OPC_TriTriOverlap.h 9.05 KB
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//! if OPC_TRITRI_EPSILON_TEST is true then we do a check (if |dv|<EPSILON then dv=0.0;) else no check is done (which is less robust, but faster)
#define LOCAL_EPSILON 0.000001f

//! sort so that a<=b
#define SORT(a,b)			\
	if(a>b)					\
	{						\
		const float c=a;	\
		a=b;				\
		b=c;				\
	}

//! Edge to edge test based on Franlin Antonio's gem: "Faster Line Segment Intersection", in Graphics Gems III, pp. 199-202
#define EDGE_EDGE_TEST(V0, U0, U1)						\
	Bx = U0[i0] - U1[i0];								\
	By = U0[i1] - U1[i1];								\
	Cx = V0[i0] - U0[i0];								\
	Cy = V0[i1] - U0[i1];								\
	f  = Ay*Bx - Ax*By;									\
	d  = By*Cx - Bx*Cy;									\
	if((f>0.0f && d>=0.0f && d<=f) || (f<0.0f && d<=0.0f && d>=f))	\
	{													\
		const float e=Ax*Cy - Ay*Cx;					\
		if(f>0.0f)										\
		{												\
			if(e>=0.0f && e<=f) return TRUE;			\
		}												\
		else											\
		{												\
			if(e<=0.0f && e>=f) return TRUE;			\
		}												\
	}

//! TO BE DOCUMENTED
#define EDGE_AGAINST_TRI_EDGES(V0, V1, U0, U1, U2)		\
{														\
	float Bx,By,Cx,Cy,d,f;								\
	const float Ax = V1[i0] - V0[i0];					\
	const float Ay = V1[i1] - V0[i1];					\
	/* test edge U0,U1 against V0,V1 */					\
	EDGE_EDGE_TEST(V0, U0, U1);							\
	/* test edge U1,U2 against V0,V1 */					\
	EDGE_EDGE_TEST(V0, U1, U2);							\
	/* test edge U2,U1 against V0,V1 */					\
	EDGE_EDGE_TEST(V0, U2, U0);							\
}

//! TO BE DOCUMENTED
#define POINT_IN_TRI(V0, U0, U1, U2)					\
{														\
	/* is T1 completly inside T2? */					\
	/* check if V0 is inside tri(U0,U1,U2) */			\
	float a  = U1[i1] - U0[i1];							\
	float b  = -(U1[i0] - U0[i0]);						\
	float c  = -a*U0[i0] - b*U0[i1];					\
	float d0 = a*V0[i0] + b*V0[i1] + c;					\
														\
	a  = U2[i1] - U1[i1];								\
	b  = -(U2[i0] - U1[i0]);							\
	c  = -a*U1[i0] - b*U1[i1];							\
	const float d1 = a*V0[i0] + b*V0[i1] + c;			\
														\
	a  = U0[i1] - U2[i1];								\
	b  = -(U0[i0] - U2[i0]);							\
	c  = -a*U2[i0] - b*U2[i1];							\
	const float d2 = a*V0[i0] + b*V0[i1] + c;			\
	if(d0*d1>0.0f)										\
	{													\
		if(d0*d2>0.0f) return TRUE;						\
	}													\
}

//! TO BE DOCUMENTED
BOOL CoplanarTriTri(const Point& n, const Point& v0, const Point& v1, const Point& v2, const Point& u0, const Point& u1, const Point& u2)
{
	float A[3];
	short i0,i1;
	/* first project onto an axis-aligned plane, that maximizes the area */
	/* of the triangles, compute indices: i0,i1. */
	A[0] = fabsf(n[0]);
	A[1] = fabsf(n[1]);
	A[2] = fabsf(n[2]);
	if(A[0]>A[1])
	{
		if(A[0]>A[2])
		{
			i0=1;      /* A[0] is greatest */
			i1=2;
		}
		else
		{
			i0=0;      /* A[2] is greatest */
			i1=1;
		}
	}
	else   /* A[0]<=A[1] */
	{
		if(A[2]>A[1])
		{
			i0=0;      /* A[2] is greatest */
			i1=1;
		}
		else
		{
			i0=0;      /* A[1] is greatest */
			i1=2;
		}
	}

