909 lines
25 KiB
C++
909 lines
25 KiB
C++
|
|
/***
|
|
* ---------------------------------
|
|
* Copyright (c)2012 Daniel Fiser <danfis@danfis.cz>
|
|
*
|
|
* This file was ported from mpr.c file, part of libccd.
|
|
* The Minkoski Portal Refinement implementation was ported
|
|
* to OpenCL by Erwin Coumans for the Bullet 3 Physics library.
|
|
* The original MPR idea and implementation is by Gary Snethen
|
|
* in XenoCollide, see http://github.com/erwincoumans/xenocollide
|
|
*
|
|
* Distributed under the OSI-approved BSD License (the "License");
|
|
* see <http://www.opensource.org/licenses/bsd-license.php>.
|
|
* This software is distributed WITHOUT ANY WARRANTY; without even the
|
|
* implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
|
|
* See the License for more information.
|
|
*/
|
|
|
|
///2014 Oct, Erwin Coumans, Use templates to avoid void* casts
|
|
|
|
#ifndef BT_MPR_PENETRATION_H
|
|
#define BT_MPR_PENETRATION_H
|
|
|
|
#define BT_DEBUG_MPR1
|
|
|
|
#include "LinearMath/btTransform.h"
|
|
#include "LinearMath/btAlignedObjectArray.h"
|
|
|
|
//#define MPR_AVERAGE_CONTACT_POSITIONS
|
|
|
|
|
|
struct btMprCollisionDescription
|
|
{
|
|
btVector3 m_firstDir;
|
|
int m_maxGjkIterations;
|
|
btScalar m_maximumDistanceSquared;
|
|
btScalar m_gjkRelError2;
|
|
|
|
btMprCollisionDescription()
|
|
: m_firstDir(0,1,0),
|
|
m_maxGjkIterations(1000),
|
|
m_maximumDistanceSquared(1e30f),
|
|
m_gjkRelError2(1.0e-6)
|
|
{
|
|
}
|
|
virtual ~btMprCollisionDescription()
|
|
{
|
|
}
|
|
};
|
|
|
|
struct btMprDistanceInfo
|
|
{
|
|
btVector3 m_pointOnA;
|
|
btVector3 m_pointOnB;
|
|
btVector3 m_normalBtoA;
|
|
btScalar m_distance;
|
|
};
|
|
|
|
#ifdef __cplusplus
|
|
#define BT_MPR_SQRT sqrtf
|
|
#else
|
|
#define BT_MPR_SQRT sqrt
|
|
#endif
|
|
#define BT_MPR_FMIN(x, y) ((x) < (y) ? (x) : (y))
|
|
#define BT_MPR_FABS fabs
|
|
|
|
#define BT_MPR_TOLERANCE 1E-6f
|
|
#define BT_MPR_MAX_ITERATIONS 1000
|
|
|
|
struct _btMprSupport_t
|
|
{
|
|
btVector3 v; //!< Support point in minkowski sum
|
|
btVector3 v1; //!< Support point in obj1
|
|
btVector3 v2; //!< Support point in obj2
|
|
};
|
|
typedef struct _btMprSupport_t btMprSupport_t;
|
|
|
|
struct _btMprSimplex_t
|
|
{
|
|
btMprSupport_t ps[4];
|
|
int last; //!< index of last added point
|
|
};
|
|
typedef struct _btMprSimplex_t btMprSimplex_t;
|
|
|
|
inline btMprSupport_t* btMprSimplexPointW(btMprSimplex_t *s, int idx)
|
|
{
|
|
return &s->ps[idx];
|
|
}
|
|
|
|
inline void btMprSimplexSetSize(btMprSimplex_t *s, int size)
|
|
{
|
|
s->last = size - 1;
|
|
}
|
|
|
|
#ifdef DEBUG_MPR
|
|
inline void btPrintPortalVertex(_btMprSimplex_t* portal, int index)
|
|
{
|
|
printf("portal[%d].v = %f,%f,%f, v1=%f,%f,%f, v2=%f,%f,%f\n", index, portal->ps[index].v.x(),portal->ps[index].v.y(),portal->ps[index].v.z(),
|
|
portal->ps[index].v1.x(),portal->ps[index].v1.y(),portal->ps[index].v1.z(),
|
|
portal->ps[index].v2.x(),portal->ps[index].v2.y(),portal->ps[index].v2.z());
|
|
}
|
|
#endif //DEBUG_MPR
|
|
|
|
|
|
|
|
|
|
inline int btMprSimplexSize(const btMprSimplex_t *s)
|
|
{
|
|
return s->last + 1;
|
|
}
|
|
|
|
|
|
