blender/extern/bullet/Bullet/NarrowPhaseCollision/VoronoiSimplexSolver.cpp

/*
 * Copyright (c) 2005 Erwin Coumans http://continuousphysics.com/Bullet/
 *
 * Permission to use, copy, modify, distribute and sell this software
 * and its documentation for any purpose is hereby granted without fee,
 * provided that the above copyright notice appear in all copies.
 * Erwin Coumans makes no representations about the suitability 
 * of this software for any purpose.  
 * It is provided "as is" without express or implied warranty.
 *
	
	Elsevier CDROM license agreements grants nonexclusive license to use the software
	for any purpose, commercial or non-commercial as long as the following credit is included
	identifying the original source of the software:

	Parts of the source are "from the book Real-Time Collision Detection by
	Christer Ericson, published by Morgan Kaufmann Publishers,
	(c) 2005 Elsevier Inc."
		
*/


#include "VoronoiSimplexSolver.h"
#include <assert.h>
#include <stdio.h>

#define VERTA  0
#define VERTB  1
#define VERTC  2
#define VERTD  3

#define CATCH_DEGENERATE_TETRAHEDRON 1
void	VoronoiSimplexSolver::removeVertex(int index)
{
	
	assert(m_numVertices>0);
	m_numVertices--;
	m_simplexVectorW[index] = m_simplexVectorW[m_numVertices];
	m_simplexPointsP[index] = m_simplexPointsP[m_numVertices];
	m_simplexPointsQ[index] = m_simplexPointsQ[m_numVertices];
}

void	VoronoiSimplexSolver::ReduceVertices (const UsageBitfield& usedVerts)
{
	if ((numVertices() >= 4) && (!usedVerts.usedVertexD))
		removeVertex(3);

	if ((numVertices() >= 3) && (!usedVerts.usedVertexC))
		removeVertex(2);

	if ((numVertices() >= 2) && (!usedVerts.usedVertexB))
		removeVertex(1);
	
	if ((numVertices() >= 1) && (!usedVerts.usedVertexA))
		removeVertex(0);

}





//clear the simplex, remove all the vertices
void VoronoiSimplexSolver::reset()
{
	m_cachedValidClosest = false;
	m_numVertices = 0;
	m_needsUpdate = true;
	m_lastW = SimdVector3(1e30f,1e30f,1e30f);
	m_cachedBC.Reset();
}



	//add a vertex
void VoronoiSimplexSolver::addVertex(const SimdVector3& w, const SimdPoint3& p, const SimdPoint3& q)
{
	m_lastW = w;
	m_needsUpdate = true;

	m_simplexVectorW[m_numVertices] = w;
	m_simplexPointsP[m_numVertices] = p;
	m_simplexPointsQ[m_numVertices] = q;

	m_numVertices++;
}

bool	VoronoiSimplexSolver::UpdateClosestVectorAndPoints()
{
	
	if (m_needsUpdate)
	{
		m_cachedBC.Reset();

		m_needsUpdate = false;

		switch (numVertices())
		{
		case 0:
				m_cachedValidClosest = false;
				break;
		case 1:
			{
				m_cachedP1 = m_simplexPointsP[0];
				m_cachedP2 = m_simplexPointsQ[0];
				m_cachedV = m_cachedP1-m_cachedP2; //== m_simplexVectorW[0]
				m_cachedBC.Reset();
				m_cachedBC.SetBarycentricCoordinates(1.f,0.f,0.f,0.f);
				m_cachedValidClosest = m_cachedBC.IsValid();
				break;
			};
		case 2:
			{
			//closest point origin from line segment
					const SimdVector3& from = m_simplexVectorW[0];
					const SimdVector3& to = m_simplexVectorW[1];
					SimdVector3 nearest;

