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godot/thirdparty/bullet/Bullet3Collision/NarrowPhaseCollision/shared/b3MprPenetration.h

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/***
* ---------------------------------
* 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.
* at http://github.com/erwincoumans/bullet3
*
* 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.
*/
#ifndef B3_MPR_PENETRATION_H
#define B3_MPR_PENETRATION_H
#include "Bullet3Common/shared/b3PlatformDefinitions.h"
#include "Bullet3Common/shared/b3Float4.h"
#include "Bullet3Collision/NarrowPhaseCollision/shared/b3RigidBodyData.h"
#include "Bullet3Collision/NarrowPhaseCollision/shared/b3ConvexPolyhedronData.h"
#include "Bullet3Collision/NarrowPhaseCollision/shared/b3Collidable.h"
#ifdef __cplusplus
#define B3_MPR_SQRT sqrtf
#else
#define B3_MPR_SQRT sqrt
#endif
#define B3_MPR_FMIN(x, y) ((x) < (y) ? (x) : (y))
#define B3_MPR_FABS fabs
#define B3_MPR_TOLERANCE 1E-6f
#define B3_MPR_MAX_ITERATIONS 1000
struct _b3MprSupport_t
{
b3Float4 v; //!< Support point in minkowski sum
b3Float4 v1; //!< Support point in obj1
b3Float4 v2; //!< Support point in obj2
};
typedef struct _b3MprSupport_t b3MprSupport_t;
struct _b3MprSimplex_t
{
b3MprSupport_t ps[4];
int last; //!< index of last added point
};
typedef struct _b3MprSimplex_t b3MprSimplex_t;
inline b3MprSupport_t *b3MprSimplexPointW(b3MprSimplex_t *s, int idx)
{
return &s->ps[idx];
}
inline void b3MprSimplexSetSize(b3MprSimplex_t *s, int size)
{
s->last = size - 1;
}
inline int b3MprSimplexSize(const b3MprSimplex_t *s)
{
return s->last + 1;
}
inline const b3MprSupport_t *b3MprSimplexPoint(const b3MprSimplex_t *s, int idx)
{
// here is no check on boundaries
return &s->ps[idx];
}
inline void b3MprSupportCopy(b3MprSupport_t *d, const b3MprSupport_t *s)
{
*d = *s;
}
inline void b3MprSimplexSet(b3MprSimplex_t *s, size_t pos, const b3MprSupport_t *a)
{
b3MprSupportCopy(s->ps + pos, a);
}
inline void b3MprSimplexSwap(b3MprSimplex_t *s, size_t pos1, size_t pos2)
{
b3MprSupport_t supp;
b3MprSupportCopy(&supp, &s->ps[pos1]);
b3MprSupportCopy(&s->ps[pos1], &s->ps[pos2]);
b3MprSupportCopy(&s->ps[pos2], &supp);
}
inline int b3MprIsZero(float val)
{
return B3_MPR_FABS(val) < FLT_EPSILON;
}
inline int b3MprEq(float _a, float _b)
{
float ab;
float a, b;
ab = B3_MPR_FABS(_a - _b);
if (B3_MPR_FABS(ab) < FLT_EPSILON)
return 1;
a = B3_MPR_FABS(_a);
b = B3_MPR_FABS(_b);
if (b > a)
{
return ab < FLT_EPSILON * b;
}
else
{
return ab < FLT_EPSILON * a;
}
}
inline int b3MprVec3Eq(const b3Float4 *a, const b3Float4 *b)
{
return b3MprEq((*a).x, (*b).x) && b3MprEq((*a).y, (*b).y) && b3MprEq((*a).z, (*b).z);
}
inline b3Float4 b3LocalGetSupportVertex(b3Float4ConstArg supportVec, __global const b3ConvexPolyhedronData_t *hull, b3ConstArray(b3Float4) verticesA)
{
b3Float4 supVec = b3MakeFloat4(0, 0, 0, 0);
float maxDot = -B3_LARGE_FLOAT;
if (0 < hull->m_numVertices)
{
const b3Float4 scaled = supportVec;
int index = b3MaxDot(scaled, &verticesA[hull->m_vertexOffset], hull->m_numVertices, &maxDot);
