Torque3D/Engine/lib/opcode/OPC_TriBoxOverlap.h

//! 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;
}