					SimdVector3 p (0.f,0.f,0.f);
					SimdVector3 diff = p - from;
					SimdVector3 v = to - from;
					float t = v.dot(diff);
					
					if (t > 0) {
						float dotVV = v.dot(v);
						if (t < dotVV) {
							t /= dotVV;
							diff -= t*v;
							m_cachedBC.m_usedVertices.usedVertexA = true;
							m_cachedBC.m_usedVertices.usedVertexB = true;
						} else {
							t = 1;
							diff -= v;
							//reduce to 1 point
							m_cachedBC.m_usedVertices.usedVertexB = true;
						}
					} else
					{
						t = 0;
						//reduce to 1 point
						m_cachedBC.m_usedVertices.usedVertexA = true;
					}
					m_cachedBC.SetBarycentricCoordinates(1-t,t);
					nearest = from + t*v;

					m_cachedP1 = m_simplexPointsP[0] + t * (m_simplexPointsP[1] - m_simplexPointsP[0]);
					m_cachedP2 = m_simplexPointsQ[0] + t * (m_simplexPointsQ[1] - m_simplexPointsQ[0]);
					m_cachedV = m_cachedP1 - m_cachedP2;
					
					ReduceVertices(m_cachedBC.m_usedVertices);

					m_cachedValidClosest = m_cachedBC.IsValid();
					break;
			}
		case 3:
			{
				//closest point origin from triangle
				SimdVector3 p (0.f,0.f,0.f);
				
				const SimdVector3& a = m_simplexVectorW[0];
				const SimdVector3& b = m_simplexVectorW[1];
				const SimdVector3& c = m_simplexVectorW[2];

				ClosestPtPointTriangle(p,a,b,c,m_cachedBC);
				m_cachedP1 = m_simplexPointsP[0] * m_cachedBC.m_barycentricCoords[0] +
								m_simplexPointsP[1] * m_cachedBC.m_barycentricCoords[1] +
								m_simplexPointsP[2] * m_cachedBC.m_barycentricCoords[2] +
								m_simplexPointsP[3] * m_cachedBC.m_barycentricCoords[3];

				m_cachedP2 = m_simplexPointsQ[0] * m_cachedBC.m_barycentricCoords[0] +
					m_simplexPointsQ[1] * m_cachedBC.m_barycentricCoords[1] +
					m_simplexPointsQ[2] * m_cachedBC.m_barycentricCoords[2] +
					m_simplexPointsQ[3] * m_cachedBC.m_barycentricCoords[3];

				m_cachedV = m_cachedP1-m_cachedP2;

				ReduceVertices (m_cachedBC.m_usedVertices);
				m_cachedValidClosest =  m_cachedBC.IsValid();

				break;
			}
		case 4:
			{

				
				SimdVector3 p (0.f,0.f,0.f);
				
				const SimdVector3& a = m_simplexVectorW[0];
				const SimdVector3& b = m_simplexVectorW[1];
				const SimdVector3& c = m_simplexVectorW[2];
				const SimdVector3& d = m_simplexVectorW[3];

				bool hasSeperation = ClosestPtPointTetrahedron(p,a,b,c,d,m_cachedBC);

				if (hasSeperation)
				{

					m_cachedP1 = m_simplexPointsP[0] * m_cachedBC.m_barycentricCoords[0] +
						m_simplexPointsP[1] * m_cachedBC.m_barycentricCoords[1] +
						m_simplexPointsP[2] * m_cachedBC.m_barycentricCoords[2] +
						m_simplexPointsP[3] * m_cachedBC.m_barycentricCoords[3];

					m_cachedP2 = m_simplexPointsQ[0] * m_cachedBC.m_barycentricCoords[0] +
						m_simplexPointsQ[1] * m_cachedBC.m_barycentricCoords[1] +
						m_simplexPointsQ[2] * m_cachedBC.m_barycentricCoords[2] +
						m_simplexPointsQ[3] * m_cachedBC.m_barycentricCoords[3];

					m_cachedV = m_cachedP1-m_cachedP2;
					ReduceVertices (m_cachedBC.m_usedVertices);
				} else
				{
//					printf("sub distance got penetration\n");

					if (m_cachedBC.m_degenerate)
					{
						m_cachedValidClosest = false;
					} else
					{
						m_cachedValidClosest = true;
						//degenerate case == false, penetration = true + zero
						m_cachedV.setValue(0.f,0.f,0.f);
					}
					break;
				}

				m_cachedValidClosest = m_cachedBC.IsValid();

				//closest point origin from tetrahedron
				break;
			}
		default:
			{
				m_cachedValidClosest = false;
			}
		};
	}

	return m_cachedValidClosest;

