1036 lines
35 KiB
C++
1036 lines
35 KiB
C++
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/*
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Bullet Continuous Collision Detection and Physics Library
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Copyright (c) 2003-2014 Erwin Coumans http://continuousphysics.com/Bullet/
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This software is provided 'as-is', without any express or implied warranty.
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In no event will the authors be held liable for any damages arising from the
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use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it
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freely,
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subject to the following restrictions:
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1. The origin of this software must not be misrepresented; you must not
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claim that you wrote the original software. If you use this software in a
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product, an acknowledgment in the product documentation would be appreciated
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but is not required.
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2. Altered source versions must be plainly marked as such, and must not be
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misrepresented as being the original software.
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3. This notice may not be removed or altered from any source distribution.
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*/
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/*
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Initial GJK-EPA collision solver by Nathanael Presson, 2008
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Improvements and refactoring by Erwin Coumans, 2008-2014
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*/
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#ifndef BT_GJK_EPA3_H
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#define BT_GJK_EPA3_H
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#include "LinearMath/btTransform.h"
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#include "btGjkCollisionDescription.h"
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struct btGjkEpaSolver3
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{
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struct sResults
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{
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enum eStatus
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{
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Separated, /* Shapes doesnt penetrate */
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Penetrating, /* Shapes are penetrating */
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GJK_Failed, /* GJK phase fail, no big issue, shapes are probably just 'touching' */
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EPA_Failed /* EPA phase fail, bigger problem, need to save parameters, and debug */
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} status;
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btVector3 witnesses[2];
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btVector3 normal;
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btScalar distance;
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};
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};
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#if defined(DEBUG) || defined (_DEBUG)
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#include <stdio.h> //for debug printf
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#ifdef __SPU__
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#include <spu_printf.h>
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#define printf spu_printf
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#endif //__SPU__
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#endif
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// Config
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/* GJK */
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#define GJK_MAX_ITERATIONS 128
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#define GJK_ACCURARY ((btScalar)0.0001)
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#define GJK_MIN_DISTANCE ((btScalar)0.0001)
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#define GJK_DUPLICATED_EPS ((btScalar)0.0001)
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#define GJK_SIMPLEX2_EPS ((btScalar)0.0)
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#define GJK_SIMPLEX3_EPS ((btScalar)0.0)
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#define GJK_SIMPLEX4_EPS ((btScalar)0.0)
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/* EPA */
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#define EPA_MAX_VERTICES 64
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#define EPA_MAX_FACES (EPA_MAX_VERTICES*2)
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#define EPA_MAX_ITERATIONS 255
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#define EPA_ACCURACY ((btScalar)0.0001)
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#define EPA_FALLBACK (10*EPA_ACCURACY)
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#define EPA_PLANE_EPS ((btScalar)0.00001)
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#define EPA_INSIDE_EPS ((btScalar)0.01)
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// Shorthands
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typedef unsigned int U;
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typedef unsigned char U1;
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// MinkowskiDiff
