blender/extern/bullet/Bullet/NarrowPhaseCollision/BU_VertexPoly.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.
*/


#include "BU_VertexPoly.h"
#include "BU_Screwing.h"
#include <SimdTransform.h>
#include <SimdPoint3.h>
#include <SimdVector3.h>

#define USE_ALGEBRAIC
#ifdef USE_ALGEBRAIC
	#include "BU_AlgebraicPolynomialSolver.h"
	#define BU_Polynomial BU_AlgebraicPolynomialSolver
#else
	#include "BU_IntervalArithmeticPolynomialSolver.h"
	#define BU_Polynomial BU_IntervalArithmeticPolynomialSolver
#endif

inline bool      TestFuzzyZero(SimdScalar x) { return SimdFabs(x) < 0.0001f; }


BU_VertexPoly::BU_VertexPoly()
{

}
//return true if a collision will occur between [0..1]
//false otherwise. If true, minTime contains the time of impact
bool BU_VertexPoly::GetTimeOfImpact(
		const BU_Screwing& screwAB,
		const SimdPoint3& a,
		const SimdVector4& planeEq,
		SimdScalar &minTime,bool swapAB)
{

	bool hit = false;

	// precondition: s=0 and w= 0 is catched by caller!
	if (TestFuzzyZero(screwAB.GetS()) &&
		TestFuzzyZero(screwAB.GetW()))
	{
		return false;
	}


	//case w<>0 and s<> 0
	const SimdScalar w=screwAB.GetW();
	const SimdScalar s=screwAB.GetS();

	SimdScalar coefs[4];
	const SimdScalar p=planeEq[0];
	const SimdScalar q=planeEq[1];
	const SimdScalar r=planeEq[2];
	const SimdScalar d=planeEq[3];

	const SimdVector3 norm(p,q,r);
	BU_Polynomial polynomialSolver;
	int numroots = 0;

	SimdScalar eps=1e-80f;
	SimdScalar eps2=1e-100f;
	
	if (TestFuzzyZero(screwAB.GetS()) )	
	{
		//S = 0 , W <> 0
		
		//ax^3+bx^2+cx+d=0
		coefs[0]=0.;
		coefs[1]=(-p*a.x()-q*a.y()+r*a.z()-d);
		coefs[2]=-2*p*a.y()+2*q*a.x();
		coefs[3]=p*a.x()+q*a.y()+r*a.z()-d;

//		numroots = polynomialSolver.Solve3Cubic(coefs[0],coefs[1],coefs[2],coefs[3]);
		numroots = polynomialSolver.Solve2QuadraticFull(coefs[1],coefs[2],coefs[3]);

	} else
	{
		if (TestFuzzyZero(screwAB.GetW()))
		{
			// W = 0 , S <> 0
			//pax+qay+r(az+st)=d
			
			SimdScalar dist = (d - a.dot(norm));

			if (TestFuzzyZero(r))
			{
				if (TestFuzzyZero(dist))
				{
					// no hit
				} else
				{
					// todo a a' might hit sides of polygon T
					//printf("unhandled case, w=0,s<>0,r<>0, a a' might hit sides of polygon T \n");
				}
				
			} else
			{
				SimdScalar etoi = (dist)/(r*screwAB.GetS());
				if (swapAB)
					etoi *= -1;

				if (etoi >= 0. && etoi <= minTime)
				{
					minTime = etoi;
					hit = true;
				}
			}

		} else
		{
				//ax^3+bx^2+cx+d=0

				//degenerate coefficients mess things up :(
				SimdScalar ietsje = (r*s)/SimdTan(w/2.f);
				if (ietsje*ietsje < 0.01f)
					ietsje = 0.f;

				coefs[0]=ietsje;//(r*s)/tan(w/2.);
				coefs[1]=(-p*a.x()-q*a.y()+r*a.z()-d);
				coefs[2]=-2.f*p*a.y()+2.f*q*a.x()+ietsje;//((r*s)/(tan(w/2.)));
				coefs[3]=p*a.x()+q*a.y()+r*a.z()-d;

				numroots = polynomialSolver.Solve3Cubic(coefs[0],coefs[1],coefs[2],coefs[3]);
		}
	}


	for (int i=0;i<numroots;i++)
	{
		SimdScalar tau = polynomialSolver.GetRoot(i);

		SimdScalar t = 2.f*SimdAtan(tau)/w;
		//tau = tan (wt/2) so 2*atan (tau)/w
		if (swapAB)
		{
			t *= -1.;
		}
		if (t>=0 && t<minTime)
		{
			minTime = t;
			hit = true;
		}
	}
	
	return hit;
}