inline const btMprSupport_t* btMprSimplexPoint(const btMprSimplex_t* s, int idx)
|
|
{
|
|
// here is no check on boundaries
|
|
return &s->ps[idx];
|
|
}
|
|
|
|
inline void btMprSupportCopy(btMprSupport_t *d, const btMprSupport_t *s)
|
|
{
|
|
*d = *s;
|
|
}
|
|
|
|
inline void btMprSimplexSet(btMprSimplex_t *s, size_t pos, const btMprSupport_t *a)
|
|
{
|
|
btMprSupportCopy(s->ps + pos, a);
|
|
}
|
|
|
|
|
|
inline void btMprSimplexSwap(btMprSimplex_t *s, size_t pos1, size_t pos2)
|
|
{
|
|
btMprSupport_t supp;
|
|
|
|
btMprSupportCopy(&supp, &s->ps[pos1]);
|
|
btMprSupportCopy(&s->ps[pos1], &s->ps[pos2]);
|
|
btMprSupportCopy(&s->ps[pos2], &supp);
|
|
}
|
|
|
|
|
|
inline int btMprIsZero(float val)
|
|
{
|
|
return BT_MPR_FABS(val) < FLT_EPSILON;
|
|
}
|
|
|
|
|
|
|
|
inline int btMprEq(float _a, float _b)
|
|
{
|
|
float ab;
|
|
float a, b;
|
|
|
|
ab = BT_MPR_FABS(_a - _b);
|
|
if (BT_MPR_FABS(ab) < FLT_EPSILON)
|
|
return 1;
|
|
|
|
a = BT_MPR_FABS(_a);
|
|
b = BT_MPR_FABS(_b);
|
|
if (b > a){
|
|
return ab < FLT_EPSILON * b;
|
|
}else{
|
|
return ab < FLT_EPSILON * a;
|
|
}
|
|
}
|
|
|
|
|
|
inline int btMprVec3Eq(const btVector3* a, const btVector3 *b)
|
|
{
|
|
return btMprEq((*a).x(), (*b).x())
|
|
&& btMprEq((*a).y(), (*b).y())
|
|
&& btMprEq((*a).z(), (*b).z());
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
template <typename btConvexTemplate>
|
|
inline void btFindOrigin(const btConvexTemplate& a, const btConvexTemplate& b, const btMprCollisionDescription& colDesc,btMprSupport_t *center)
|
|
{
|
|
|
|
center->v1 = a.getObjectCenterInWorld();
|
|
center->v2 = b.getObjectCenterInWorld();
|
|
center->v = center->v1 - center->v2;
|
|
}
|
|
|
|
inline void btMprVec3Set(btVector3 *v, float x, float y, float z)
|
|
{
|
|
v->setValue(x,y,z);
|
|
}
|
|
|
|
inline void btMprVec3Add(btVector3 *v, const btVector3 *w)
|
|
{
|
|
*v += *w;
|
|
}
|
|
|
|
inline void btMprVec3Copy(btVector3 *v, const btVector3 *w)
|
|
{
|
|
*v = *w;
|
|
}
|
|
|
|
inline void btMprVec3Scale(btVector3 *d, float k)
|
|
{
|
|
*d *= k;
|
|
}
|
|
|
|
inline float btMprVec3Dot(const btVector3 *a, const btVector3 *b)
|
|
{
|
|
float dot;
|
|
|
|
dot = btDot(*a,*b);
|
|
return dot;
|
|
}
|
|
|
|
|
|
inline float btMprVec3Len2(const btVector3 *v)
|
|
{
|
|
return btMprVec3Dot(v, v);
|
|
}
|
|
|
|
inline void btMprVec3Normalize(btVector3 *d)
|
|
{
|
|
float k = 1.f / BT_MPR_SQRT(btMprVec3Len2(d));
|
|
btMprVec3Scale(d, k);
|
|
}
|
|
|
|
inline void btMprVec3Cross(btVector3 *d, const btVector3 *a, const btVector3 *b)
|
|
{
|
|
*d = btCross(*a,*b);
|
|
|
|
}
|
|
|
|
|
|
inline void btMprVec3Sub2(btVector3 *d, const btVector3 *v, const btVector3 *w)
|
|
{
|
|
*d = *v - *w;
|
|
}
|
|
|
|
inline void btPortalDir(const btMprSimplex_t *portal, btVector3 *dir)
|
|
{
|
|
btVector3 v2v1, v3v1;
|
|
|
|
btMprVec3Sub2(&v2v1, &btMprSimplexPoint(portal, 2)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
btMprVec3Sub2(&v3v1, &btMprSimplexPoint(portal, 3)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
btMprVec3Cross(dir, &v2v1, &v3v1);
|
|
btMprVec3Normalize(dir);
|
|
}
|
|
|
|
|
|
inline int portalEncapsulesOrigin(const btMprSimplex_t *portal,
|
|
