[372] | 1 | #ifndef _AxisAlignedBox3_H__
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| 2 | #define _AxisAlignedBox3_H__
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| 3 |
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| 4 | #include "Rectangle3.h"
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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 Ray;
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| 10 | class Polygon3;
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[486] | 11 | class Mesh;
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[372] | 12 | // --------------------------------------------------------
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| 13 | // CAABox class.
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| 14 | // This is a box in 3-space, defined by min and max
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| 15 | // corner vectors. Many useful operations are defined
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| 16 | // on this
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| 17 | // --------------------------------------------------------
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| 18 | class AxisAlignedBox3
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| 19 | {
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| 20 | protected:
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| 21 | Vector3 mMin, mMax;
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| 22 | public:
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| 23 | // Constructors.
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| 24 | AxisAlignedBox3() { }
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| 25 | AxisAlignedBox3(const Vector3 &nMin, const Vector3 &nMax)
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| 26 | {
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| 27 | mMin = nMin; mMax = nMax;
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| 28 | }
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| 29 |
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| 30 | // AxisAlignedBox3(const Vector3 ¢er, const float radius):min(center - Vector3(radius)),
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| 31 | // max(center + Vector3(radius)) {}
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| 32 |
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| 33 | // initialization to the non existing bounding box
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| 34 | void Initialize() {
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| 35 | mMin = Vector3(MAXFLOAT);
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| 36 | mMax = Vector3(-MAXFLOAT);
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| 37 | }
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| 38 |
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| 39 | // The center of the box
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| 40 | Vector3 Center() const { return 0.5 * (mMin + mMax); }
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| 41 |
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| 42 | // The diagonal of the box
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| 43 | Vector3 Diagonal() const { return (mMax -mMin); }
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| 44 |
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| 45 | float Center(const int axis) const {
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| 46 | return 0.5f * (mMin[axis] + mMax[axis]);
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| 47 | }
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| 48 |
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| 49 | float Min(const int axis) const {
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| 50 | return mMin[axis];
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| 51 | }
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| 52 |
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| 53 | float Max(const int axis) const {
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| 54 | return mMax[axis];
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| 55 | }
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[387] | 56 |
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[459] | 57 | float Size(const int axis) const {
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[387] | 58 | return Max(axis) - Min(axis);
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| 59 | }
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| 60 |
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[372] | 61 | // Read-only const access tomMin and max vectors using references
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| 62 | const Vector3& Min() const { return mMin;}
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| 63 | const Vector3& Max() const { return mMax;}
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| 64 |
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| 65 | void Enlarge (const Vector3 &v) {
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| 66 | mMax += v;
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| 67 | mMin -= v;
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| 68 | }
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| 69 |
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[492] | 70 |
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[372] | 71 | void SetMin(const Vector3 &v) {
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| 72 | mMin = v;
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| 73 | }
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| 74 |
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| 75 | void SetMax(const Vector3 &v) {
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| 76 | mMax = v;
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| 77 | }
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| 78 |
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| 79 | void SetMin(int axis, const float value) {
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| 80 | mMin[axis] = value;
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| 81 | }
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| 82 |
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| 83 | void SetMax(int axis, const float value) {
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| 84 | mMax[axis] = value;
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| 85 | }
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| 86 |
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| 87 | // Decrease box by given splitting plane
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| 88 | void Reduce(int axis, int right, float value) {
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| 89 | if ( (value >=mMin[axis]) && (value <= mMax[axis]) )
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| 90 | if (right)
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[376] | 91 | mMin[axis] = value;
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[372] | 92 | else
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| 93 | mMax[axis] = value;
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| 94 | }
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[376] | 95 |
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[372] | 96 | // the size of the box along all the axes
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| 97 | Vector3 Size() const { return mMax - mMin; }
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| 98 |
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| 99 | // Return whether the box is unbounded. Unbounded boxes appear
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| 100 | // when unbounded objects such as quadric surfaces are included.
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| 101 | bool Unbounded() const;
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| 102 |
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| 103 | // Expand the axis-aligned box to include the given object.