	/* test all edges of triangle 1 against the edges of triangle 2 */
	EDGE_AGAINST_TRI_EDGES(v0, v1, u0, u1, u2);
	EDGE_AGAINST_TRI_EDGES(v1, v2, u0, u1, u2);
	EDGE_AGAINST_TRI_EDGES(v2, v0, u0, u1, u2);

	/* finally, test if tri1 is totally contained in tri2 or vice versa */
	POINT_IN_TRI(v0, u0, u1, u2);
	POINT_IN_TRI(u0, v0, v1, v2);

	return FALSE;
}

//! TO BE DOCUMENTED
#define NEWCOMPUTE_INTERVALS(VV0, VV1, VV2, D0, D1, D2, D0D1, D0D2, A, B, C, X0, X1)	\
{																						\
	if(D0D1>0.0f)																		\
	{																					\
		/* here we know that D0D2<=0.0 */												\
		/* that is D0, D1 are on the same side, D2 on the other or on the plane */		\
		A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1;				\
	}																					\
	else if(D0D2>0.0f)																	\
	{																					\
		/* here we know that d0d1<=0.0 */												\
		A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2;				\
	}																					\
	else if(D1*D2>0.0f || D0!=0.0f)														\
	{																					\
		/* here we know that d0d1<=0.0 or that D0!=0.0 */								\
		A=VV0; B=(VV1 - VV0)*D0; C=(VV2 - VV0)*D0; X0=D0 - D1; X1=D0 - D2;				\
	}																					\
	else if(D1!=0.0f)																	\
	{																					\
		A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2;				\
	}																					\
	else if(D2!=0.0f)																	\
	{																					\
		A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1;				\
	}																					\
	else																				\
	{																					\
		/* triangles are coplanar */													\
		return CoplanarTriTri(N1, V0, V1, V2, U0, U1, U2);								\
	}																					\
}

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
 *	Triangle/triangle intersection test routine,
 *	by Tomas Moller, 1997.
 *	See article "A Fast Triangle-Triangle Intersection Test",
 *	Journal of Graphics Tools, 2(2), 1997
 *
 *	Updated June 1999: removed the divisions -- a little faster now!
 *	Updated October 1999: added {} to CROSS and SUB macros 
 *
 *	int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
 *                      float U0[3],float U1[3],float U2[3])
 *
 *	\param		V0		[in] triangle 0, vertex 0
 *	\param		V1		[in] triangle 0, vertex 1
 *	\param		V2		[in] triangle 0, vertex 2
 *	\param		U0		[in] triangle 1, vertex 0
 *	\param		U1		[in] triangle 1, vertex 1
 *	\param		U2		[in] triangle 1, vertex 2
 *	\return		true if triangles overlap
 */
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
inline_ BOOL AABBTreeCollider::TriTriOverlap(const Point& V0, const Point& V1, const Point& V2, const Point& U0, const Point& U1, const Point& U2)
{
	// Stats
	mNbPrimPrimTests++;

	// Compute plane equation of triangle(V0,V1,V2)
	Point E1 = V1 - V0;
	Point E2 = V2 - V0;
	const Point N1 = E1 ^ E2;
	const float d1 =-N1 | V0;
	// Plane equation 1: N1.X+d1=0

	// Put U0,U1,U2 into plane equation 1 to compute signed distances to the plane
	float du0 = (N1|U0) + d1;
	float du1 = (N1|U1) + d1;
	float du2 = (N1|U2) + d1;