const btVector3 *dir)
|
|
{
|
|
float dot;
|
|
dot = btMprVec3Dot(dir, &btMprSimplexPoint(portal, 1)->v);
|
|
return btMprIsZero(dot) || dot > 0.f;
|
|
}
|
|
|
|
inline int portalReachTolerance(const btMprSimplex_t *portal,
|
|
const btMprSupport_t *v4,
|
|
const btVector3 *dir)
|
|
{
|
|
float dv1, dv2, dv3, dv4;
|
|
float dot1, dot2, dot3;
|
|
|
|
// find the smallest dot product of dir and {v1-v4, v2-v4, v3-v4}
|
|
|
|
dv1 = btMprVec3Dot(&btMprSimplexPoint(portal, 1)->v, dir);
|
|
dv2 = btMprVec3Dot(&btMprSimplexPoint(portal, 2)->v, dir);
|
|
dv3 = btMprVec3Dot(&btMprSimplexPoint(portal, 3)->v, dir);
|
|
dv4 = btMprVec3Dot(&v4->v, dir);
|
|
|
|
dot1 = dv4 - dv1;
|
|
dot2 = dv4 - dv2;
|
|
dot3 = dv4 - dv3;
|
|
|
|
dot1 = BT_MPR_FMIN(dot1, dot2);
|
|
dot1 = BT_MPR_FMIN(dot1, dot3);
|
|
|
|
return btMprEq(dot1, BT_MPR_TOLERANCE) || dot1 < BT_MPR_TOLERANCE;
|
|
}
|
|
|
|
inline int portalCanEncapsuleOrigin(const btMprSimplex_t *portal,
|
|
const btMprSupport_t *v4,
|
|
const btVector3 *dir)
|
|
{
|
|
float dot;
|
|
dot = btMprVec3Dot(&v4->v, dir);
|
|
return btMprIsZero(dot) || dot > 0.f;
|
|
}
|
|
|
|
inline void btExpandPortal(btMprSimplex_t *portal,
|
|
const btMprSupport_t *v4)
|
|
{
|
|
float dot;
|
|
btVector3 v4v0;
|
|
|
|
btMprVec3Cross(&v4v0, &v4->v, &btMprSimplexPoint(portal, 0)->v);
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 1)->v, &v4v0);
|
|
if (dot > 0.f){
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 2)->v, &v4v0);
|
|
if (dot > 0.f){
|
|
btMprSimplexSet(portal, 1, v4);
|
|
}else{
|
|
btMprSimplexSet(portal, 3, v4);
|
|
}
|
|
}else{
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 3)->v, &v4v0);
|
|
if (dot > 0.f){
|
|
btMprSimplexSet(portal, 2, v4);
|
|
}else{
|
|
btMprSimplexSet(portal, 1, v4);
|
|
}
|
|
}
|
|
}
|
|
template <typename btConvexTemplate>
|
|
inline void btMprSupport(const btConvexTemplate& a, const btConvexTemplate& b,
|
|
const btMprCollisionDescription& colDesc,
|
|
const btVector3& dir, btMprSupport_t *supp)
|
|
{
|
|
btVector3 seperatingAxisInA = dir* a.getWorldTransform().getBasis();
|
|
btVector3 seperatingAxisInB = -dir* b.getWorldTransform().getBasis();
|
|
|
|
btVector3 pInA = a.getLocalSupportWithMargin(seperatingAxisInA);
|
|
btVector3 qInB = b.getLocalSupportWithMargin(seperatingAxisInB);
|
|
|
|
supp->v1 = a.getWorldTransform()(pInA);
|
|
supp->v2 = b.getWorldTransform()(qInB);
|
|
supp->v = supp->v1 - supp->v2;
|
|
}
|
|
|
|
|
|
template <typename btConvexTemplate>
|
|
static int btDiscoverPortal(const btConvexTemplate& a, const btConvexTemplate& b,
|
|
const btMprCollisionDescription& colDesc,
|
|
btMprSimplex_t *portal)
|
|
{
|
|
btVector3 dir, va, vb;
|
|
float dot;
|
|
int cont;
|
|
|
|
|
|
|
|
// vertex 0 is center of portal
|
|
btFindOrigin(a,b,colDesc, btMprSimplexPointW(portal, 0));
|
|
|
|
|
|
// vertex 0 is center of portal
|
|
btMprSimplexSetSize(portal, 1);
|
|
|
|
|
|
|
|
btVector3 zero = btVector3(0,0,0);
|
|
btVector3* org = &zero;
|
|
|
|
if (btMprVec3Eq(&btMprSimplexPoint(portal, 0)->v, org)){
|
|
// Portal's center lies on origin (0,0,0) => we know that objects
|
|
// intersect but we would need to know penetration info.
