//! This macro quickly finds the min & max values among 3 variables
#define FINDMINMAX(x0, x1, x2, min, max) \
min = max = x0; \
if(x1<min) min=x1; \
if(x1>max) max=x1; \
if(x2<min) min=x2; \
if(x2>max) max=x2;
//! TO BE DOCUMENTED
inline_ BOOL planeBoxOverlap(const Point& normal, const float d, const Point& maxbox)
{
Point vmin, vmax;
for(udword q=0;q<=2;q++)
{
if(normal[q]>0.0f) { vmin[q]=-maxbox[q]; vmax[q]=maxbox[q]; }
else { vmin[q]=maxbox[q]; vmax[q]=-maxbox[q]; }
}
if((normal|vmin)+d>0.0f) return FALSE;
if((normal|vmax)+d>=0.0f) return TRUE;
return FALSE;
}
//! TO BE DOCUMENTED
#define AXISTEST_X01(a, b, fa, fb) \
min = a*v0.y - b*v0.z; \
max = a*v2.y - b*v2.z; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.y + fb * extents.z; \
if(min>rad || max<-rad) return FALSE;
//! TO BE DOCUMENTED
#define AXISTEST_X2(a, b, fa, fb) \
min = a*v0.y - b*v0.z; \
max = a*v1.y - b*v1.z; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.y + fb * extents.z; \
if(min>rad || max<-rad) return FALSE;
//! TO BE DOCUMENTED
#define AXISTEST_Y02(a, b, fa, fb) \
min = b*v0.z - a*v0.x; \
max = b*v2.z - a*v2.x; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.x + fb * extents.z; \
if(min>rad || max<-rad) return FALSE;
//! TO BE DOCUMENTED
#define AXISTEST_Y1(a, b, fa, fb) \
min = b*v0.z - a*v0.x; \
max = b*v1.z - a*v1.x; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.x + fb * extents.z; \
if(min>rad || max<-rad) return FALSE;
//! TO BE DOCUMENTED
#define AXISTEST_Z12(a, b, fa, fb) \
min = a*v1.x - b*v1.y; \
max = a*v2.x - b*v2.y; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.x + fb * extents.y; \
if(min>rad || max<-rad) return FALSE;
//! TO BE DOCUMENTED
#define AXISTEST_Z0(a, b, fa, fb) \
min = a*v0.x - b*v0.y; \
max = a*v1.x - b*v1.y; \
if(min>max) {const float tmp=max; max=min; min=tmp; } \
rad = fa * extents.x + fb * extents.y; \
if(min>rad || max<-rad) return FALSE;
// compute triangle edges
// - edges lazy evaluated to take advantage of early exits
// - fabs precomputed (half less work, possible since extents are always >0)
// - customized macros to take advantage of the null component
// - axis vector discarded, possibly saves useless movs
#define IMPLEMENT_CLASS3_TESTS \
float rad; \
float min, max; \
\
const float fey0 = fabsf(e0.y); \
const float fez0 = fabsf(e0.z); \
AXISTEST_X01(e0.z, e0.y, fez0, fey0); \
const float fex0 = fabsf(e0.x); \
AXISTEST_Y02(e0.z, e0.x, fez0, fex0); \
AXISTEST_Z12(e0.y, e0.x, fey0, fex0); \
\
const float fey1 = fabsf(e1.y); \
const float fez1 = fabsf(e1.z); \
AXISTEST_X01(e1.z, e1.y, fez1, fey1); \
const float fex1 = fabsf(e1.x); \
AXISTEST_Y02(e1.z, e1.x, fez1, fex1); \
AXISTEST_Z0(e1.y, e1.x, fey1, fex1); \
\
const Point e2 = mLeafVerts[0] - mLeafVerts[2]; \
const float fey2 = fabsf(e2.y); \
const float fez2 = fabsf(e2.z); \
AXISTEST_X2(e2.z, e2.y, fez2, fey2); \
const float fex2 = fabsf(e2.x); \
AXISTEST_Y1(e2.z, e2.x, fez2, fex2); \
AXISTEST_Z12(e2.y, e2.x, fey2, fex2);
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Triangle-Box overlap test using the separating axis theorem.
* This is the code from Tomas Möller, a bit optimized:
* - with some more lazy evaluation (faster path on PC)
* - with a tiny bit of assembly
* - with "SAT-lite" applied if needed
* - and perhaps with some more minor modifs...