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template <typename btConvexTemplate>
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struct MinkowskiDiff
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{
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const btConvexTemplate* m_convexAPtr;
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const btConvexTemplate* m_convexBPtr;
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btMatrix3x3 m_toshape1;
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btTransform m_toshape0;
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bool m_enableMargin;
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MinkowskiDiff(const btConvexTemplate& a, const btConvexTemplate& b)
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:m_convexAPtr(&a),
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m_convexBPtr(&b)
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{
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}
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void EnableMargin(bool enable)
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{
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m_enableMargin = enable;
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}
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inline btVector3 Support0(const btVector3& d) const
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{
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return m_convexAPtr->getLocalSupportWithMargin(d);
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}
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inline btVector3 Support1(const btVector3& d) const
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{
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return m_toshape0*m_convexBPtr->getLocalSupportWithMargin(m_toshape1*d);
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}
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inline btVector3 Support(const btVector3& d) const
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{
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return(Support0(d)-Support1(-d));
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}
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btVector3 Support(const btVector3& d,U index) const
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{
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if(index)
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return(Support1(d));
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else
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return(Support0(d));
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}
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};
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enum eGjkStatus
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{
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eGjkValid,
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eGjkInside,
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eGjkFailed
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};
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// GJK
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template <typename btConvexTemplate>
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struct GJK
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{
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/* Types */
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struct sSV
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{
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btVector3 d,w;
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};
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struct sSimplex
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{
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sSV* c[4];
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btScalar p[4];
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U rank;
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};
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/* Fields */
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MinkowskiDiff<btConvexTemplate> m_shape;
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btVector3 m_ray;
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btScalar m_distance;
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sSimplex m_simplices[2];
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sSV m_store[4];
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sSV* m_free[4];
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U m_nfree;
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U m_current;
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sSimplex* m_simplex;
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eGjkStatus m_status;
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/* Methods */
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GJK(const btConvexTemplate& a, const btConvexTemplate& b)
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:m_shape(a,b)
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{
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Initialize();
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}
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void Initialize()
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{
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m_ray = btVector3(0,0,0);
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m_nfree = 0;
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m_status = eGjkFailed;
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m_current = 0;
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m_distance = 0;
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}