}

//return/calculate the closest vertex
bool VoronoiSimplexSolver::closest(SimdVector3& v)
{
	bool succes = UpdateClosestVectorAndPoints();
	v = m_cachedV;
	return succes;
}



SimdScalar VoronoiSimplexSolver::maxVertex()
{
	int i, numverts = numVertices();
	SimdScalar maxV = 0.f;
	for (i=0;i<numverts;i++)
	{
		SimdScalar curLen2 = m_simplexVectorW[i].length2();
		if (maxV < curLen2)
			maxV = curLen2;
	}
	return maxV;
}



	//return the current simplex
int VoronoiSimplexSolver::getSimplex(SimdPoint3 *pBuf, SimdPoint3 *qBuf, SimdVector3 *yBuf) const
{
	int i;
	for (i=0;i<numVertices();i++)
	{
		yBuf[i] = m_simplexVectorW[i];
		pBuf[i] = m_simplexPointsP[i];
		qBuf[i] = m_simplexPointsQ[i];
	}
	return numVertices();
}




bool VoronoiSimplexSolver::inSimplex(const SimdVector3& w)
{
	bool found = false;
	int i, numverts = numVertices();
	SimdScalar maxV = 0.f;
	
	//w is in the current (reduced) simplex
	for (i=0;i<numverts;i++)
	{
		if (m_simplexVectorW[i] == w)
			found = true;
	}

	//check in case lastW is already removed
	if (w == m_lastW)
		return true;
    	
	return found;
}

void VoronoiSimplexSolver::backup_closest(SimdVector3& v) 
{
	v = m_cachedV;
}


bool VoronoiSimplexSolver::emptySimplex() const 
{
	return (numVertices() == 0);

}

void VoronoiSimplexSolver::compute_points(SimdPoint3& p1, SimdPoint3& p2) 
{
	UpdateClosestVectorAndPoints();
	p1 = m_cachedP1;
	p2 = m_cachedP2;

}




bool	VoronoiSimplexSolver::ClosestPtPointTriangle(const SimdPoint3& p, const SimdPoint3& a, const SimdPoint3& b, const SimdPoint3& c,SubSimplexClosestResult& result)
{
	result.m_usedVertices.reset();

    // Check if P in vertex region outside A
    SimdVector3 ab = b - a;
    SimdVector3 ac = c - a;
    SimdVector3 ap = p - a;
    float d1 = ab.dot(ap);
    float d2 = ac.dot(ap);
    if (d1 <= 0.0f && d2 <= 0.0f) 
	{
		result.m_closestPointOnSimplex = a;
		result.m_usedVertices.usedVertexA = true;
		result.SetBarycentricCoordinates(1,0,0);
		return true;// a; // barycentric coordinates (1,0,0)
	}

    // Check if P in vertex region outside B
    SimdVector3 bp = p - b;
    float d3 = ab.dot(bp);
    float d4 = ac.dot(bp);
    if (d3 >= 0.0f && d4 <= d3) 
	{
		result.m_closestPointOnSimplex = b;
		result.m_usedVertices.usedVertexB = true;
		result.SetBarycentricCoordinates(0,1,0);

		return true; // b; // barycentric coordinates (0,1,0)
	}
    // Check if P in edge region of AB, if so return projection of P onto AB
    float vc = d1*d4 - d3*d2;
    if (vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f) {
        float v = d1 / (d1 - d3);
		result.m_closestPointOnSimplex = a + v * ab;
		result.m_usedVertices.usedVertexA = true;
		result.m_usedVertices.usedVertexB = true;
		result.SetBarycentricCoordinates(1-v,v,0);
		return true;
        //return a + v * ab; // barycentric coordinates (1-v,v,0)
    }

    // Check if P in vertex region outside C
    SimdVector3 cp = p - c;
    float d5 = ab.dot(cp);
    float d6 = ac.dot(cp);
    if (d6 >= 0.0f && d5 <= d6) 
	{
		result.m_closestPointOnSimplex = c;
		result.m_usedVertices.usedVertexC = true;
		result.SetBarycentricCoordinates(0,0,1);
		return true;//c; // barycentric coordinates (0,0,1)
	}