|
|
// So move center little bit...
|
|
btMprVec3Set(&va, FLT_EPSILON * 10.f, 0.f, 0.f);
|
|
btMprVec3Add(&btMprSimplexPointW(portal, 0)->v, &va);
|
|
}
|
|
|
|
|
|
// vertex 1 = support in direction of origin
|
|
btMprVec3Copy(&dir, &btMprSimplexPoint(portal, 0)->v);
|
|
btMprVec3Scale(&dir, -1.f);
|
|
btMprVec3Normalize(&dir);
|
|
|
|
|
|
btMprSupport(a,b,colDesc, dir, btMprSimplexPointW(portal, 1));
|
|
|
|
btMprSimplexSetSize(portal, 2);
|
|
|
|
// test if origin isn't outside of v1
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 1)->v, &dir);
|
|
|
|
|
|
if (btMprIsZero(dot) || dot < 0.f)
|
|
return -1;
|
|
|
|
|
|
// vertex 2
|
|
btMprVec3Cross(&dir, &btMprSimplexPoint(portal, 0)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
if (btMprIsZero(btMprVec3Len2(&dir))){
|
|
if (btMprVec3Eq(&btMprSimplexPoint(portal, 1)->v, org)){
|
|
// origin lies on v1
|
|
return 1;
|
|
}else{
|
|
// origin lies on v0-v1 segment
|
|
return 2;
|
|
}
|
|
}
|
|
|
|
btMprVec3Normalize(&dir);
|
|
btMprSupport(a,b,colDesc, dir, btMprSimplexPointW(portal, 2));
|
|
|
|
|
|
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 2)->v, &dir);
|
|
if (btMprIsZero(dot) || dot < 0.f)
|
|
return -1;
|
|
|
|
btMprSimplexSetSize(portal, 3);
|
|
|
|
// vertex 3 direction
|
|
btMprVec3Sub2(&va, &btMprSimplexPoint(portal, 1)->v,
|
|
&btMprSimplexPoint(portal, 0)->v);
|
|
btMprVec3Sub2(&vb, &btMprSimplexPoint(portal, 2)->v,
|
|
&btMprSimplexPoint(portal, 0)->v);
|
|
btMprVec3Cross(&dir, &va, &vb);
|
|
btMprVec3Normalize(&dir);
|
|
|
|
// it is better to form portal faces to be oriented "outside" origin
|
|
dot = btMprVec3Dot(&dir, &btMprSimplexPoint(portal, 0)->v);
|
|
if (dot > 0.f){
|
|
btMprSimplexSwap(portal, 1, 2);
|
|
btMprVec3Scale(&dir, -1.f);
|
|
}
|
|
|
|
while (btMprSimplexSize(portal) < 4){
|
|
btMprSupport(a,b,colDesc, dir, btMprSimplexPointW(portal, 3));
|
|
|
|
dot = btMprVec3Dot(&btMprSimplexPoint(portal, 3)->v, &dir);
|
|
if (btMprIsZero(dot) || dot < 0.f)
|
|
return -1;
|
|
|
|
cont = 0;
|
|
|
|
// test if origin is outside (v1, v0, v3) - set v2 as v3 and
|
|
// continue
|
|
btMprVec3Cross(&va, &btMprSimplexPoint(portal, 1)->v,
|
|
&btMprSimplexPoint(portal, 3)->v);
|
|
dot = btMprVec3Dot(&va, &btMprSimplexPoint(portal, 0)->v);
|
|
if (dot < 0.f && !btMprIsZero(dot)){
|
|
btMprSimplexSet(portal, 2, btMprSimplexPoint(portal, 3));
|
|
cont = 1;
|
|
}
|
|
|
|
if (!cont){
|
|
// test if origin is outside (v3, v0, v2) - set v1 as v3 and
|
|
// continue
|
|
btMprVec3Cross(&va, &btMprSimplexPoint(portal, 3)->v,
|
|
&btMprSimplexPoint(portal, 2)->v);
|
|
dot = btMprVec3Dot(&va, &btMprSimplexPoint(portal, 0)->v);
|
|
if (dot < 0.f && !btMprIsZero(dot)){
|
|
btMprSimplexSet(portal, 1, btMprSimplexPoint(portal, 3));
|
|
cont = 1;
|
|
}
|
|
}
|
|
|
|
if (cont){
|
|
btMprVec3Sub2(&va, &btMprSimplexPoint(portal, 1)->v,
|
|
&btMprSimplexPoint(portal, 0)->v);
|
|
btMprVec3Sub2(&vb, &btMprSimplexPoint(portal, 2)->v,
