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1///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
2/**
3 * OBB-OBB overlap test using the separating axis theorem.
4 * - original code by Gomez / Gamasutra (similar to Gottschalk's one in RAPID)
5 * - optimized for AABB trees by computing the rotation matrix once (SOLID-fashion)
6 * - the fabs matrix is precomputed as well and epsilon-tweaked (RAPID-style, we found this almost mandatory)
7 * - Class III axes can be disabled... (SOLID & Intel fashion)
8 * - ...or enabled to perform some profiling
9 * - CPU comparisons used when appropriate
10 * - lazy evaluation sometimes saves some work in case of early exits (unlike SOLID)
11 *
12 * \param ea [in] extents from box A
13 * \param ca [in] center from box A
14 * \param eb [in] extents from box B
15 * \param cb [in] center from box B
16 * \return true if boxes overlap
17 */
18///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
19inline_ BOOL AABBTreeCollider::BoxBoxOverlap(const Point& ea, const Point& ca, const Point& eb, const Point& cb)
20{
21 // Stats
22 mNbBVBVTests++;
23
24 float t,t2;
25
26 // Class I : A's basis vectors
27 float Tx = (mR1to0.m[0][0]*cb.x + mR1to0.m[1][0]*cb.y + mR1to0.m[2][0]*cb.z) + mT1to0.x - ca.x;
28 t = ea.x + eb.x*mAR.m[0][0] + eb.y*mAR.m[1][0] + eb.z*mAR.m[2][0];
29 if(GREATER(Tx, t)) return FALSE;
30
31 float Ty = (mR1to0.m[0][1]*cb.x + mR1to0.m[1][1]*cb.y + mR1to0.m[2][1]*cb.z) + mT1to0.y - ca.y;
32 t = ea.y + eb.x*mAR.m[0][1] + eb.y*mAR.m[1][1] + eb.z*mAR.m[2][1];
33 if(GREATER(Ty, t)) return FALSE;
34
35 float Tz = (mR1to0.m[0][2]*cb.x + mR1to0.m[1][2]*cb.y + mR1to0.m[2][2]*cb.z) + mT1to0.z - ca.z;
36 t = ea.z + eb.x*mAR.m[0][2] + eb.y*mAR.m[1][2] + eb.z*mAR.m[2][2];
37 if(GREATER(Tz, t)) return FALSE;
38
39 // Class II : B's basis vectors
40 t = Tx*mR1to0.m[0][0] + Ty*mR1to0.m[0][1] + Tz*mR1to0.m[0][2]; t2 = ea.x*mAR.m[0][0] + ea.y*mAR.m[0][1] + ea.z*mAR.m[0][2] + eb.x;
41 if(GREATER(t, t2)) return FALSE;
42
43 t = Tx*mR1to0.m[1][0] + Ty*mR1to0.m[1][1] + Tz*mR1to0.m[1][2]; t2 = ea.x*mAR.m[1][0] + ea.y*mAR.m[1][1] + ea.z*mAR.m[1][2] + eb.y;
44 if(GREATER(t, t2)) return FALSE;
45
46 t = Tx*mR1to0.m[2][0] + Ty*mR1to0.m[2][1] + Tz*mR1to0.m[2][2]; t2 = ea.x*mAR.m[2][0] + ea.y*mAR.m[2][1] + ea.z*mAR.m[2][2] + eb.z;
47 if(GREATER(t, t2)) return FALSE;
48
49 // Class III : 9 cross products
50 // Cool trick: always perform the full test for first level, regardless of settings.
51 // That way pathological cases (such as the pencils scene) are quickly rejected anyway !
