// This is collision detection. If you do another distance test for collision *response*,
// if might be useful to simply *skip* the test below completely, and report a collision.
// - if sphere-triangle overlap, result is ok
// - if they don't, we'll discard them during collision response with a similar test anyway
// Overall this approach should run faster.

// Original code by David Eberly in Magic.
BOOL SphereCollider::SphereTriOverlap(const IcePoint& vert0, const IcePoint& vert1, const IcePoint& vert2)
{
	// Stats
	mNbVolumePrimTests++;

	// Early exit if one of the vertices is inside the sphere
	IcePoint kDiff = vert2 - mCenter;
	float fC = kDiff.SquareMagnitude();
	if(fC <= mRadius2)	return TRUE;

	kDiff = vert1 - mCenter;
	fC = kDiff.SquareMagnitude();
	if(fC <= mRadius2)	return TRUE;

	kDiff = vert0 - mCenter;
	fC = kDiff.SquareMagnitude();
	if(fC <= mRadius2)	return TRUE;

	// Else do the full distance test
	IcePoint TriEdge0	= vert1 - vert0;
	IcePoint TriEdge1	= vert2 - vert0;

//IcePoint kDiff	= vert0 - mCenter;
	float fA00	= TriEdge0.SquareMagnitude();
	float fA01	= TriEdge0 | TriEdge1;
	float fA11	= TriEdge1.SquareMagnitude();
	float fB0	= kDiff | TriEdge0;
	float fB1	= kDiff | TriEdge1;
//float fC	= kDiff.SquareMagnitude();
	float fDet	= fabsf(fA00*fA11 - fA01*fA01);
	float u		= fA01*fB1-fA11*fB0;
	float v		= fA01*fB0-fA00*fB1;
	float SqrDist;

	if(u + v <= fDet)
	{
		if(u < 0.0f)
		{
			if(v < 0.0f)  // region 4
			{
				if(fB0 < 0.0f)
				{
//					v = 0.0f;
					if(-fB0>=fA00)			{ /*u = 1.0f;*/		SqrDist = fA00+2.0f*fB0+fC;	}
					else					{ u = -fB0/fA00;	SqrDist = fB0*u+fC;			}
				}
				else
				{
//					u = 0.0f;
					if(fB1>=0.0f)			{ /*v = 0.0f;*/		SqrDist = fC;				}
					else if(-fB1>=fA11)		{ /*v = 1.0f;*/		SqrDist = fA11+2.0f*fB1+fC;	}
					else					{ v = -fB1/fA11;	SqrDist = fB1*v+fC;			}
				}
			}
			else  // region 3
			{
//				u = 0.0f;
				if(fB1>=0.0f)				{ /*v = 0.0f;*/		SqrDist = fC;				}
				else if(-fB1>=fA11)			{ /*v = 1.0f;*/		SqrDist = fA11+2.0f*fB1+fC;	}
				else						{ v = -fB1/fA11;	SqrDist = fB1*v+fC;			}
			}
		}
		else if(v < 0.0f)  // region 5
		{
//			v = 0.0f;
			if(fB0>=0.0f)					{ /*u = 0.0f;*/		SqrDist = fC;				}
			else if(-fB0>=fA00)				{ /*u = 1.0f;*/		SqrDist = fA00+2.0f*fB0+fC;	}
			else							{ u = -fB0/fA00;	SqrDist = fB0*u+fC;			}
		}
		else  // region 0
		{
			// minimum at interior IcePoint
			if(fDet==0.0f)
			{
//				u = 0.0f;
//				v = 0.0f;
				SqrDist = MAX_FLOAT;
			}
			else
			{
				float fInvDet = 1.0f/fDet;
				u *= fInvDet;
				v *= fInvDet;
				SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
			}
		}
	}
	else
	{
		float fTmp0, fTmp1, fNumer, fDenom;

		if(u < 0.0f)  // region 2
		{
			fTmp0 = fA01 + fB0;
			fTmp1 = fA11 + fB1;
			if(fTmp1 > fTmp0)
			{
				fNumer = fTmp1 - fTmp0;
				fDenom = fA00-2.0f*fA01+fA11;
				if(fNumer >= fDenom)
				{
//					u = 1.0f;
//					v = 0.0f;
					SqrDist = fA00+2.0f*fB0+fC;
				}
				else
				{
					u = fNumer/fDenom;
					v = 1.0f - u;
					SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
				}
			}
			else
			{
//				u = 0.0f;
				if(fTmp1 <= 0.0f)		{ /*v = 1.0f;*/		SqrDist = fA11+2.0f*fB1+fC;	}
				else if(fB1 >= 0.0f)	{ /*v = 0.0f;*/		SqrDist = fC;				}
				else					{ v = -fB1/fA11;	SqrDist = fB1*v+fC;			}
			}
		}
		else if(v < 0.0f)  // region 6
		{
			fTmp0 = fA01 + fB1;
			fTmp1 = fA00 + fB0;
			if(fTmp1 > fTmp0)
			{
				fNumer = fTmp1 - fTmp0;
				fDenom = fA00-2.0f*fA01+fA11;
				if(fNumer >= fDenom)
				{
//					v = 1.0f;
//					u = 0.0f;
					SqrDist = fA11+2.0f*fB1+fC;
				}
				else
				{
					v = fNumer/fDenom;
					u = 1.0f - v;
					SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
				}
			}
			else
			{
//				v = 0.0f;
				if(fTmp1 <= 0.0f)		{ /*u = 1.0f;*/		SqrDist = fA00+2.0f*fB0+fC;	}
				else if(fB0 >= 0.0f)	{ /*u = 0.0f;*/		SqrDist = fC;				}
				else					{ u = -fB0/fA00;	SqrDist = fB0*u+fC;			}
			}
		}
		else  // region 1
		{
			fNumer = fA11 + fB1 - fA01 - fB0;
			if(fNumer <= 0.0f)
			{
//				u = 0.0f;
//				v = 1.0f;
				SqrDist = fA11+2.0f*fB1+fC;
			}
			else
			{
				fDenom = fA00-2.0f*fA01+fA11;
				if(fNumer >= fDenom)
				{
//					u = 1.0f;
//					v = 0.0f;
					SqrDist = fA00+2.0f*fB0+fC;
				}
				else
				{
					u = fNumer/fDenom;
					v = 1.0f - u;
					SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
				}
			}
		}
	}

	return fabsf(SqrDist) < mRadius2;
}