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eGjkStatus Evaluate(const MinkowskiDiff<btConvexTemplate>& shapearg,const btVector3& guess)
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{
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U iterations=0;
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btScalar sqdist=0;
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btScalar alpha=0;
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btVector3 lastw[4];
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U clastw=0;
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/* Initialize solver */
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m_free[0] = &m_store[0];
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m_free[1] = &m_store[1];
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m_free[2] = &m_store[2];
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m_free[3] = &m_store[3];
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m_nfree = 4;
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m_current = 0;
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m_status = eGjkValid;
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m_shape = shapearg;
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m_distance = 0;
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/* Initialize simplex */
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m_simplices[0].rank = 0;
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m_ray = guess;
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const btScalar sqrl= m_ray.length2();
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appendvertice(m_simplices[0],sqrl>0?-m_ray:btVector3(1,0,0));
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m_simplices[0].p[0] = 1;
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m_ray = m_simplices[0].c[0]->w;
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sqdist = sqrl;
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lastw[0] =
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lastw[1] =
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lastw[2] =
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lastw[3] = m_ray;
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/* Loop */
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do {
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const U next=1-m_current;
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sSimplex& cs=m_simplices[m_current];
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sSimplex& ns=m_simplices[next];
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/* Check zero */
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const btScalar rl=m_ray.length();
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if(rl<GJK_MIN_DISTANCE)
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{/* Touching or inside */
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m_status=eGjkInside;
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break;
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}
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/* Append new vertice in -'v' direction */
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appendvertice(cs,-m_ray);
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const btVector3& w=cs.c[cs.rank-1]->w;
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bool found=false;
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for(U i=0;i<4;++i)
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{
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if((w-lastw[i]).length2()<GJK_DUPLICATED_EPS)
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{ found=true;break; }
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}
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if(found)
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{/* Return old simplex */
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removevertice(m_simplices[m_current]);
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break;
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}
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else
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{/* Update lastw */
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lastw[clastw=(clastw+1)&3]=w;
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}
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/* Check for termination */
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const btScalar omega=btDot(m_ray,w)/rl;
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alpha=btMax(omega,alpha);
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if(((rl-alpha)-(GJK_ACCURARY*rl))<=0)
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{/* Return old simplex */
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removevertice(m_simplices[m_current]);
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break;
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}
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/* Reduce simplex */
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btScalar weights[4];
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U mask=0;
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switch(cs.rank)
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{
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case 2: sqdist=projectorigin( cs.c[0]->w,
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cs.c[1]->w,
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weights,mask);break;
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case 3: sqdist=projectorigin( cs.c[0]->w,
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cs.c[1]->w,
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cs.c[2]->w,
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weights,mask);break;
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case 4: sqdist=projectorigin( cs.c[0]->w,