52 if(mFullBoxBoxTest || mNbBVBVTests==1)
53 {
54 t = Tz*mR1to0.m[0][1] - Ty*mR1to0.m[0][2]; t2 = ea.y*mAR.m[0][2] + ea.z*mAR.m[0][1] + eb.y*mAR.m[2][0] + eb.z*mAR.m[1][0]; if(GREATER(t, t2)) return FALSE; // L = A0 x B0
55 t = Tz*mR1to0.m[1][1] - Ty*mR1to0.m[1][2]; t2 = ea.y*mAR.m[1][2] + ea.z*mAR.m[1][1] + eb.x*mAR.m[2][0] + eb.z*mAR.m[0][0]; if(GREATER(t, t2)) return FALSE; // L = A0 x B1
56 t = Tz*mR1to0.m[2][1] - Ty*mR1to0.m[2][2]; t2 = ea.y*mAR.m[2][2] + ea.z*mAR.m[2][1] + eb.x*mAR.m[1][0] + eb.y*mAR.m[0][0]; if(GREATER(t, t2)) return FALSE; // L = A0 x B2
57 t = Tx*mR1to0.m[0][2] - Tz*mR1to0.m[0][0]; t2 = ea.x*mAR.m[0][2] + ea.z*mAR.m[0][0] + eb.y*mAR.m[2][1] + eb.z*mAR.m[1][1]; if(GREATER(t, t2)) return FALSE; // L = A1 x B0
58 t = Tx*mR1to0.m[1][2] - Tz*mR1to0.m[1][0]; t2 = ea.x*mAR.m[1][2] + ea.z*mAR.m[1][0] + eb.x*mAR.m[2][1] + eb.z*mAR.m[0][1]; if(GREATER(t, t2)) return FALSE; // L = A1 x B1
59 t = Tx*mR1to0.m[2][2] - Tz*mR1to0.m[2][0]; t2 = ea.x*mAR.m[2][2] + ea.z*mAR.m[2][0] + eb.x*mAR.m[1][1] + eb.y*mAR.m[0][1]; if(GREATER(t, t2)) return FALSE; // L = A1 x B2
60 t = Ty*mR1to0.m[0][0] - Tx*mR1to0.m[0][1]; t2 = ea.x*mAR.m[0][1] + ea.y*mAR.m[0][0] + eb.y*mAR.m[2][2] + eb.z*mAR.m[1][2]; if(GREATER(t, t2)) return FALSE; // L = A2 x B0
61 t = Ty*mR1to0.m[1][0] - Tx*mR1to0.m[1][1]; t2 = ea.x*mAR.m[1][1] + ea.y*mAR.m[1][0] + eb.x*mAR.m[2][2] + eb.z*mAR.m[0][2]; if(GREATER(t, t2)) return FALSE; // L = A2 x B1
62 t = Ty*mR1to0.m[2][0] - Tx*mR1to0.m[2][1]; t2 = ea.x*mAR.m[2][1] + ea.y*mAR.m[2][0] + eb.x*mAR.m[1][2] + eb.y*mAR.m[0][2]; if(GREATER(t, t2)) return FALSE; // L = A2 x B2
63 }
64 return TRUE;
65}
66
67//! A dedicated version when one box is constant
68inline_ BOOL OBBCollider::BoxBoxOverlap(const Point& extents, const Point& center)
69{
70 // Stats
71 mNbVolumeBVTests++;
72
73 float t,t2;
74
75 // Class I : A's basis vectors
76 float Tx = mTBoxToModel.x - center.x; t = extents.x + mBBx1; if(GREATER(Tx, t)) return FALSE;
77 float Ty = mTBoxToModel.y - center.y; t = extents.y + mBBy1; if(GREATER(Ty, t)) return FALSE;
78 float Tz = mTBoxToModel.z - center.z; t = extents.z + mBBz1; if(GREATER(Tz, t)) return FALSE;
79
80 // Class II : B's basis vectors
81 t = Tx*mRBoxToModel.m[0][0] + Ty*mRBoxToModel.m[0][1] + Tz*mRBoxToModel.m[0][2];
82 t2 = extents.x*mAR.m[0][0] + extents.y*mAR.m[0][1] + extents.z*mAR.m[0][2] + mBoxExtents.x;
83 if(GREATER(t, t2)) return FALSE;
84
85 t = Tx*mRBoxToModel.m[1][0] + Ty*mRBoxToModel.m[1][1] + Tz*mRBoxToModel.m[1][2];
86 t2 = extents.x*mAR.m[1][0] + extents.y*mAR.m[1][1] + extents.z*mAR.m[1][2] + mBoxExtents.y;
87 if(GREATER(t, t2)) return FALSE;
88
89 t = Tx*mRBoxToModel.m[2][0] + Ty*mRBoxToModel.m[2][1] + Tz*mRBoxToModel.m[2][2];
90 t2 = extents.x*mAR.m[2][0] + extents.y*mAR.m[2][1] + extents.z*mAR.m[2][2] + mBoxExtents.z;
91 if(GREATER(t, t2)) return FALSE;
92
93 // Class III : 9 cross products
94 // Cool trick: always perform the full test for first level, regardless of settings.