	// Coplanarity robustness check
#ifdef OPC_TRITRI_EPSILON_TEST
    float absd1 = FastFabs(d1), sqmagN1 = N1.SquareMagnitude();
    if (absd1>=sqmagN1)
    {
		if(FastFabs(du0)<=LOCAL_EPSILON*absd1) du0 = 0.0f;
		if(FastFabs(du1)<=LOCAL_EPSILON*absd1) du1 = 0.0f;
		if(FastFabs(du2)<=LOCAL_EPSILON*absd1) du2 = 0.0f;
	}
	else
	{
		if(FastFabs(du0)<=LOCAL_EPSILON*FCMax2(absd1, FCMin2(sqmagN1, U0.SquareMagnitude()))) du0 = 0.0f;
		if(FastFabs(du1)<=LOCAL_EPSILON*FCMax2(absd1, FCMin2(sqmagN1, U1.SquareMagnitude()))) du1 = 0.0f;
		if(FastFabs(du2)<=LOCAL_EPSILON*FCMax2(absd1, FCMin2(sqmagN1, U2.SquareMagnitude()))) du2 = 0.0f;
	}
#endif
	const float du0du1 = du0 * du1;
	const float du0du2 = du0 * du2;

	if(du0du1>0.0f && du0du2>0.0f)	// same sign on all of them + not equal 0 ?
		return FALSE;				// no intersection occurs

	// Compute plane of triangle (U0,U1,U2)
	E1 = U1 - U0;
	E2 = U2 - U0;
	const Point N2 = E1 ^ E2;
	const float d2=-N2 | U0;
	// plane equation 2: N2.X+d2=0

	// put V0,V1,V2 into plane equation 2
	float dv0 = (N2|V0) + d2;
	float dv1 = (N2|V1) + d2;
	float dv2 = (N2|V2) + d2;

#ifdef OPC_TRITRI_EPSILON_TEST
    float absd2 = FastFabs(d2), sqmagN2 = N2.SquareMagnitude();
    if (absd2>=sqmagN2)
    {
		if(FastFabs(dv0)<=LOCAL_EPSILON*absd2) dv0 = 0.0f;
		if(FastFabs(dv1)<=LOCAL_EPSILON*absd2) dv1 = 0.0f;
		if(FastFabs(dv2)<=LOCAL_EPSILON*absd2) dv2 = 0.0f;
	}
	else
	{
		if(FastFabs(dv0)<=LOCAL_EPSILON*FCMax2(absd2, FCMin2(sqmagN2, V0.SquareMagnitude()))) dv0 = 0.0f;
		if(FastFabs(dv1)<=LOCAL_EPSILON*FCMax2(absd2, FCMin2(sqmagN2, V1.SquareMagnitude()))) dv1 = 0.0f;
		if(FastFabs(dv2)<=LOCAL_EPSILON*FCMax2(absd2, FCMin2(sqmagN2, V2.SquareMagnitude()))) dv2 = 0.0f;
	}
#endif

	const float dv0dv1 = dv0 * dv1;
	const float dv0dv2 = dv0 * dv2;

	if(dv0dv1>0.0f && dv0dv2>0.0f)	// same sign on all of them + not equal 0 ?
		return FALSE;				// no intersection occurs

	// Compute direction of intersection line
	const Point D = N1^N2;

	// Compute and index to the largest component of D
	float max=fabsf(D[0]);
	short index=0;
	float bb=fabsf(D[1]);
	float cc=fabsf(D[2]);
	if(bb>max) max=bb,index=1;
	if(cc>max) max=cc,index=2;

	// This is the simplified projection onto L
	const float vp0 = V0[index];
	const float vp1 = V1[index];
	const float vp2 = V2[index];

	const float up0 = U0[index];
	const float up1 = U1[index];
	const float up2 = U2[index];

	// Compute interval for triangle 1
	float a,b,c,x0,x1;
	NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);

	// Compute interval for triangle 2
	float d,e,f,y0,y1;
	NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);

	const float xx=x0*x1;
	const float yy=y0*y1;
	const float xxyy=xx*yy;

	float isect1[2], isect2[2];

	float tmp=a*xxyy;
	isect1[0]=tmp+b*x1*yy;
	isect1[1]=tmp+c*x0*yy;

	tmp=d*xxyy;
	isect2[0]=tmp+e*xx*y1;
	isect2[1]=tmp+f*xx*y0;

	SORT(isect1[0],isect1[1]);
	SORT(isect2[0],isect2[1]);

	if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return FALSE;
	return TRUE;
}