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cs.c[1]->w,
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cs.c[2]->w,
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cs.c[3]->w,
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weights,mask);break;
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}
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if(sqdist>=0)
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{/* Valid */
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ns.rank = 0;
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m_ray = btVector3(0,0,0);
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m_current = next;
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for(U i=0,ni=cs.rank;i<ni;++i)
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{
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if(mask&(1<<i))
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{
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ns.c[ns.rank] = cs.c[i];
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ns.p[ns.rank++] = weights[i];
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m_ray += cs.c[i]->w*weights[i];
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}
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else
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{
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m_free[m_nfree++] = cs.c[i];
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}
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}
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if(mask==15) m_status=eGjkInside;
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}
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else
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{/* Return old simplex */
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removevertice(m_simplices[m_current]);
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break;
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}
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m_status=((++iterations)<GJK_MAX_ITERATIONS)?m_status:eGjkFailed;
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} while(m_status==eGjkValid);
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m_simplex=&m_simplices[m_current];
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switch(m_status)
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{
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case eGjkValid: m_distance=m_ray.length();break;
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case eGjkInside: m_distance=0;break;
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default:
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{
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}
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}
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return(m_status);
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}
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bool EncloseOrigin()
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{
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switch(m_simplex->rank)
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{
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case 1:
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{
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for(U i=0;i<3;++i)
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{
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btVector3 axis=btVector3(0,0,0);
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axis[i]=1;
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appendvertice(*m_simplex, axis);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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appendvertice(*m_simplex,-axis);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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}
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}
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break;
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case 2:
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{
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const btVector3 d=m_simplex->c[1]->w-m_simplex->c[0]->w;
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for(U i=0;i<3;++i)
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{
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btVector3 axis=btVector3(0,0,0);
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axis[i]=1;
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const btVector3 p=btCross(d,axis);
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if(p.length2()>0)
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{
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appendvertice(*m_simplex, p);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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appendvertice(*m_simplex,-p);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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}
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}
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}
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break;
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case 3:
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{
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const btVector3 n=btCross(m_simplex->c[1]->w-m_simplex->c[0]->w,
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m_simplex->c[2]->w-m_simplex->c[0]->w);
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if(n.length2()>0)
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{
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appendvertice(*m_simplex,n);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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appendvertice(*m_simplex,-n);