*
* \param center [in] box center
* \param extents [in] box extents
* \return true if triangle & box overlap
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
inline_ BOOL AABBTreeCollider::TriBoxOverlap(const Point& center, const Point& extents)
{
// Stats
mNbBVPrimTests++;
// use separating axis theorem to test overlap between triangle and box
// need to test for overlap in these directions:
// 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle
// we do not even need to test these)
// 2) normal of the triangle
// 3) crossproduct(edge from tri, {x,y,z}-directin)
// this gives 3x3=9 more tests
// move everything so that the boxcenter is in (0,0,0)
Point v0, v1, v2;
v0.x = mLeafVerts[0].x - center.x;
v1.x = mLeafVerts[1].x - center.x;
v2.x = mLeafVerts[2].x - center.x;
// First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
// find min, max of the triangle in x-direction, and test for overlap in X
if(FCMin3(v0.x, v1.x, v2.x)>extents.x) return FALSE;
if(FCMax3(v0.x, v1.x, v2.x)<-extents.x) return FALSE;
// same for Y
v0.y = mLeafVerts[0].y - center.y;
v1.y = mLeafVerts[1].y - center.y;
v2.y = mLeafVerts[2].y - center.y;
if(FCMin3(v0.y, v1.y, v2.y)>extents.y) return FALSE;
if(FCMax3(v0.y, v1.y, v2.y)<-extents.y) return FALSE;
// same for Z
v0.z = mLeafVerts[0].z - center.z;
v1.z = mLeafVerts[1].z - center.z;
v2.z = mLeafVerts[2].z - center.z;
if(FCMin3(v0.z, v1.z, v2.z)>extents.z) return FALSE;
if(FCMax3(v0.z, v1.z, v2.z)<-extents.z) return FALSE;
#else
float min,max;
// Find min, max of the triangle in x-direction, and test for overlap in X
FINDMINMAX(v0.x, v1.x, v2.x, min, max);
if(min>extents.x || max<-extents.x) return FALSE;
// Same for Y
v0.y = mLeafVerts[0].y - center.y;
v1.y = mLeafVerts[1].y - center.y;
v2.y = mLeafVerts[2].y - center.y;
FINDMINMAX(v0.y, v1.y, v2.y, min, max);
if(min>extents.y || max<-extents.y) return FALSE;
// Same for Z
v0.z = mLeafVerts[0].z - center.z;
v1.z = mLeafVerts[1].z - center.z;
v2.z = mLeafVerts[2].z - center.z;
FINDMINMAX(v0.z, v1.z, v2.z, min, max);
if(min>extents.z || max<-extents.z) return FALSE;
#endif
// 2) Test if the box intersects the plane of the triangle
// compute plane equation of triangle: normal*x+d=0
// ### could be precomputed since we use the same leaf triangle several times
const Point e0 = v1 - v0;
const Point e1 = v2 - v1;
const Point normal = e0 ^ e1;
const float d = -normal|v0;
if(!planeBoxOverlap(normal, d, extents)) return FALSE;
// 3) "Class III" tests
if(mFullPrimBoxTest)
{
IMPLEMENT_CLASS3_TESTS
}
return TRUE;
}
//! A dedicated version where the box is constant
inline_ BOOL OBBCollider::TriBoxOverlap()
{
// Stats
mNbVolumePrimTests++;
// Hook
const Point& extents = mBoxExtents;
const Point& v0 = mLeafVerts[0];
const Point& v1 = mLeafVerts[1];
const Point& v2 = mLeafVerts[2];
// use separating axis theorem to test overlap between triangle and box
// need to test for overlap in these directions:
// 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle
// we do not even need to test these)
// 2) normal of the triangle
// 3) crossproduct(edge from tri, {x,y,z}-directin)
// this gives 3x3=9 more tests
// Box center is already in (0,0,0)
// First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
// find min, max of the triangle in x-direction, and test for overlap in X
if(FCMin3(v0.x, v1.x, v2.x)>mBoxExtents.x) return FALSE;
if(FCMax3(v0.x, v1.x, v2.x)<-mBoxExtents.x) return FALSE;
if(FCMin3(v0.y, v1.y, v2.y)>mBoxExtents.y) return FALSE;
if(FCMax3(v0.y, v1.y, v2.y)<-mBoxExtents.y) return FALSE;