    // Check if P in edge region of AC, if so return projection of P onto AC
    float vb = d5*d2 - d1*d6;
    if (vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f) {
        float w = d2 / (d2 - d6);
		result.m_closestPointOnSimplex = a + w * ac;
		result.m_usedVertices.usedVertexA = true;
		result.m_usedVertices.usedVertexC = true;
		result.SetBarycentricCoordinates(1-w,0,w);
		return true;
        //return a + w * ac; // barycentric coordinates (1-w,0,w)
    }

    // Check if P in edge region of BC, if so return projection of P onto BC
    float va = d3*d6 - d5*d4;
    if (va <= 0.0f && (d4 - d3) >= 0.0f && (d5 - d6) >= 0.0f) {
        float w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
		
		result.m_closestPointOnSimplex = b + w * (c - b);
		result.m_usedVertices.usedVertexB = true;
		result.m_usedVertices.usedVertexC = true;
		result.SetBarycentricCoordinates(0,1-w,w);
		return true;		
       // return b + w * (c - b); // barycentric coordinates (0,1-w,w)
    }

    // P inside face region. Compute Q through its barycentric coordinates (u,v,w)
    float denom = 1.0f / (va + vb + vc);
    float v = vb * denom;
    float w = vc * denom;
    
	result.m_closestPointOnSimplex = a + ab * v + ac * w;
	result.m_usedVertices.usedVertexA = true;
	result.m_usedVertices.usedVertexB = true;
	result.m_usedVertices.usedVertexC = true;
	result.SetBarycentricCoordinates(1-v-w,v,w);
	
	return true;
//	return a + ab * v + ac * w; // = u*a + v*b + w*c, u = va * denom = 1.0f - v - w

}





/// Test if point p and d lie on opposite sides of plane through abc
int VoronoiSimplexSolver::PointOutsideOfPlane(const SimdPoint3& p, const SimdPoint3& a, const SimdPoint3& b, const SimdPoint3& c, const SimdPoint3& d)
{
	SimdVector3 normal = (b-a).cross(c-a);

    float signp = (p - a).dot(normal); // [AP AB AC]
    float signd = (d - a).dot( normal); // [AD AB AC]

#ifdef CATCH_DEGENERATE_TETRAHEDRON
	if (signd * signd < (1e-4f * 1e-4f))
	{
//		printf("affine dependent/degenerate\n");//
		return -1;
	}
#endif
	// Points on opposite sides if expression signs are opposite
    return signp * signd < 0.f;
}


bool	VoronoiSimplexSolver::ClosestPtPointTetrahedron(const SimdPoint3& p, const SimdPoint3& a, const SimdPoint3& b, const SimdPoint3& c, const SimdPoint3& d, SubSimplexClosestResult& finalResult)
{
	SubSimplexClosestResult tempResult;

    // Start out assuming point inside all halfspaces, so closest to itself
	finalResult.m_closestPointOnSimplex = p;
	finalResult.m_usedVertices.reset();
    finalResult.m_usedVertices.usedVertexA = true;
	finalResult.m_usedVertices.usedVertexB = true;
	finalResult.m_usedVertices.usedVertexC = true;
	finalResult.m_usedVertices.usedVertexD = true;

    int pointOutsideABC = PointOutsideOfPlane(p, a, b, c, d);
	int pointOutsideACD = PointOutsideOfPlane(p, a, c, d, b);
  	int	pointOutsideADB = PointOutsideOfPlane(p, a, d, b, c);
	int	pointOutsideBDC = PointOutsideOfPlane(p, b, d, c, a);

   if (pointOutsideABC < 0 || pointOutsideACD < 0 || pointOutsideADB < 0 || pointOutsideBDC < 0)
   {
	   finalResult.m_degenerate = true;
	   return false;
   }

   if (!pointOutsideABC  && !pointOutsideACD && !pointOutsideADB && !pointOutsideBDC)
	 {
		 return false;
	 }


    float bestSqDist = FLT_MAX;
    // If point outside face abc then compute closest point on abc
	if (pointOutsideABC) 
	{
        ClosestPtPointTriangle(p, a, b, c,tempResult);
		SimdPoint3 q = tempResult.m_closestPointOnSimplex;
		