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if(EncloseOrigin()) return(true);
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removevertice(*m_simplex);
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}
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}
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break;
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case 4:
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{
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if(btFabs(det( m_simplex->c[0]->w-m_simplex->c[3]->w,
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m_simplex->c[1]->w-m_simplex->c[3]->w,
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m_simplex->c[2]->w-m_simplex->c[3]->w))>0)
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return(true);
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}
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break;
|
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}
|
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return(false);
|
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}
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/* Internals */
|
||
|
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void getsupport(const btVector3& d,sSV& sv) const
|
||
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{
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sv.d = d/d.length();
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sv.w = m_shape.Support(sv.d);
|
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}
|
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void removevertice(sSimplex& simplex)
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||
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{
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||
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m_free[m_nfree++]=simplex.c[--simplex.rank];
|
||
|
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}
|
||
|
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void appendvertice(sSimplex& simplex,const btVector3& v)
|
||
|
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{
|
||
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simplex.p[simplex.rank]=0;
|
||
|
|
simplex.c[simplex.rank]=m_free[--m_nfree];
|
||
|
|
getsupport(v,*simplex.c[simplex.rank++]);
|
||
|
|
}
|
||
|
|
static btScalar det(const btVector3& a,const btVector3& b,const btVector3& c)
|
||
|
|
{
|
||
|
|
return( a.y()*b.z()*c.x()+a.z()*b.x()*c.y()-
|
||
|
|
a.x()*b.z()*c.y()-a.y()*b.x()*c.z()+
|
||
|
|
a.x()*b.y()*c.z()-a.z()*b.y()*c.x());
|
||
|
|
}
|
||
|
|
static btScalar projectorigin( const btVector3& a,
|
||
|
|
const btVector3& b,
|
||
|
|
btScalar* w,U& m)
|
||
|
|
{
|
||
|
|
const btVector3 d=b-a;
|
||
|
|
const btScalar l=d.length2();
|
||
|
|
if(l>GJK_SIMPLEX2_EPS)
|
||
|
|
{
|
||
|
|
const btScalar t(l>0?-btDot(a,d)/l:0);
|
||
|
|
if(t>=1) { w[0]=0;w[1]=1;m=2;return(b.length2()); }
|
||
|
|
else if(t<=0) { w[0]=1;w[1]=0;m=1;return(a.length2()); }
|
||
|
|
else { w[0]=1-(w[1]=t);m=3;return((a+d*t).length2()); }
|
||
|
|
}
|
||
|
|
return(-1);
|
||
|
|
}
|
||
|
|
static btScalar projectorigin( const btVector3& a,
|
||
|
|
const btVector3& b,
|
||
|
|
const btVector3& c,
|
||
|
|
btScalar* w,U& m)
|
||
|
|
{
|
||
|
|
static const U imd3[]={1,2,0};
|
||
|
|
const btVector3* vt[]={&a,&b,&c};
|
||
|
|
const btVector3 dl[]={a-b,b-c,c-a};
|
||
|
|
const btVector3 n=btCross(dl[0],dl[1]);
|
||
|
|
const btScalar l=n.length2();
|
||
|
|
if(l>GJK_SIMPLEX3_EPS)
|
||
|
|
{
|
||
|
|
btScalar mindist=-1;
|
||
|
|
btScalar subw[2]={0.f,0.f};
|
||
|
|
U subm(0);
|
||
|
|
for(U i=0;i<3;++i)
|
||
|
|
{
|
||
|
|
if(btDot(*vt[i],btCross(dl[i],n))>0)
|
||
|
|
{
|
||
|
|
const U j=imd3[i];
|
||
|
|
const btScalar subd(projectorigin(*vt[i],*vt[j],subw,subm));
|
||
|
|
if((mindist<0)||(subd<mindist))
|
||
|
|
{
|
||
|
|
mindist = subd;
|
||
|
|
m = static_cast<U>(((subm&1)?1<<i:0)+((subm&2)?1<<j:0));
|
||
|
|
w[i] = subw[0];
|
||
|
|
w[j] = subw[1];
|
||
|
|
w[imd3[j]] = 0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if(mindist<0)
|
||
|
|
{
|
||
|
|
const btScalar d=btDot(a,n);
|
||
|
|
const btScalar s=btSqrt(l);
|
||
|
|
const btVector3 p=n*(d/l);
|
||
|
|
mindist = p.length2();
|
||
|
|
m = 7;
|
||
|
|
w[0] = (btCross(dl[1],b-p)).length()/s;
|
||
|
|
w[1] = (btCross(dl[2],c-p)).length()/s;
|
||
|
|
w[2] = 1-(w[0]+w[1]);
|
||
|
|
}
|
||
|
|
return(mindist);
|
||
|
|
}
|
||
|
|
return(-1);
|
||
|
|
}
|
||
|
|
static btScalar projectorigin( const btVector3& a,
|
||
|
|
const btVector3& b,
|
||
|
|
const btVector3& c,
|
||
|
|
const btVector3& d,
|
||
|
|
btScalar* w,U& m)
|
||
|
|
{
|
||
|
|
static const U imd3[]={1,2,0};
|
||
|
|
const btVector3* vt[]={&a,&b,&c,&d};
|
||
|
|
const btVector3 dl[]={a-d,b-d,c-d};
|
||
|
|
const btScalar vl=det(dl[0],dl[1],dl[2]);
|
||
|
|
const bool ng=(vl*btDot(a,btCross(b-c,a-b)))<=0;
|
||
|
|
if(ng&&(btFabs(vl)>GJK_SIMPLEX4_EPS))
|
||
|
|
{
|
||
|
|
btScalar mindist=-1;
|
||
|
|
btScalar subw[3]={0.f,0.f,0.f};
|
||
|
|
U subm(0);
|
||
|
|
for(U i=0;i<3;++i)
|
||
|
|
{
|
||
|
|
const U j=imd3[i];
|
||
|
|
const btScalar s=vl*btDot(d,btCross(dl[i],dl[j]));
|
||
|
|
if(s>0)
|
||
|
|
{
|
||
|
|
const btScalar subd=projectorigin(*vt[i],*vt[j],d,subw,subm);
|
||
|
|
if((mindist<0)||(subd<mindist))
|
||
|
|
{
|
||
|
|
mindist = subd;
|
||
|
|
m = static_cast<U>((subm&1?1<<i:0)+
|
||
|
|
(subm&2?1<<j:0)+
|
||
|
|
(subm&4?8:0));
|
||
|
|
w[i] = subw[0];
|
||
|
|
w[j] = subw[1];
|
||
|
|
w[imd3[j]] = 0;
|
||
|
|
w[3] = subw[2];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if(mindist<0)
|
||
|
|
{
|
||
|
|
mindist = 0;
|
||
|
|
m = 15;
|
||
|
|
w[0] = det(c,b,d)/vl;
|
||
|
|
w[1] = det(a,c,d)/vl;
|
||
|
|
w[2] = det(b,a,d)/vl;
|
||
|
|
w[3] = 1-(w[0]+w[1]+w[2]);
|
||
|
|
}
|
||
|
|
return(mindist);
|
||
|
|
}
|
||
|
|