95 // That way pathological cases (such as the pencils scene) are quickly rejected anyway !
96 if(mFullBoxBoxTest || mNbVolumeBVTests==1)
97 {
98 t = Tz*mRBoxToModel.m[0][1] - Ty*mRBoxToModel.m[0][2]; t2 = extents.y*mAR.m[0][2] + extents.z*mAR.m[0][1] + mBB_1; if(GREATER(t, t2)) return FALSE; // L = A0 x B0
99 t = Tz*mRBoxToModel.m[1][1] - Ty*mRBoxToModel.m[1][2]; t2 = extents.y*mAR.m[1][2] + extents.z*mAR.m[1][1] + mBB_2; if(GREATER(t, t2)) return FALSE; // L = A0 x B1
100 t = Tz*mRBoxToModel.m[2][1] - Ty*mRBoxToModel.m[2][2]; t2 = extents.y*mAR.m[2][2] + extents.z*mAR.m[2][1] + mBB_3; if(GREATER(t, t2)) return FALSE; // L = A0 x B2
101 t = Tx*mRBoxToModel.m[0][2] - Tz*mRBoxToModel.m[0][0]; t2 = extents.x*mAR.m[0][2] + extents.z*mAR.m[0][0] + mBB_4; if(GREATER(t, t2)) return FALSE; // L = A1 x B0
102 t = Tx*mRBoxToModel.m[1][2] - Tz*mRBoxToModel.m[1][0]; t2 = extents.x*mAR.m[1][2] + extents.z*mAR.m[1][0] + mBB_5; if(GREATER(t, t2)) return FALSE; // L = A1 x B1
103 t = Tx*mRBoxToModel.m[2][2] - Tz*mRBoxToModel.m[2][0]; t2 = extents.x*mAR.m[2][2] + extents.z*mAR.m[2][0] + mBB_6; if(GREATER(t, t2)) return FALSE; // L = A1 x B2
104 t = Ty*mRBoxToModel.m[0][0] - Tx*mRBoxToModel.m[0][1]; t2 = extents.x*mAR.m[0][1] + extents.y*mAR.m[0][0] + mBB_7; if(GREATER(t, t2)) return FALSE; // L = A2 x B0
105 t = Ty*mRBoxToModel.m[1][0] - Tx*mRBoxToModel.m[1][1]; t2 = extents.x*mAR.m[1][1] + extents.y*mAR.m[1][0] + mBB_8; if(GREATER(t, t2)) return FALSE; // L = A2 x B1
106 t = Ty*mRBoxToModel.m[2][0] - Tx*mRBoxToModel.m[2][1]; t2 = extents.x*mAR.m[2][1] + extents.y*mAR.m[2][0] + mBB_9; if(GREATER(t, t2)) return FALSE; // L = A2 x B2
107 }
108 return TRUE;
109}
110
111//! A special version for 2 axis-aligned boxes
112inline_ BOOL AABBCollider::AABBAABBOverlap(const Point& extents, const Point& center)
113{
114 // Stats
115 mNbVolumeBVTests++;
116
117 float tx = mBox.mCenter.x - center.x; float ex = extents.x + mBox.mExtents.x; if(GREATER(tx, ex)) return FALSE;
118 float ty = mBox.mCenter.y - center.y; float ey = extents.y + mBox.mExtents.y; if(GREATER(ty, ey)) return FALSE;
119 float tz = mBox.mCenter.z - center.z; float ez = extents.z + mBox.mExtents.z; if(GREATER(tz, ez)) return FALSE;
120
121 return TRUE;
122}
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