x.mMin.x >= y.mMax.x || |
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| 354 | x.mMax.y <= y.mMin.y || |
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| 355 | x.mMin.y >= y.mMax.y || |
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| 356 | x.mMax.z <= y.mMin.z || |
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| 357 | x.mMin.z >= y.mMax.z) { |
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| 358 | return false; |
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| 359 | } |
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| 360 | return true; |
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| 361 | } |
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| 362 | |
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| 363 | inline bool |
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| 364 | Overlap(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y, float eps) |
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| 365 | { |
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| 366 | if ( (x.mMax.x - eps) < y.mMin.x || |
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| 367 | (x.mMin.x + eps) > y.mMax.x || |
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| 368 | (x.mMax.y - eps) < y.mMin.y || |
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| 369 | (x.mMin.y + eps) > y.mMax.y || |
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| 370 | (x.mMax.z - eps) < y.mMin.z || |
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| 371 | (x.mMin.z + eps) > y.mMax.z ) { |
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| 372 | return false; |
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| 373 | } |
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| 374 | return true; |
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| 375 | } |
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| 376 | |
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| 377 | inline AxisAlignedBox3 |
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| 378 | Intersect(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y) |
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| 379 | { |
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| 380 | if (x.Unbounded()) |
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| 381 | return y; |
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| 382 | else |
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| 383 | if (y.Unbounded()) |
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| 384 | return x; |
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| 385 | AxisAlignedBox3 ret = x; |
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| 386 | if (Overlap(ret, y)) { |
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| 387 | Maximize(ret.mMin, y.mMin); |
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| 388 | Minimize(ret.mMax, y.mMax); |
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| 389 | return ret; |
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| 390 | } |
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| 391 | else // Null intersection. |
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| 392 | return AxisAlignedBox3(Vector3(0), Vector3(0)); |
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| 393 | // return AxisAlignedBox3(Vector3(0), Vector3(-1)); |
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| 394 | } |
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| 395 | |
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| 396 | inline AxisAlignedBox3 |
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| 397 | Union(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y) |
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| 398 | { |
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| 399 | Vector3 min = x.mMin; |
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| 400 | Vector3 max = x.mMax; |
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| 401 | Minimize(min, y.mMin); |
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| 402 | Maximize(max, y.mMax); |
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| 403 | return AxisAlignedBox3(min, max); |
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| 404 | } |
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| 405 | |
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| 406 | inline AxisAlignedBox3 |
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| 407 | Transform(const AxisAlignedBox3 &box, const Matrix4x4 &tform) |
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| 408 | { |
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| 409 | Vector3 mmin(MAXFLOAT); |
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| 410 | Vector3 mmax(-MAXFLOAT); |
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| 411 | |
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| 412 | AxisAlignedBox3 ret(mmin, mmax); |
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| 413 | ret.Include(tform * Vector3(box.mMin.x, box.mMin.y, box.mMin.z)); |
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| 414 | ret.Include(tform * Vector3(box.mMin.x, box.mMin.y, box.mMax.z)); |
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| 415 | ret.Include(tform * Vector3(box.mMin.x, box.mMax.y, box.mMin.z)); |
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| 416 | ret.Include(tform * Vector3(box.mMin.x, box.mMax.y, box.mMax.z)); |
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| 417 | ret.Include(tform * Vector3(box.mMax.x, box.mMin.y, box.mMin.z)); |
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| 418 | ret.Include(tform * Vector3(box.mMax.x, box.mMin.y, box.mMax.z)); |
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| 419 | ret.Include(tform * Vector3(box.mMax.x, box.mMax.y, box.mMin.z)); |
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| 420 | ret.Include(tform * Vector3(box.mMax.x, box.mMax.y, box.mMax.z)); |
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| 421 | return ret; |
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| 422 | } |
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| 423 | |
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| 424 | |
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| 425 | inline int operator==(const AxisAlignedBox3 &A, const AxisAlignedBox3 &B) |
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| 426 | { |
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| 427 | return (A.mMin == B.mMin) && (A.mMax == B.mMax); |
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| 428 | } |
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| 429 | |
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| 430 | |
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| 431 | |
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| 432 | |
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| 433 | |
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| 434 | #endif |
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