return(-1);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
enum eEpaStatus
|
||
|
|
{
|
||
|
|
eEpaValid,
|
||
|
|
eEpaTouching,
|
||
|
|
eEpaDegenerated,
|
||
|
|
eEpaNonConvex,
|
||
|
|
eEpaInvalidHull,
|
||
|
|
eEpaOutOfFaces,
|
||
|
|
eEpaOutOfVertices,
|
||
|
|
eEpaAccuraryReached,
|
||
|
|
eEpaFallBack,
|
||
|
|
eEpaFailed
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
// EPA
|
||
|
|
template <typename btConvexTemplate>
|
||
|
|
struct EPA
|
||
|
|
{
|
||
|
|
/* Types */
|
||
|
|
|
||
|
|
struct sFace
|
||
|
|
{
|
||
|
|
btVector3 n;
|
||
|
|
btScalar d;
|
||
|
|
typename GJK<btConvexTemplate>::sSV* c[3];
|
||
|
|
sFace* f[3];
|
||
|
|
sFace* l[2];
|
||
|
|
U1 e[3];
|
||
|
|
U1 pass;
|
||
|
|
};
|
||
|
|
struct sList
|
||
|
|
{
|
||
|
|
sFace* root;
|
||
|
|
U count;
|
||
|
|
sList() : root(0),count(0) {}
|
||
|
|
};
|
||
|
|
struct sHorizon
|
||
|
|
{
|
||
|
|
sFace* cf;
|
||
|
|
sFace* ff;
|
||
|
|
U nf;
|
||
|
|
sHorizon() : cf(0),ff(0),nf(0) {}
|
||
|
|
};
|
||
|
|
|
||
|
|
/* Fields */
|
||
|
|
eEpaStatus m_status;
|
||
|
|
typename GJK<btConvexTemplate>::sSimplex m_result;
|
||
|
|
btVector3 m_normal;
|
||
|
|
btScalar m_depth;
|
||
|
|
typename GJK<btConvexTemplate>::sSV m_sv_store[EPA_MAX_VERTICES];
|
||
|
|
sFace m_fc_store[EPA_MAX_FACES];
|
||
|
|
U m_nextsv;
|
||
|
|
sList m_hull;
|
||
|
|
sList m_stock;
|
||
|
|
/* Methods */
|
||
|
|
EPA()
|
||
|
|
{
|
||
|
|
Initialize();
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
static inline void bind(sFace* fa,U ea,sFace* fb,U eb)
|
||
|
|
{
|
||
|
|
fa->e[ea]=(U1)eb;fa->f[ea]=fb;
|
||
|
|
fb->e[eb]=(U1)ea;fb->f[eb]=fa;
|
||
|
|
}
|
||
|
|
static inline void append(sList& list,sFace* face)
|
||
|
|
{
|
||
|
|
face->l[0] = 0;
|
||
|
|
face->l[1] = list.root;
|
||
|
|
if(list.root) list.root->l[0]=face;
|
||
|
|
list.root = face;
|
||
|
|
++list.count;
|
||
|
|
}
|
||
|
|
static inline void remove(sList& list,sFace* face)
|
||
|
|
{
|
||
|
|
if(face->l[1]) face->l[1]->l[0]=face->l[0];
|
||
|
|
if(face->l[0]) face->l[0]->l[1]=face->l[1];
|
||
|
|
if(face==list.root) list.root=face->l[1];
|
||
|
|
--list.count;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
void Initialize()
|
||
|
|
{
|
||
|
|
m_status = eEpaFailed;
|
||
|
|
m_normal = btVector3(0,0,0);
|
||
|
|
m_depth = 0;
|
||
|
|
m_nextsv = 0;
|
||
|
|
for(U i=0;i<EPA_MAX_FACES;++i)
|
||
|
|
{
|
||
|
|
append(m_stock,&m_fc_store[EPA_MAX_FACES-i-1]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
eEpaStatus Evaluate(GJK<btConvexTemplate>& gjk,const btVector3& guess)
|
||
|
|
{
|
||
|
|
typename GJK<btConvexTemplate>::sSimplex& simplex=*gjk.m_simplex;
|
||
|
|
if((simplex.rank>1)&&gjk.EncloseOrigin())
|
||
|
|
{
|
||
|
|
|
||
|
|
/* Clean up */
|
||
|
|
while(m_hull.root)
|
||
|
|
{
|
||
|
|
sFace* f = m_hull.root;
|
||
|
|
remove(m_hull,f);
|
||
|
|
append(m_stock,f);
|
||
|
|
}
|
||
|
|
m_status = eEpaValid;
|
||
|
|
m_nextsv = 0;
|
||
|
|
/* Orient simplex */
|
||
|
|
if(gjk.det( simplex.c[0]->w-simplex.c[3]->w,
|
||
|
|
simplex.c[1]->w-simplex.c[3]->w,
|
||
|
|
simplex.c[2]->w-simplex.c[3]->w)<0)
|
||
|
|
{
|
||
|
|
btSwap(simplex.c[0],simplex.c[1]);
|
||
|
|
btSwap(simplex.p[0],simplex.p[1]);
|
||
|
|
}
|
||
|
|
/* Build initial hull */
|
||
|
|
sFace* tetra[]={newface(simplex.c[0],simplex.c[1],simplex.c[2],true),
|
||
|
|
newface(simplex.c[1],simplex.c[0],simplex.c[3],true),
|
||
|
|
newface(simplex.c[2],simplex.c[1],simplex.c[3],true),
|
||
|
|
newface(simplex.c[0],simplex.c[2],simplex.c[3],true)};
|
||
|
|
if(m_hull.count==4)
|
||
|
|
{
|
||
|
|
sFace* best=findbest();
|
||
|
|
sFace outer=*best;
|
||
|
|
U pass=0;
|
||
|
|
U iterations=0;
|
||
|
|
bind(tetra[0],0,tetra[1],0);
|
||
|
|
bind(tetra[0],1,tetra[2],0);
|
||
|
|
bind(tetra[0],2,tetra[3],0);
|
||
|
|
bind(tetra[1],1,tetra[3],2);
|
||
|
|
bind(tetra[1],2,tetra[2],1);
|
||
|
|
bind(tetra[2],2,tetra[3],1);
|
||
|
|
m_status=eEpaValid;
|
||
|
|
for(;iterations<EPA_MAX_ITERATIONS;++iterations)
|
||
|
|
{
|
||
|
|
if(m_nextsv<EPA_MAX_VERTICES)
|
||
|
|
{
|
||
|
|
sHorizon horizon;
|
||
|
|
typename GJK<btConvexTemplate>::sSV* w=&m_sv_store[m_nextsv++];
|
||
|
|
bool valid=true;
|
||
|
|
best->pass = (U1)(++pass);
|
||
|
|
gjk.getsupport(best->n,*w);
|
||
|
|
const btScalar wdist=btDot(best->n,w->w)-best->d;
|
||
|
|
if(wdist>EPA_ACCURACY)
|
||
|
|
{
|
||
|
|
for(U j=0;(j<3)&&valid;++j)
|
||
|
|
{
|
||
|
|
valid&=expand( pass,w,
|
||
|
|
best->f[j],best->e[j],
|
||
|
|
horizon);
|
||
|
|
}
|
||
|
|
if(valid&&(horizon.nf>=3))
|
||
|
|
{
|
||
|
|
bind(horizon.cf,1,horizon.ff,2);
|
||
|
|
remove(m_hull,best);
|
||
|
|
append(m_stock,best);
|
||
|
|
best=findbest();
|
||
|
|
outer=*best;
|
||
|
|
} else { m_status=eEpaInvalidHull;break; }
|
||
|
|
} else { m_status=eEpaAccuraryReached;break; }
|
||
|
|
} else { m_status=eEpaOutOfVertices;break; }
|
||
|
|
}
|
||
|
|
const btVector3 projection=outer.n*outer.d;
|
||
|
|
m_normal = outer.n;
|
||
|
|
m_depth = outer.d;
|
||
|
|
m_result.rank = 3;
|
||
|
|
m_result.c[0] = outer.c[0];
|
||
|
|
m_result.c[1] = outer.c[1];
|
||
|
|
m_result.c[2] = outer.c[2];
|
||
|
|
m_result.p[0] = btCross( outer.c[1]->w-projection,
|
||
|
|
outer.c[2]->w-projection).length();
|
||
|
|
m_result.p[1] = btCross( outer.c[2]->w-projection,
|
||
|
|
outer.c[0]->w-projection).length();
|
||
|
|
m_result.p[2] = btCross( outer.c[0]->w-projection,
|
||
|
|
outer.c[1]->w-projection).length();
|
||
|
|
const btScalar sum=m_result.p[0]+m_result.p[1]+m_result.p[2];
|
||
|
|
m_result.p[0] /= sum;
|
||
|
|
m_result.p[1] /= sum;
|
||
|
|
m_result.p[2] /= sum;
|
||
|
|
return(m_status);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* Fallback */
|
||
|
|
m_status = eEpaFallBack;
|
||
|
|
m_normal = -guess;
|
||
|
|
const btScalar nl=m_normal.length();
|
||
|
|
if(nl>0)
|
||
|
|
m_normal = m_normal/nl;
|
||
|
|
else
|
||
|
|
m_normal = btVector3(1,0,0);
|
||
|
|
m_depth = 0;
|
||
|
|
m_result.rank=1;
|
||
|
|
m_result.c[0]=simplex.c[0];