|
|
&btMprSimplexPoint(portal, 0)->v);
|
|
btMprVec3Cross(&dir, &va, &vb);
|
|
btMprVec3Normalize(&dir);
|
|
}else{
|
|
btMprSimplexSetSize(portal, 4);
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
template <typename btConvexTemplate>
|
|
static int btRefinePortal(const btConvexTemplate& a, const btConvexTemplate& b,const btMprCollisionDescription& colDesc,
|
|
btMprSimplex_t *portal)
|
|
{
|
|
btVector3 dir;
|
|
btMprSupport_t v4;
|
|
|
|
for (int i=0;i<BT_MPR_MAX_ITERATIONS;i++)
|
|
//while (1)
|
|
{
|
|
// compute direction outside the portal (from v0 throught v1,v2,v3
|
|
// face)
|
|
btPortalDir(portal, &dir);
|
|
|
|
// test if origin is inside the portal
|
|
if (portalEncapsulesOrigin(portal, &dir))
|
|
return 0;
|
|
|
|
// get next support point
|
|
|
|
btMprSupport(a,b,colDesc, dir, &v4);
|
|
|
|
|
|
// test if v4 can expand portal to contain origin and if portal
|
|
// expanding doesn't reach given tolerance
|
|
if (!portalCanEncapsuleOrigin(portal, &v4, &dir)
|
|
|| portalReachTolerance(portal, &v4, &dir))
|
|
{
|
|
return -1;
|
|
}
|
|
|
|
// v1-v2-v3 triangle must be rearranged to face outside Minkowski
|
|
// difference (direction from v0).
|
|
btExpandPortal(portal, &v4);
|
|
}
|
|
|
|
return -1;
|
|
}
|
|
|
|
static void btFindPos(const btMprSimplex_t *portal, btVector3 *pos)
|
|
{
|
|
|
|
btVector3 zero = btVector3(0,0,0);
|
|
btVector3* origin = &zero;
|
|
|
|
btVector3 dir;
|
|
size_t i;
|
|
float b[4], sum, inv;
|
|
btVector3 vec, p1, p2;
|
|
|
|
btPortalDir(portal, &dir);
|
|
|
|
// use barycentric coordinates of tetrahedron to find origin
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 1)->v,
|
|
&btMprSimplexPoint(portal, 2)->v);
|
|
b[0] = btMprVec3Dot(&vec, &btMprSimplexPoint(portal, 3)->v);
|
|
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 3)->v,
|
|
&btMprSimplexPoint(portal, 2)->v);
|
|
b[1] = btMprVec3Dot(&vec, &btMprSimplexPoint(portal, 0)->v);
|
|
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 0)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
b[2] = btMprVec3Dot(&vec, &btMprSimplexPoint(portal, 3)->v);
|
|
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 2)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
b[3] = btMprVec3Dot(&vec, &btMprSimplexPoint(portal, 0)->v);
|
|
|
|
sum = b[0] + b[1] + b[2] + b[3];
|
|
|
|
if (btMprIsZero(sum) || sum < 0.f){
|
|
b[0] = 0.f;
|
|
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 2)->v,
|
|
&btMprSimplexPoint(portal, 3)->v);
|
|
b[1] = btMprVec3Dot(&vec, &dir);
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 3)->v,
|
|
&btMprSimplexPoint(portal, 1)->v);
|
|
b[2] = btMprVec3Dot(&vec, &dir);
|
|
btMprVec3Cross(&vec, &btMprSimplexPoint(portal, 1)->v,
|
|
&btMprSimplexPoint(portal, 2)->v);
|
|
b[3] = btMprVec3Dot(&vec, &dir);
|
|
|
|
sum = b[1] + b[2] + b[3];
|
|
}
|
|
|
|
inv = 1.f / sum;
|
|
|
|
btMprVec3Copy(&p1, origin);
|
|
btMprVec3Copy(&p2, origin);