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| 104 | void Include(const Vector3 &newpt);
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| 105 | void Include(const Polygon3 &newpoly);
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| 106 | void Include(const AxisAlignedBox3 &bbox);
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[538] | 107 | void Include(Mesh *mesh);
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[372] | 108 | // Expand the axis-aligned box to include given values in particular axis
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| 109 | void Include(const int &axis, const float &newBound);
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| 110 |
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| 111 |
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| 112 | int
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| 113 | Side(const Plane3 &plane) const;
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| 114 |
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| 115 | // Overlap returns 1 if the two axis-aligned boxes overlap .. even weakly
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| 116 | friend inline bool Overlap(const AxisAlignedBox3 &, const AxisAlignedBox3 &);
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| 117 |
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| 118 | // Overlap returns 1 if the two axis-aligned boxes overlap .. only strongly
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| 119 | friend inline bool OverlapS(const AxisAlignedBox3 &,const AxisAlignedBox3 &);
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| 120 |
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| 121 | // Overlap returns 1 if the two axis-aligned boxes overlap for a given
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| 122 | // epsilon. If eps > 0.0, then the boxes has to have the real intersection
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| 123 | // box, if eps < 0.0, then the boxes need not intersect really, they
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| 124 | // can be at eps distance in the projection
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| 125 | friend inline bool Overlap(const AxisAlignedBox3 &,
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| 126 | const AxisAlignedBox3 &,
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| 127 | float eps);
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| 128 |
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| 129 | // Includes returns true if a includes b (completely
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| 130 | bool Includes(const AxisAlignedBox3 &b) const;
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| 131 |
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| 132 | virtual int IsInside(const Vector3 &v) const;
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| 133 |
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| 134 | // Test if the box is really sensefull
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| 135 | virtual bool IsCorrect();
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| 136 |
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| 137 | // To answer true requires the box of real volume of non-zero value
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| 138 | bool IsSingularOrIncorrect() const;
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| 139 |
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| 140 | // When the box is not of non-zero or negative surface area
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| 141 | bool IsCorrectAndNotPoint() const;
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| 142 |
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| 143 | // Returns true when the box degenerates to a point
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| 144 | bool IsPoint() const;
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| 145 |
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[492] | 146 | void Scale(const float scale) {
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| 147 | Vector3 newSize = Size()*(scale*0.5f);
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| 148 | Vector3 center = Center();
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| 149 | mMin = center - newSize;
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| 150 | mMax = center + newSize;
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| 151 | }
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| 152 |
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[372] | 153 | void
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| 154 | GetSqrDistances(const Vector3 &point,
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| 155 | float &minDistance,
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| 156 | float &maxDistance
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| 157 | ) const;
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| 158 |
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| 159 | // returns true, when the sphere specified by the origin and radius
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| 160 | // fully contains the box
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| 161 | bool IsFullyContainedInSphere(const Vector3 ¢er, float radius) const;
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| 162 |
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| 163 | // returns true, when the volume of the sphere and volume of the
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| 164 | // axis aligned box has no intersection
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| 165 | bool HasNoIntersectionWithSphere(const Vector3 ¢er,
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| 166 | float radius) const;
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| 167 |
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| 168 |
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| 169 | // Given a sphere described by the center and radius,
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| 170 | // the fullowing function returns:
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| 171 | // -1 ... the sphere and the box are completely separate
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| 172 | // 0 ... the sphere and the box only partially overlap
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| 173 | // 1 ... the sphere contains fully the box
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| 174 | // Note: the case when box fully contains the sphere is not reported
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| 175 | // since it was not required.
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| 176 | int MutualPositionWithSphere(const Vector3 ¢er, float radius) const;
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| 177 |
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| 178 | // Given a cube described by the center and half-size (radius),
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| 179 | // the following function returns:
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| 180 | // -1 ... the cube and the box are completely separate
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| 181 | // 0 ... the cube and the box only partially overlap
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| 182 | // 1 ... the cube contains fully the box
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| 183 | int MutualPositionWithCube(const Vector3 ¢er, float halfSize) const;
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| 184 |
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| 185 |
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[487] | 186 | Vector3 GetRandomPoint() const {
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[372] | 187 | Vector3 size = Size();
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[534] | 188 | return mMin + Vector3(RandomValue(0.0f, size.x),
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| 189 | RandomValue(0.0f, size.y),
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| 190 | RandomValue(0.0f, size.z));
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[372] | 191 | }
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[492] | 192 |
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| 193 |
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| 194 | Vector3 GetPoint(const Vector3 &p) const {
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| 195 | return mMin + p*Size();
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| 196 | }
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| 197 |
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[372] | 198 | // Returns the smallest axis-aligned box that includes all points
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| 199 | // inside the two given boxes.
