/*
 *	OPCODE - Optimized Collision Detection
 * http://www.codercorner.com/Opcode.htm
 * 
 * Copyright (c) 2001-2008 Pierre Terdiman,  pierre@codercorner.com

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/

// 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 Point& vert0, const Point& vert1, const Point& vert2)
{
	// Stats
	mNbVolumePrimTests++;

	// Early exit if one of the vertices is inside the sphere
	Point 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
	Point TriEdge0	= vert1 - vert0;
	Point TriEdge1	= vert2 - vert0;

//Point 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 point
			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;
}