|
||
|
|
m_result.p[0]=1;
|
||
|
|
return(m_status);
|
||
|
|
}
|
||
|
|
bool getedgedist(sFace* face, typename GJK<btConvexTemplate>::sSV* a, typename GJK<btConvexTemplate>::sSV* b, btScalar& dist)
|
||
|
|
{
|
||
|
|
const btVector3 ba = b->w - a->w;
|
||
|
|
const btVector3 n_ab = btCross(ba, face->n); // Outward facing edge normal direction, on triangle plane
|
||
|
|
const btScalar a_dot_nab = btDot(a->w, n_ab); // Only care about the sign to determine inside/outside, so not normalization required
|
||
|
|
|
||
|
|
if(a_dot_nab < 0)
|
||
|
|
{
|
||
|
|
// Outside of edge a->b
|
||
|
|
|
||
|
|
const btScalar ba_l2 = ba.length2();
|
||
|
|
const btScalar a_dot_ba = btDot(a->w, ba);
|
||
|
|
const btScalar b_dot_ba = btDot(b->w, ba);
|
||
|
|
|
||
|
|
if(a_dot_ba > 0)
|
||
|
|
{
|
||
|
|
// Pick distance vertex a
|
||
|
|
dist = a->w.length();
|
||
|
|
}
|
||
|
|
else if(b_dot_ba < 0)
|
||
|
|
{
|
||
|
|
// Pick distance vertex b
|
||
|
|
dist = b->w.length();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// Pick distance to edge a->b
|
||
|
|
const btScalar a_dot_b = btDot(a->w, b->w);
|
||
|
|
dist = btSqrt(btMax((a->w.length2() * b->w.length2() - a_dot_b * a_dot_b) / ba_l2, (btScalar)0));
|
||
|
|
}
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
sFace* newface(typename GJK<btConvexTemplate>::sSV* a,typename GJK<btConvexTemplate>::sSV* b,typename GJK<btConvexTemplate>::sSV* c,bool forced)
|
||
|
|
{
|
||
|
|
if(m_stock.root)
|
||
|
|
{
|
||
|
|
sFace* face=m_stock.root;
|
||
|
|
remove(m_stock,face);
|
||
|
|
append(m_hull,face);
|
||
|
|
face->pass = 0;
|
||
|
|
face->c[0] = a;
|
||
|
|
face->c[1] = b;
|
||
|
|
face->c[2] = c;
|
||
|
|
face->n = btCross(b->w-a->w,c->w-a->w);
|
||
|
|
const btScalar l=face->n.length();
|
||
|
|
const bool v=l>EPA_ACCURACY;
|
||
|
|
|
||
|
|
if(v)
|
||
|
|
{
|
||
|
|
if(!(getedgedist(face, a, b, face->d) ||
|
||
|
|
getedgedist(face, b, c, face->d) ||
|
||
|
|
getedgedist(face, c, a, face->d)))
|
||
|
|
{
|
||
|
|
// Origin projects to the interior of the triangle
|
||
|
|
// Use distance to triangle plane
|
||
|
|
face->d = btDot(a->w, face->n) / l;
|
||
|
|
}
|
||
|
|
|
||
|
|
face->n /= l;
|
||
|
|
if(forced || (face->d >= -EPA_PLANE_EPS))
|
||
|
|
{
|
||
|
|
return face;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
m_status=eEpaNonConvex;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
m_status=eEpaDegenerated;
|
||
|
|
|
||
|
|
remove(m_hull, face);
|
||
|
|
append(m_stock, face);
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
}
|
||
|
|
m_status = m_stock.root ? eEpaOutOfVertices : eEpaOutOfFaces;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
sFace* findbest()
|
||
|
|
{
|
||
|
|
sFace* minf=m_hull.root;
|
||
|
|
btScalar mind=minf->d*minf->d;
|
||
|
|
for(sFace* f=minf->l[1];f;f=f->l[1])
|
||
|
|
{
|
||
|
|
const btScalar sqd=f->d*f->d;
|
||
|
|
if(sqd<mind)
|
||
|
|
{
|
||
|
|
minf=f;
|
||
|
|
mind=sqd;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return(minf);
|
||
|
|
}
|
||
|
|
bool expand(U pass,typename GJK<btConvexTemplate>::sSV* w,sFace* f,U e,sHorizon& horizon)
|
||
|
|
{
|
||
|
|
static const U i1m3[]={1,2,0};
|
||
|
|
static const U i2m3[]={2,0,1};
|
||
|
|
if(f->pass!=pass)
|
||
|
|
{
|
||
|
|
const U e1=i1m3[e];
|
||
|
|
if((btDot(f->n,w->w)-f->d)<-EPA_PLANE_EPS)
|
||
|
|
{
|
||
|
|
sFace* nf=newface(f->c[e1],f->c[e],w,false);
|
||
|
|
if(nf)
|
||
|
|
{
|
||
|
|
bind(nf,0,f,e);
|
||
|
|
if(horizon.cf) bind(horizon.cf,1,nf,2); else horizon.ff=nf;
|
||
|
|
horizon.cf=nf;
|
||
|
|
++horizon.nf;
|
||
|
|
return(true);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
const U e2=i2m3[e];
|
||
|
|
f->pass = (U1)pass;
|
||
|
|
if( expand(pass,w,f->f[e1],f->e[e1],horizon)&&
|
||
|
|
expand(pass,w,f->f[e2],f->e[e2],horizon))
|
||
|
|
{
|
||
|
|
remove(m_hull,f);
|
||
|
|
append(m_stock,f);
|
||
|
|
return(true);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return(false);
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename btConvexTemplate>
|
||
|
|
static void Initialize( const btConvexTemplate& a, const btConvexTemplate& b,
|
||
|
|
btGjkEpaSolver3::sResults& results,
|
||
|
|
MinkowskiDiff<btConvexTemplate>& shape)
|
||
|
|
{
|
||
|
|
/* Results */
|
||
|
|
results.witnesses[0] =
|
||
|
|
results.witnesses[1] = btVector3(0,0,0);
|
||
|
|
results.status = btGjkEpaSolver3::sResults::Separated;
|
||
|
|
/* Shape */
|
||
|
|
|
||
|
|
shape.m_toshape1 = b.getWorldTransform().getBasis().transposeTimes(a.getWorldTransform().getBasis());
|
||
|
|
shape.m_toshape0 = a.getWorldTransform().inverseTimes(b.getWorldTransform());
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
//
|
||
|
|
// Api
|
||
|
|
//
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
//
|
||
|
|
template <typename btConvexTemplate>
|
||
|
|
bool btGjkEpaSolver3_Distance(const btConvexTemplate& a, const btConvexTemplate& b,
|
||
|
|
const btVector3& guess,
|
||
|
|
btGjkEpaSolver3::sResults& results)
|
||
|
|
{
|
||
|
|
MinkowskiDiff<btConvexTemplate> shape(a,b);
|
||
|
|
Initialize(a,b,results,shape);
|
||
|
|
GJK<btConvexTemplate> gjk(a,b);
|
||
|
|
eGjkStatus gjk_status=gjk.Evaluate(shape,guess);
|
||
|
|
if(gjk_status==eGjkValid)
|
||
|
|
{
|
||
|
|
btVector3 w0=btVector3(0,0,0);
|
||
|
|
btVector3 w1=btVector3(0,0,0);
|
||
|
|
for(U i=0;i<gjk.m_simplex->rank;++i)
|
||
|
|
{
|
||
|
|
const btScalar p=gjk.m_simplex->p[i];
|
||
|
|
w0+=shape.Support( gjk.m_simplex->c[i]->d,0)*p;
|
||
|
|
w1+=shape.Support(-gjk.m_simplex->c[i]->d,1)*p;
|
||
|
|
}
|
||
|
|
results.witnesses[0] = a.getWorldTransform()*w0;
|
||
|
|
results.witnesses[1] = a.getWorldTransform()*w1;
|
||
|
|
results.normal = w0-w1;
|
||
|
|
results.distance = results.normal.length();
|
||
|
|
results.normal /= results.distance>GJK_MIN_DISTANCE?results.distance:1;
|
||
|
|
return(true);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
results.status = gjk_status==eGjkInside?