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| 200 | friend inline AxisAlignedBox3 Union(const AxisAlignedBox3 &x,
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| 201 | const AxisAlignedBox3 &y);
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| 202 |
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| 203 | // Returns the intersection of two axis-aligned boxes.
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| 204 | friend inline AxisAlignedBox3 Intersect(const AxisAlignedBox3 &x,
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| 205 | const AxisAlignedBox3 &y);
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| 206 |
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| 207 | // Given 4x4 matrix, transform the current box to new one.
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| 208 | friend inline AxisAlignedBox3 Transform(const AxisAlignedBox3 &box,
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| 209 | const Matrix4x4 &tform);
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| 210 |
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| 211 |
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| 212 | // returns true when two boxes are completely equal
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| 213 | friend inline int operator== (const AxisAlignedBox3 &A, const AxisAlignedBox3 &B);
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| 214 |
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| 215 | virtual float SurfaceArea() const;
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| 216 | virtual float GetVolume() const {
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| 217 | return (mMax.x - mMin.x) * (mMax.y - mMin.y) * (mMax.z - mMin.z);
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| 218 | }
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| 219 |
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| 220 | // Six faces are distuinguished by their name.
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| 221 | enum EFaces { ID_Back = 0, ID_Left = 1, ID_Bottom = 2, ID_Front = 3,
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| 222 | ID_Right = 4, ID_Top = 5};
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| 223 |
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[492] | 224 | int
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| 225 | ComputeMinMaxT(const Vector3 &origin,
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| 226 | const Vector3 &direction,
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| 227 | float *tmin,
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| 228 | float *tmax) const;
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| 229 |
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[372] | 230 | // Compute tmin and tmax for a ray, whenever required .. need not pierce box
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| 231 | int ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax) const;
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| 232 |
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| 233 | // Compute tmin and tmax for a ray, whenever required .. need not pierce box
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[492] | 234 | int ComputeMinMaxT(const Ray &ray,
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| 235 | float *tmin,
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| 236 | float *tmax,
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| 237 | EFaces &entryFace,
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| 238 | EFaces &exitFace) const;
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[372] | 239 |
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| 240 | // If a ray pierces the box .. returns 1, otherwise 0.
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| 241 | // Computes the signed distances for case: tmin < tmax and tmax > 0
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| 242 | int GetMinMaxT(const Ray &ray, float *tmin, float *tmax) const;
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| 243 | // computes the signed distances for case: tmin < tmax and tmax > 0
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| 244 | int GetMinMaxT(const Ray &ray, float *tmin, float *tmax,
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| 245 | EFaces &entryFace, EFaces &exitFace) const;
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| 246 |
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| 247 | // Writes a brief description of the object, indenting by the given
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| 248 | // number of spaces first.
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| 249 | virtual void Describe(ostream& app, int ind) const;
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| 250 |
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| 251 | // For edge .. number <0..11> returns two incident vertices
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| 252 | void GetEdge(const int edge, Vector3 *a, Vector3 *b) const;
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| 253 |
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| 254 | // Compute the coordinates of one vertex of the box for 0/1 in each axis
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| 255 | // 0 .. smaller coordinates, 1 .. large coordinates
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| 256 | Vector3 GetVertex(int xAxis, int yAxis, int zAxis) const;
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| 257 |
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| 258 | // Compute the vertex for number N=<0..7>, N = 4*x + 2*y + z, where
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| 259 | // x,y,z are either 0 or 1; (0 .. lower coordinate, 1 .. large coordinate)
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| 260 | // (xmin,ymin, zmin) .. N = 0, (xmax, ymax, zmax) .. N= 7
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| 261 | void GetVertex(const int N, Vector3 &vertex) const;
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| 262 |
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| 263 | Vector3 GetVertex(const int N) const {
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| 264 | Vector3 v;
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| 265 | GetVertex(N, v);
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| 266 | return v;
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| 267 | }
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| 268 |
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| 269 | // Returns 1, if the box includes on arbitrary face a given box
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| 270 | int IsPiercedByBox(const AxisAlignedBox3 &box, int &axis) const;
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| 271 |
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| 272 |
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| 273 | int GetFaceVisibilityMask(const Vector3 &position) const;
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| 274 | int GetFaceVisibilityMask(const Rectangle3 &rectangle) const;
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| 275 |
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| 276 | Rectangle3 GetFace(const int face) const;
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| 277 |
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| 278 | // For a given point returns the region, where the point is located
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| 279 | // there are 27 regions (0..26) .. determined by the planes embedding in the
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| 280 | // sides of the bounding box (0 .. lower the position of the box,
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| 281 | // 1 .. inside the box, 2 .. greater than box). The region number is given as
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| 282 | // R = 9*x + 3*y + z ; e.g. region .. inside the box is 13.