        float sqDist = (q - p).dot( q - p);
        // Update best closest point if (squared) distance is less than current best
        if (sqDist < bestSqDist) {
			bestSqDist = sqDist;
			finalResult.m_closestPointOnSimplex = q;
			//convert result bitmask!
			finalResult.m_usedVertices.reset();
			finalResult.m_usedVertices.usedVertexA = tempResult.m_usedVertices.usedVertexA;
			finalResult.m_usedVertices.usedVertexB = tempResult.m_usedVertices.usedVertexB;
			finalResult.m_usedVertices.usedVertexC = tempResult.m_usedVertices.usedVertexC;
			finalResult.SetBarycentricCoordinates(
					tempResult.m_barycentricCoords[VERTA],
					tempResult.m_barycentricCoords[VERTB],
					tempResult.m_barycentricCoords[VERTC],
					0
			);

		}
    }
  

	// Repeat test for face acd
	if (pointOutsideACD) 
	{
        ClosestPtPointTriangle(p, a, c, d,tempResult);
		SimdPoint3 q = tempResult.m_closestPointOnSimplex;
		//convert result bitmask!

        float sqDist = (q - p).dot( q - p);
        if (sqDist < bestSqDist) 
		{
			bestSqDist = sqDist;
			finalResult.m_closestPointOnSimplex = q;
			finalResult.m_usedVertices.reset();
			finalResult.m_usedVertices.usedVertexA = tempResult.m_usedVertices.usedVertexA;
			finalResult.m_usedVertices.usedVertexC = tempResult.m_usedVertices.usedVertexB;
			finalResult.m_usedVertices.usedVertexD = tempResult.m_usedVertices.usedVertexC;
			finalResult.SetBarycentricCoordinates(
					tempResult.m_barycentricCoords[VERTA],
					0,
					tempResult.m_barycentricCoords[VERTB],
					tempResult.m_barycentricCoords[VERTC]
			);

		}
    }
    // Repeat test for face adb

	
	if (pointOutsideADB)
	{
		ClosestPtPointTriangle(p, a, d, b,tempResult);
		SimdPoint3 q = tempResult.m_closestPointOnSimplex;
		//convert result bitmask!

        float sqDist = (q - p).dot( q - p);
        if (sqDist < bestSqDist) 
		{
			bestSqDist = sqDist;
			finalResult.m_closestPointOnSimplex = q;
			finalResult.m_usedVertices.reset();
			finalResult.m_usedVertices.usedVertexA = tempResult.m_usedVertices.usedVertexA;
			finalResult.m_usedVertices.usedVertexD = tempResult.m_usedVertices.usedVertexB;
			finalResult.m_usedVertices.usedVertexB = tempResult.m_usedVertices.usedVertexC;
			finalResult.SetBarycentricCoordinates(
					tempResult.m_barycentricCoords[VERTA],
					tempResult.m_barycentricCoords[VERTC],
					0,
					tempResult.m_barycentricCoords[VERTB]
			);

		}
    }
    // Repeat test for face bdc
    

	if (pointOutsideBDC)
	{
        ClosestPtPointTriangle(p, b, d, c,tempResult);
		SimdPoint3 q = tempResult.m_closestPointOnSimplex;
		//convert result bitmask!
        float sqDist = (q - p).dot( q - p);
        if (sqDist < bestSqDist) 
		{
			bestSqDist = sqDist;
			finalResult.m_closestPointOnSimplex = q;
			finalResult.m_usedVertices.reset();
			finalResult.m_usedVertices.usedVertexB = tempResult.m_usedVertices.usedVertexA;
			finalResult.m_usedVertices.usedVertexD = tempResult.m_usedVertices.usedVertexB;
			finalResult.m_usedVertices.usedVertexC = tempResult.m_usedVertices.usedVertexC;

			finalResult.SetBarycentricCoordinates(
					0,
					tempResult.m_barycentricCoords[VERTA],
					tempResult.m_barycentricCoords[VERTC],
					tempResult.m_barycentricCoords[VERTB]
			);

		}
    }

	//help! we ended up full !
	
	if (finalResult.m_usedVertices.usedVertexA &&
		finalResult.m_usedVertices.usedVertexB &&
		finalResult.m_usedVertices.usedVertexC &&
		finalResult.m_usedVertices.usedVertexD) 
	{
		return true;
	}

    return true;
}