|
||
|
|
btGjkEpaSolver3::sResults::Penetrating :
|
||
|
|
btGjkEpaSolver3::sResults::GJK_Failed ;
|
||
|
|
return(false);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <typename btConvexTemplate>
|
||
|
|
bool btGjkEpaSolver3_Penetration(const btConvexTemplate& a,
|
||
|
|
const btConvexTemplate& b,
|
||
|
|
const btVector3& guess,
|
||
|
|
btGjkEpaSolver3::sResults& results)
|
||
|
|
{
|
||
|
|
MinkowskiDiff<btConvexTemplate> shape(a,b);
|
||
|
|
Initialize(a,b,results,shape);
|
||
|
|
GJK<btConvexTemplate> gjk(a,b);
|
||
|
|
eGjkStatus gjk_status=gjk.Evaluate(shape,-guess);
|
||
|
|
switch(gjk_status)
|
||
|
|
{
|
||
|
|
case eGjkInside:
|
||
|
|
{
|
||
|
|
EPA<btConvexTemplate> epa;
|
||
|
|
eEpaStatus epa_status=epa.Evaluate(gjk,-guess);
|
||
|
|
if(epa_status!=eEpaFailed)
|
||
|
|
{
|
||
|
|
btVector3 w0=btVector3(0,0,0);
|
||
|
|
for(U i=0;i<epa.m_result.rank;++i)
|
||
|
|
{
|
||
|
|
w0+=shape.Support(epa.m_result.c[i]->d,0)*epa.m_result.p[i];
|
||
|
|
}
|
||
|
|
results.status = btGjkEpaSolver3::sResults::Penetrating;
|
||
|
|
results.witnesses[0] = a.getWorldTransform()*w0;
|
||
|
|
results.witnesses[1] = a.getWorldTransform()*(w0-epa.m_normal*epa.m_depth);
|
||
|
|
results.normal = -epa.m_normal;
|
||
|
|
results.distance = -epa.m_depth;
|
||
|
|
return(true);
|
||
|
|
} else results.status=btGjkEpaSolver3::sResults::EPA_Failed;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case eGjkFailed:
|
||
|
|
results.status=btGjkEpaSolver3::sResults::GJK_Failed;
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
{
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return(false);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if 0
|
||
|
|
int btComputeGjkEpaPenetration2(const btCollisionDescription& colDesc, btDistanceInfo* distInfo)
|
||
|
|
{
|
||
|
|
btGjkEpaSolver3::sResults results;
|
||
|
|
btVector3 guess = colDesc.m_firstDir;
|
||
|
|
|
||
|
|
bool res = btGjkEpaSolver3::Penetration(colDesc.m_objA,colDesc.m_objB,
|
||
|
|
colDesc.m_transformA,colDesc.m_transformB,
|
||
|
|
colDesc.m_localSupportFuncA,colDesc.m_localSupportFuncB,
|
||
|
|
guess,
|
||
|
|
results);
|
||
|
|
if (res)
|
||
|
|
{
|
||
|
|
if ((results.status==btGjkEpaSolver3::sResults::Penetrating) || results.status==GJK::eStatus::Inside)
|
||
|
|
{
|
||
|
|
//normal could be 'swapped'
|
||
|
|
|
||
|
|
distInfo->m_distance = results.distance;
|
||
|
|
distInfo->m_normalBtoA = results.normal;
|
||
|
|
btVector3 tmpNormalInB = results.witnesses[1]-results.witnesses[0];
|
||
|
|
btScalar lenSqr = tmpNormalInB.length2();
|
||
|
|
if (lenSqr <= (SIMD_EPSILON*SIMD_EPSILON))
|
||
|
|
{
|
||
|
|
tmpNormalInB = results.normal;
|
||
|
|
lenSqr = results.normal.length2();
|
||
|
|
}
|
||
|
|
|
||
|
|
if (lenSqr > (SIMD_EPSILON*SIMD_EPSILON))
|
||
|
|
{
|
||
|
|
tmpNormalInB /= btSqrt(lenSqr);
|
||
|
|
btScalar distance2 = -(results.witnesses[0]-results.witnesses[1]).length();
|
||
|
|
//only replace valid penetrations when the result is deeper (check)
|
||
|
|
//if ((distance2 < results.distance))
|
||
|
|
{
|
||
|
|
distInfo->m_distance = distance2;
|
||
|
|
distInfo->m_pointOnA= results.witnesses[0];
|
||
|
|
distInfo->m_pointOnB= results.witnesses[1];
|
||
|
|
distInfo->m_normalBtoA= tmpNormalInB;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
return -1;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
template <typename btConvexTemplate, typename btDistanceInfoTemplate>
|
||
|
|
int btComputeGjkDistance(const btConvexTemplate& a, const btConvexTemplate& b,
|
||
|
|
const btGjkCollisionDescription& colDesc, btDistanceInfoTemplate* distInfo)
|
||
|
|
{
|
||
|
|
btGjkEpaSolver3::sResults results;
|
||
|
|
btVector3 guess = colDesc.m_firstDir;
|
||
|
|
|
||
|
|
bool isSeparated = btGjkEpaSolver3_Distance( a,b,
|
||
|
|
guess,
|
||
|
|
results);
|
||
|
|
if (isSeparated)
|
||
|
|
{
|
||
|
|
distInfo->m_distance = results.distance;
|
||
|
|
distInfo->m_pointOnA= results.witnesses[0];
|
||
|
|
distInfo->m_pointOnB= results.witnesses[1];
|
||
|
|
distInfo->m_normalBtoA= results.normal;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
return -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Symbols cleanup */
|
||
|
|
|
||
|
|
#undef GJK_MAX_ITERATIONS
|
||
|
|
#undef GJK_ACCURARY
|
||
|
|
#undef GJK_MIN_DISTANCE
|
||
|
|
#undef GJK_DUPLICATED_EPS
|
||
|
|
#undef GJK_SIMPLEX2_EPS
|
||
|
|
#undef GJK_SIMPLEX3_EPS
|
||
|
|
#undef GJK_SIMPLEX4_EPS
|
||
|
|
|
||
|
|
#undef EPA_MAX_VERTICES
|
||
|
|
#undef EPA_MAX_FACES
|
||
|
|
#undef EPA_MAX_ITERATIONS
|
||
|
|
#undef EPA_ACCURACY
|
||
|
|
#undef EPA_FALLBACK
|
||
|
|
#undef EPA_PLANE_EPS
|
||
|
|
#undef EPA_INSIDE_EPS
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
#endif //BT_GJK_EPA3_H
|
||
|
|
|