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| 283 | int GetRegionID(const Vector3 &point) const;
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| 284 |
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| 285 | // Set the corner point of rectangle on the face of bounding box
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| 286 | // given by the index number and the rectangle lying on this face
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| 287 | // void GetFaceRectCorner(const CRectLeaf2D *rect, EFaces faceIndx,
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| 288 | // const int &cornerIndx, Vector3 &cornerPoint);
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| 289 |
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| 290 | // Project the box to a plane given a normal vector of this plane. Computes
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| 291 | // the surface area of projected silhouettes for parallel projection.
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| 292 | float ProjectToPlaneSA(const Vector3 &normal) const;
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| 293 |
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| 294 | // Computes projected surface area of the box to a given viewing plane
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| 295 | // given a viewpoint. This corresponds the probability, the box will
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| 296 | // be hit by the ray .. moreover returns .. the region number (0-26).
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| 297 | // the function supposes all the points lie of the box lies in the viewing
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| 298 | // frustrum !!! The positive halfspace of viewplane has to contain
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| 299 | // viewpoint. "projectionType" == 0 .. perspective projection,
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| 300 | // == 1 .. parallel projection.
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| 301 | float ProjectToPlaneSA(const Plane3 &viewplane,
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| 302 | const Vector3 &viewpoint,
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| 303 | int *tcase,
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| 304 | const float &maxSA,
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| 305 | int projectionType) const;
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| 306 |
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| 307 | // Computes projected surface area of the box to a given viewing plane
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| 308 | // and viewpoint. It clipps the area by all the planes given .. they should
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| 309 | // define the viewing frustrum. Variable tclip defines, which planes are
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| 310 | // used for clipping, parameter 31 is the most general, clip all the plane.
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| 311 | // 1 .. clip left, 2 .. clip top, 4 .. clip right, 8 .. clip bottom,
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| 312 | // 16 .. clip supporting plane(its normal towards the viewing frustrum).
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| 313 | // "typeProjection" == 0 .. perspective projection,
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| 314 | // == 1 .. parallel projection
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| 315 | float ProjectToPlaneSA(const Plane3 &viewplane,
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| 316 | const Vector3 &viewpoint,
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| 317 | int *tcase, int &tclip,
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| 318 | const Plane3 &leftPlane,
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| 319 | const Plane3 &topPlane,
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| 320 | const Plane3 &rightPlane,
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| 321 | const Plane3 &bottomPlane,
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| 322 | const Plane3 &suppPlane,
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| 323 | const float &maxSA,
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| 324 | int typeProjection) const;
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| 325 |
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| 326 | // Projects the box to a unit sphere enclosing a given viewpoint and
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| 327 | // returns the solid angle of the box projected to a unit sphere
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| 328 | float ProjectToSphereSA(const Vector3 &viewpoint, int *tcase) const;
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| 329 |
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| 330 | /** Returns vertex indices of edge.
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| 331 | */
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| 332 | void GetEdge(const int edge, int &aIdx, int &bIdx) const;
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| 333 |
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| 334 | /** Computes cross section of plane with box (i.e., bounds box).
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| 335 | @returns the cross section
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| 336 | */
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[448] | 337 | Polygon3 *CrossSection(const Plane3 &plane) const;
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[372] | 338 |
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[448] | 339 | /** Computes minimal and maximal t of ray, including the object intersections.
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| 340 | @returns true if ray hits the bounding box.
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| 341 | */
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[459] | 342 | bool GetRaySegment(const Ray &ray,
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[448] | 343 | float &minT,
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| 344 | float &maxT) const;
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| 345 |
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[482] | 346 | /** If the boxes are intersecting on a common face, this function
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| 347 | returns the face intersection, false otherwise.
