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-rw-r--r--src/BulletCollision/NarrowPhaseCollision/btMprPenetration.h1768
1 files changed, 884 insertions, 884 deletions
diff --git a/src/BulletCollision/NarrowPhaseCollision/btMprPenetration.h b/src/BulletCollision/NarrowPhaseCollision/btMprPenetration.h
index ea946e2da..358bc95d8 100644
--- a/src/BulletCollision/NarrowPhaseCollision/btMprPenetration.h
+++ b/src/BulletCollision/NarrowPhaseCollision/btMprPenetration.h
@@ -1,884 +1,884 @@
-
-/***
- * ---------------------------------
- * 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
+
+/***
+ * ---------------------------------
+ * 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
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