if(FCMin3(v0.z, v1.z, v2.z)>mBoxExtents.z) return FALSE;
if(FCMax3(v0.z, v1.z, v2.z)<-mBoxExtents.z) return FALSE;
#else
float min,max;
// Find min, max of the triangle in x-direction, and test for overlap in X
FINDMINMAX(v0.x, v1.x, v2.x, min, max);
if(min>mBoxExtents.x || max<-mBoxExtents.x) return FALSE;
FINDMINMAX(v0.y, v1.y, v2.y, min, max);
if(min>mBoxExtents.y || max<-mBoxExtents.y) return FALSE;
FINDMINMAX(v0.z, v1.z, v2.z, min, max);
if(min>mBoxExtents.z || max<-mBoxExtents.z) return FALSE;
#endif
// 2) Test if the box intersects the plane of the triangle
// compute plane equation of triangle: normal*x+d=0
// ### could be precomputed since we use the same leaf triangle several times
const Point e0 = v1 - v0;
const Point e1 = v2 - v1;
const Point normal = e0 ^ e1;
const float d = -normal|v0;
if(!planeBoxOverlap(normal, d, mBoxExtents)) return FALSE;
// 3) "Class III" tests - here we always do full tests since the box is a primitive (not a BV)
{
IMPLEMENT_CLASS3_TESTS
}
return TRUE;
}
//! ...and another one, jeez
inline_ BOOL AABBCollider::TriBoxOverlap()
{
// Stats
mNbVolumePrimTests++;
// Hook
const Point& center = mBox.mCenter;
const Point& extents = mBox.mExtents;
// use separating axis theorem to test overlap between triangle and box
// need to test for overlap in these directions:
// 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle
// we do not even need to test these)
// 2) normal of the triangle
// 3) crossproduct(edge from tri, {x,y,z}-directin)
// this gives 3x3=9 more tests
// move everything so that the boxcenter is in (0,0,0)
Point v0, v1, v2;
v0.x = mLeafVerts[0].x - center.x;
v1.x = mLeafVerts[1].x - center.x;
v2.x = mLeafVerts[2].x - center.x;
// First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
// find min, max of the triangle in x-direction, and test for overlap in X
if(FCMin3(v0.x, v1.x, v2.x)>extents.x) return FALSE;
if(FCMax3(v0.x, v1.x, v2.x)<-extents.x) return FALSE;
// same for Y
v0.y = mLeafVerts[0].y - center.y;
v1.y = mLeafVerts[1].y - center.y;
v2.y = mLeafVerts[2].y - center.y;
if(FCMin3(v0.y, v1.y, v2.y)>extents.y) return FALSE;
if(FCMax3(v0.y, v1.y, v2.y)<-extents.y) return FALSE;
// same for Z
v0.z = mLeafVerts[0].z - center.z;
v1.z = mLeafVerts[1].z - center.z;
v2.z = mLeafVerts[2].z - center.z;
if(FCMin3(v0.z, v1.z, v2.z)>extents.z) return FALSE;
if(FCMax3(v0.z, v1.z, v2.z)<-extents.z) return FALSE;
#else
float min,max;
// Find min, max of the triangle in x-direction, and test for overlap in X
FINDMINMAX(v0.x, v1.x, v2.x, min, max);
if(min>extents.x || max<-extents.x) return FALSE;
// Same for Y
v0.y = mLeafVerts[0].y - center.y;
v1.y = mLeafVerts[1].y - center.y;
v2.y = mLeafVerts[2].y - center.y;
FINDMINMAX(v0.y, v1.y, v2.y, min, max);
if(min>extents.y || max<-extents.y) return FALSE;
// Same for Z
v0.z = mLeafVerts[0].z - center.z;
v1.z = mLeafVerts[1].z - center.z;
v2.z = mLeafVerts[2].z - center.z;
FINDMINMAX(v0.z, v1.z, v2.z, min, max);
if(min>extents.z || max<-extents.z) return FALSE;
#endif
// 2) Test if the box intersects the plane of the triangle
// compute plane equation of triangle: normal*x+d=0
// ### could be precomputed since we use the same leaf triangle several times
const Point e0 = v1 - v0;
const Point e1 = v2 - v1;
const Point normal = e0 ^ e1;
const float d = -normal|v0;
if(!planeBoxOverlap(normal, d, extents)) return FALSE;
// 3) "Class III" tests - here we always do full tests since the box is a primitive (not a BV)
{
IMPLEMENT_CLASS3_TESTS
}
return TRUE;
}
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