|
|
for (i = 0; i < 4; i++){
|
|
btMprVec3Copy(&vec, &btMprSimplexPoint(portal, i)->v1);
|
|
btMprVec3Scale(&vec, b[i]);
|
|
btMprVec3Add(&p1, &vec);
|
|
|
|
btMprVec3Copy(&vec, &btMprSimplexPoint(portal, i)->v2);
|
|
btMprVec3Scale(&vec, b[i]);
|
|
btMprVec3Add(&p2, &vec);
|
|
}
|
|
btMprVec3Scale(&p1, inv);
|
|
btMprVec3Scale(&p2, inv);
|
|
#ifdef MPR_AVERAGE_CONTACT_POSITIONS
|
|
btMprVec3Copy(pos, &p1);
|
|
btMprVec3Add(pos, &p2);
|
|
btMprVec3Scale(pos, 0.5);
|
|
#else
|
|
btMprVec3Copy(pos, &p2);
|
|
#endif//MPR_AVERAGE_CONTACT_POSITIONS
|
|
}
|
|
|
|
inline float btMprVec3Dist2(const btVector3 *a, const btVector3 *b)
|
|
{
|
|
btVector3 ab;
|
|
btMprVec3Sub2(&ab, a, b);
|
|
return btMprVec3Len2(&ab);
|
|
}
|
|
|
|
inline float _btMprVec3PointSegmentDist2(const btVector3 *P,
|
|
const btVector3 *x0,
|
|
const btVector3 *b,
|
|
btVector3 *witness)
|
|
{
|
|
// The computation comes from solving equation of segment:
|
|
// S(t) = x0 + t.d
|
|
// where - x0 is initial point of segment
|
|
// - d is direction of segment from x0 (|d| > 0)
|
|
// - t belongs to <0, 1> interval
|
|
//
|
|
// Than, distance from a segment to some point P can be expressed:
|
|
// D(t) = |x0 + t.d - P|^2
|
|
// which is distance from any point on segment. Minimization
|
|
// of this function brings distance from P to segment.
|
|
// Minimization of D(t) leads to simple quadratic equation that's
|
|
// solving is straightforward.
|
|
//
|
|
// Bonus of this method is witness point for free.
|
|
|
|
float dist, t;
|
|
btVector3 d, a;
|
|
|
|
// direction of segment
|
|
btMprVec3Sub2(&d, b, x0);
|
|
|
|
// precompute vector from P to x0
|
|
btMprVec3Sub2(&a, x0, P);
|
|
|
|
t = -1.f * btMprVec3Dot(&a, &d);
|
|
t /= btMprVec3Len2(&d);
|
|
|
|
if (t < 0.f || btMprIsZero(t)){
|
|
dist = btMprVec3Dist2(x0, P);
|
|
if (witness)
|
|
btMprVec3Copy(witness, x0);
|
|
}else if (t > 1.f || btMprEq(t, 1.f)){
|
|
dist = btMprVec3Dist2(b, P);
|
|
if (witness)
|
|
btMprVec3Copy(witness, b);
|
|
}else{
|
|
if (witness){
|
|
btMprVec3Copy(witness, &d);
|
|
btMprVec3Scale(witness, t);
|
|
btMprVec3Add(witness, x0);
|
|
dist = btMprVec3Dist2(witness, P);
|
|
}else{
|
|
// recycling variables
|
|
btMprVec3Scale(&d, t);
|
|
btMprVec3Add(&d, &a);
|
|
dist = btMprVec3Len2(&d);
|
|
}
|
|
}
|
|
|
|
return dist;
|
|
}
|
|
|
|
|
|
|
|
inline float btMprVec3PointTriDist2(const btVector3 *P,
|
|
const btVector3 *x0, const btVector3 *B,
|
|
const btVector3 *C,
|
|
btVector3 *witness)
|
|
{
|
|
// Computation comes from analytic expression for triangle (x0, B, C)
|
|
// T(s, t) = x0 + s.d1 + t.d2, where d1 = B - x0 and d2 = C - x0 and
|
|
// Then equation for distance is:
|
|
// D(s, t) = | T(s, t) - P |^2
|
|
// This leads to minimization of quadratic function of two variables.
|
|
// The solution from is taken only if s is between 0 and 1, t is
|
|
// between 0 and 1 and t + s < 1, otherwise distance from segment is
|
|
// computed.