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| 348 |
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| 349 | @param neighbour the neighbouring box intersecting with this box.
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| 350 | */
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| 351 | bool GetIntersectionFace(Rectangle3 &face,
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| 352 | const AxisAlignedBox3 &neighbour) const;
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| 353 |
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[486] | 354 | /** Adds the box faces to the mesh.
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| 355 | */
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| 356 | void AddBoxToMesh(Mesh *mesh) const;
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| 357 |
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[372] | 358 | #define __EXTENT_HACK
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| 359 | // get the extent of face
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| 360 | float GetExtent(const int &face) const {
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| 361 | #if defined(__EXTENT_HACK) && defined(__VECTOR_HACK)
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| 362 | return mMin[face];
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| 363 | #else
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| 364 | if (face < 3)
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| 365 | return mMin[face];
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| 366 | else
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| 367 | return mMax[face-3];
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| 368 | #endif
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| 369 | }
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| 370 |
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| 371 | // The vertices that form boundaries of the projected bounding box
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| 372 | // for all the regions possible, number of regions is 3^3 = 27,
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| 373 | // since two parallel sides of bbox forms three disjoint spaces
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| 374 | // the vertices are given in anti-clockwise order .. stopped by -1 elem.
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| 375 | static const int bvertices[27][9];
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| 376 |
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| 377 | // The list of all faces visible from a given region (except region 13)
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| 378 | // the faces are identified by triple: (axis, min-vertex, max-vertex),
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| 379 | // that is maximaly three triples are defined. axis = 0 (x-axis),
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| 380 | // axis = 1 (y-axis), axis = 2 (z-axis), -1 .. terminator. Is is always
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| 381 | // true that: min-vertex < max-vertex for all coordinates excluding axis
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| 382 | static const int bfaces[27][10];
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| 383 |
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| 384 | // The correct corners indexed starting from entry face to exit face
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| 385 | // first index determines entry face, second index exit face, and
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| 386 | // the two numbers (indx, inc) determines: ind = the index on the exit
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| 387 | // face, when starting from the vertex 0 on entry face, 'inc' is
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| 388 | // the increment when we go on entry face in order 0,1,2,3 to create
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| 389 | // convex shaft with the rectangle on exit face. That is, inc = -1 or 1.
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| 390 | static const int pairFaceRects[6][6][2];
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| 391 |
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| 392 | // The vertices that form CLOSEST points with respect to the region
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| 393 | // for all the regions possible, number of regions is 3^3 = 27,
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| 394 | // since two parallel sides of bbox forms three disjoint spaces.
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| 395 | // The vertices are given in anti-clockwise order, stopped by -1 elem,
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| 396 | // at most 8 points, at least 1 point.
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| 397 | static const int cvertices[27][9];
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| 398 | static const int csvertices[27][6];
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| 399 |
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| 400 | // The vertices that form FARTHEST points with respect to the region
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| 401 | // for all the regions possible, number of regions is 3^3 = 27,
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| 402 | // since two parallel sides of bbox forms three disjoint spaces.
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| 403 | // The vertices are given in anti-clockwise order, stopped by -1 elem,
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| 404 | // at most 8 points, at least 1 point.