|
|
|
|
btVector3 d1, d2, a;
|
|
float u, v, w, p, q, r;
|
|
float s, t, dist, dist2;
|
|
btVector3 witness2;
|
|
|
|
btMprVec3Sub2(&d1, B, x0);
|
|
btMprVec3Sub2(&d2, C, x0);
|
|
btMprVec3Sub2(&a, x0, P);
|
|
|
|
u = btMprVec3Dot(&a, &a);
|
|
v = btMprVec3Dot(&d1, &d1);
|
|
w = btMprVec3Dot(&d2, &d2);
|
|
p = btMprVec3Dot(&a, &d1);
|
|
q = btMprVec3Dot(&a, &d2);
|
|
r = btMprVec3Dot(&d1, &d2);
|
|
|
|
btScalar div = (w * v - r * r);
|
|
if (btMprIsZero(div))
|
|
{
|
|
s=-1;
|
|
} else
|
|
{
|
|
s = (q * r - w * p) / div;
|
|
t = (-s * r - q) / w;
|
|
}
|
|
|
|
if ((btMprIsZero(s) || s > 0.f)
|
|
&& (btMprEq(s, 1.f) || s < 1.f)
|
|
&& (btMprIsZero(t) || t > 0.f)
|
|
&& (btMprEq(t, 1.f) || t < 1.f)
|
|
&& (btMprEq(t + s, 1.f) || t + s < 1.f)){
|
|
|
|
if (witness){
|
|
btMprVec3Scale(&d1, s);
|
|
btMprVec3Scale(&d2, t);
|
|
btMprVec3Copy(witness, x0);
|
|
btMprVec3Add(witness, &d1);
|
|
btMprVec3Add(witness, &d2);
|
|
|
|
dist = btMprVec3Dist2(witness, P);
|
|
}else{
|
|
dist = s * s * v;
|
|
dist += t * t * w;
|
|
dist += 2.f * s * t * r;
|
|
dist += 2.f * s * p;
|
|
dist += 2.f * t * q;
|
|
dist += u;
|
|
}
|
|
}else{
|
|
dist = _btMprVec3PointSegmentDist2(P, x0, B, witness);
|
|
|
|
dist2 = _btMprVec3PointSegmentDist2(P, x0, C, &witness2);
|
|
if (dist2 < dist){
|
|
dist = dist2;
|
|
if (witness)
|
|
btMprVec3Copy(witness, &witness2);
|
|
}
|
|
|
|
dist2 = _btMprVec3PointSegmentDist2(P, B, C, &witness2);
|
|
if (dist2 < dist){
|
|
dist = dist2;
|
|
if (witness)
|
|
btMprVec3Copy(witness, &witness2);
|
|
}
|
|
}
|
|
|
|
return dist;
|
|
}
|
|
|
|
template <typename btConvexTemplate>
|
|
static void btFindPenetr(const btConvexTemplate& a, const btConvexTemplate& b,
|
|
const btMprCollisionDescription& colDesc,
|
|
btMprSimplex_t *portal,
|
|
float *depth, btVector3 *pdir, btVector3 *pos)
|
|
{
|
|
btVector3 dir;
|
|
btMprSupport_t v4;
|
|
unsigned long iterations;
|
|
|
|
btVector3 zero = btVector3(0,0,0);
|
|
btVector3* origin = &zero;
|
|
|
|
|
|
iterations = 1UL;
|
|
for (int i=0;i<BT_MPR_MAX_ITERATIONS;i++)
|
|
//while (1)
|
|
{
|
|
// compute portal direction and obtain next support point
|
|
btPortalDir(portal, &dir);
|
|
|
|
btMprSupport(a,b,colDesc, dir, &v4);
|
|
|
|
|
|
// reached tolerance -> find penetration info
|
|
if (portalReachTolerance(portal, &v4, &dir)
|
|
|| iterations ==BT_MPR_MAX_ITERATIONS)
|
|
{
|
|
*depth = btMprVec3PointTriDist2(origin,&btMprSimplexPoint(portal, 1)->v,&btMprSimplexPoint(portal, 2)->v,&btMprSimplexPoint(portal, 3)->v,pdir);
|
|
*depth = BT_MPR_SQRT(*depth);
|
|
|
|
if (btMprIsZero((*pdir).x()) && btMprIsZero((*pdir).y()) && btMprIsZero((*pdir).z()))
|
|
{
|
|
|
|
*pdir = dir;
|
|
}
|
|
btMprVec3Normalize(pdir);
|
|
|
|
// barycentric coordinates:
|
|
btFindPos(portal, pos);
|
|
|
|
|
|
return;
|
|
}
|
|
|
|
btExpandPortal(portal, &v4);
|
|
|
|
iterations++;
|
|
}
|
|
}
|
|
|
|
static void btFindPenetrTouch(btMprSimplex_t *portal,float *depth, btVector3 *dir, btVector3 *pos)
|
|
{
|
|
// Touching contact on portal's v1 - so depth is zero and direction
|
|
// is unimportant and pos can be guessed
|
|
*depth = 0.f;
|
|
btVector3 zero = btVector3(0,0,0);
|
|
btVector3* origin = &zero;
|
|
|
|
|
|
btMprVec3Copy(dir, origin);
|
|
#ifdef MPR_AVERAGE_CONTACT_POSITIONS
|
|
btMprVec3Copy(pos, &btMprSimplexPoint(portal, 1)->v1);
|
|
btMprVec3Add(pos, &btMprSimplexPoint(portal, 1)->v2);
|
|
btMprVec3Scale(pos, 0.5);
|
|
#else
|
|
btMprVec3Copy(pos, &btMprSimplexPoint(portal, 1)->v2);
|
|
#endif
|
|
}
|
|
|
|
static void btFindPenetrSegment(btMprSimplex_t *portal,
|
|
float *depth, btVector3 *dir, btVector3 *pos)
|
|
{
|
|
|
|
// Origin lies on v0-v1 segment.
|
|
// Depth is distance to v1, direction also and position must be
|
|
// computed
|
|
#ifdef MPR_AVERAGE_CONTACT_POSITIONS
|
|
btMprVec3Copy(pos, &btMprSimplexPoint(portal, 1)->v1);
|
|
btMprVec3Add(pos, &btMprSimplexPoint(portal, 1)->v2);
|
|
btMprVec3Scale(pos, 0.5f);
|
|
#else
|
|
btMprVec3Copy(pos, &btMprSimplexPoint(portal, 1)->v2);
|
|
#endif//MPR_AVERAGE_CONTACT_POSITIONS
|
|
|
|
btMprVec3Copy(dir, &btMprSimplexPoint(portal, 1)->v);
|
|
*depth = BT_MPR_SQRT(btMprVec3Len2(dir));
|
|
btMprVec3Normalize(dir);
|
|
|
|
|
|
}
|
|
|
|
|
|
template <typename btConvexTemplate>
|
|
inline int btMprPenetration( const btConvexTemplate& a, const btConvexTemplate& b,
|
|
const btMprCollisionDescription& colDesc,
|
|
float *depthOut, btVector3* dirOut, btVector3* posOut)
|
|
{
|
|
|
|
btMprSimplex_t portal;
|
|
|
|
|
|
// Phase 1: Portal discovery
|
|
int result = btDiscoverPortal(a,b,colDesc, &portal);
|
|
|
|
|
|
//sepAxis[pairIndex] = *pdir;//or -dir?
|
|
|
|
switch (result)
|
|
{
|
|
case 0:
|
|
{
|
|
// Phase 2: Portal refinement
|
|
|
|
result = btRefinePortal(a,b,colDesc, &portal);
|
|
if (result < 0)
|
|
return -1;
|
|
|
|
// Phase 3. Penetration info
|
|
btFindPenetr(a,b,colDesc, &portal, depthOut, dirOut, posOut);
|
|
|
|
|
|
break;
|
|
}
|
|
case 1:
|
|
{
|
|
// Touching contact on portal's v1.
|
|
btFindPenetrTouch(&portal, depthOut, dirOut, posOut);
|
|
result=0;
|
|
break;
|
|
}
|
|
case 2:
|
|
{
|
|
|
|
btFindPenetrSegment( &portal, depthOut, dirOut, posOut);
|
|
result=0;
|
|
break;
|
|
}
|
|
default:
|
|
{
|
|
//if (res < 0)
|
|
//{
|
|
// Origin isn't inside portal - no collision.
|
|
result = -1;
|
|
//}
|
|
}
|
|
};
|
|
|
|
return result;
|
|
};
|
|
|
|
|
|
template<typename btConvexTemplate, typename btMprDistanceTemplate>
|
|
inline int btComputeMprPenetration( const btConvexTemplate& a, const btConvexTemplate& b, const
|
|
btMprCollisionDescription& colDesc, btMprDistanceTemplate* distInfo)
|
|
{
|
|
btVector3 dir,pos;
|
|
float depth;
|
|
|
|
int res = btMprPenetration(a,b,colDesc,&depth, &dir, &pos);
|
|
if (res==0)
|
|
{
|
|
distInfo->m_distance = -depth;
|
|
distInfo->m_pointOnB = pos;
|
|
distInfo->m_normalBtoA = -dir;
|
|
distInfo->m_pointOnA = pos-distInfo->m_distance*dir;
|
|
return 0;
|
|
}
|
|
|
|
return -1;
|
|
}
|
|
|
|
|
|
|
|
#endif //BT_MPR_PENETRATION_H
|