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| 405 | static const int fvertices[27][9];
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| 406 | static const int fsvertices[27][9];
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| 407 |
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| 408 | // input and output operator with stream
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| 409 | friend ostream& operator<<(ostream &s, const AxisAlignedBox3 &A);
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| 410 | friend istream& operator>>(istream &s, AxisAlignedBox3 &A);
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| 411 |
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| 412 | protected:
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| 413 | // definition of friend functions
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| 414 | friend class Ray;
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| 415 | };
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| 416 |
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| 417 | // --------------------------------------------------------------------------
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| 418 | // Implementation of inline (member) functions
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| 419 |
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| 420 | inline bool
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| 421 | Overlap(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y)
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| 422 | {
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| 423 | if (x.mMax.x < y.mMin.x ||
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| 424 | x.mMin.x > y.mMax.x ||
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| 425 | x.mMax.y < y.mMin.y ||
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| 426 | x.mMin.y > y.mMax.y ||
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| 427 | x.mMax.z < y.mMin.z ||
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| 428 | x.mMin.z > y.mMax.z) {
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| 429 | return false;
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| 430 | }
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| 431 | return true;
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| 432 | }
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| 433 |
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| 434 | inline bool
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| 435 | OverlapS(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y)
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| 436 | {
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| 437 | if (x.mMax.x <= y.mMin.x ||
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| 438 | x.mMin.x >= y.mMax.x ||
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| 439 | x.mMax.y <= y.mMin.y ||
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| 440 | x.mMin.y >= y.mMax.y ||
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| 441 | x.mMax.z <= y.mMin.z ||
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| 442 | x.mMin.z >= y.mMax.z) {
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| 443 | return false;
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| 444 | }
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| 445 | return true;
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| 446 | }
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| 447 |
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| 448 | inline bool
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| 449 | Overlap(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y, float eps)
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| 450 | {
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| 451 | if ( (x.mMax.x - eps) < y.mMin.x ||
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| 452 | (x.mMin.x + eps) > y.mMax.x ||
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| 453 | (x.mMax.y - eps) < y.mMin.y ||
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| 454 | (x.mMin.y + eps) > y.mMax.y ||
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| 455 | (x.mMax.z - eps) < y.mMin.z ||
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| 456 | (x.mMin.z + eps) > y.mMax.z ) {
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| 457 | return false;
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| 458 | }
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| 459 | return true;
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| 460 | }
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| 461 |
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| 462 | inline AxisAlignedBox3
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| 463 | Intersect(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y)
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| 464 | {
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| 465 | if (x.Unbounded())
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| 466 | return y;
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| 467 | else
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| 468 | if (y.Unbounded())
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| 469 | return x;
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| 470 | AxisAlignedBox3 ret = x;
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| 471 | if (Overlap(ret, y)) {
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| 472 | Maximize(ret.mMin, y.mMin);
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| 473 | Minimize(ret.mMax, y.mMax);
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| 474 | return ret;
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| 475 | }
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| 476 | else // Null intersection.
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| 477 | return AxisAlignedBox3(Vector3(0), Vector3(0));
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| 478 | // return AxisAlignedBox3(Vector3(0), Vector3(-1));
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| 479 | }
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| 480 |
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| 481 | inline AxisAlignedBox3
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| 482 | Union(const AxisAlignedBox3 &x, const AxisAlignedBox3 &y)
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| 483 | {
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| 484 | Vector3 min = x.mMin;
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| 485 | Vector3 max = x.mMax;
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| 486 | Minimize(min, y.mMin);
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| 487 | Maximize(max, y.mMax);
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| 488 | return AxisAlignedBox3(min, max);
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| 489 | }
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| 490 |
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| 491 | inline AxisAlignedBox3
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| 492 | Transform(const AxisAlignedBox3 &box, const Matrix4x4 &tform)
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| 493 | {
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| 494 | Vector3 mmin(MAXFLOAT);
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| 495 | Vector3 mmax(-MAXFLOAT);
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| 496 |
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| 497 | AxisAlignedBox3 ret(mmin, mmax);
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| 498 | ret.Include(tform * Vector3(box.mMin.x, box.mMin.y, box.mMin.z));
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| 499 | ret.Include(tform * Vector3(box.mMin.x, box.mMin.y, box.mMax.z));
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| 500 | ret.Include(tform * Vector3(box.mMin.x, box.mMax.y, box.mMin.z));
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| 501 | ret.Include(tform * Vector3(box.mMin.x, box.mMax.y, box.mMax.z));
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| 502 | ret.Include(tform * Vector3(box.mMax.x, box.mMin.y, box.mMin.z));
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| 503 | ret.Include(tform * Vector3(box.mMax.x, box.mMin.y, box.mMax.z));
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| 504 | ret.Include(tform * Vector3(box.mMax.x, box.mMax.y, box.mMin.z));
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| 505 | ret.Include(tform * Vector3(box.mMax.x, box.mMax.y, box.mMax.z));
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| 506 | return ret;
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| 507 | }
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| 508 |
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| 509 |
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| 510 | inline int operator==(const AxisAlignedBox3 &A, const AxisAlignedBox3 &B)
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| 511 | {
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| 512 | return (A.mMin == B.mMin) && (A.mMax == B.mMax);
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| 513 | }
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| 514 |
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| 515 |
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| 516 |
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| 517 |
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| 518 |
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| 519 | #endif
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