return verticesA[hull->m_vertexOffset + index];
}
return supVec;
}
B3_STATIC void b3MprConvexSupport(int pairIndex, int bodyIndex, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
const b3Float4 *_dir, b3Float4 *outp, int logme)
{
//dir is in worldspace, move to local space
b3Float4 pos = cpuBodyBuf[bodyIndex].m_pos;
b3Quat orn = cpuBodyBuf[bodyIndex].m_quat;
b3Float4 dir = b3MakeFloat4((*_dir).x, (*_dir).y, (*_dir).z, 0.f);
const b3Float4 localDir = b3QuatRotate(b3QuatInverse(orn), dir);
//find local support vertex
int colIndex = cpuBodyBuf[bodyIndex].m_collidableIdx;
b3Assert(cpuCollidables[colIndex].m_shapeType == SHAPE_CONVEX_HULL);
__global const b3ConvexPolyhedronData_t *hull = &cpuConvexData[cpuCollidables[colIndex].m_shapeIndex];
b3Float4 pInA;
if (logme)
{
// b3Float4 supVec = b3MakeFloat4(0,0,0,0);
float maxDot = -B3_LARGE_FLOAT;
if (0 < hull->m_numVertices)
{
const b3Float4 scaled = localDir;
int index = b3MaxDot(scaled, &cpuVertices[hull->m_vertexOffset], hull->m_numVertices, &maxDot);
pInA = cpuVertices[hull->m_vertexOffset + index];
}
}
else
{
pInA = b3LocalGetSupportVertex(localDir, hull, cpuVertices);
}
//move vertex to world space
*outp = b3TransformPoint(pInA, pos, orn);
}
inline void b3MprSupport(int pairIndex, int bodyIndexA, int bodyIndexB, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
const b3Float4 *_dir, b3MprSupport_t *supp)
{
b3Float4 dir;
dir = *_dir;
b3MprConvexSupport(pairIndex, bodyIndexA, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, &supp->v1, 0);
dir = *_dir * -1.f;
b3MprConvexSupport(pairIndex, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, &supp->v2, 0);
supp->v = supp->v1 - supp->v2;
}
inline void b3FindOrigin(int bodyIndexA, int bodyIndexB, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf, b3MprSupport_t *center)
{
center->v1 = cpuBodyBuf[bodyIndexA].m_pos;
center->v2 = cpuBodyBuf[bodyIndexB].m_pos;
center->v = center->v1 - center->v2;
}
inline void b3MprVec3Set(b3Float4 *v, float x, float y, float z)
{
(*v).x = x;
(*v).y = y;
(*v).z = z;
(*v).w = 0.f;
}
inline void b3MprVec3Add(b3Float4 *v, const b3Float4 *w)
{
(*v).x += (*w).x;
(*v).y += (*w).y;
(*v).z += (*w).z;
}
inline void b3MprVec3Copy(b3Float4 *v, const b3Float4 *w)
{
*v = *w;
}
inline void b3MprVec3Scale(b3Float4 *d, float k)
{
*d *= k;
}
inline float b3MprVec3Dot(const b3Float4 *a, const b3Float4 *b)
{
float dot;
dot = b3Dot3F4(*a, *b);
return dot;
}
inline float b3MprVec3Len2(const b3Float4 *v)
{
return b3MprVec3Dot(v, v);
}
inline void b3MprVec3Normalize(b3Float4 *d)
{
float k = 1.f / B3_MPR_SQRT(b3MprVec3Len2(d));
b3MprVec3Scale(d, k);
}
inline void b3MprVec3Cross(b3Float4 *d, const b3Float4 *a, const b3Float4 *b)
{
*d = b3Cross3(*a, *b);
}
inline void b3MprVec3Sub2(b3Float4 *d, const b3Float4 *v, const b3Float4 *w)
{
*d = *v - *w;
}
inline void b3PortalDir(const b3MprSimplex_t *portal, b3Float4 *dir)
{
b3Float4 v2v1, v3v1;
b3MprVec3Sub2(&v2v1, &b3MprSimplexPoint(portal, 2)->v,
&b3MprSimplexPoint(portal, 1)->v);
b3MprVec3Sub2(&v3v1, &b3MprSimplexPoint(portal, 3)->v,
&b3MprSimplexPoint(portal, 1)->v);
b3MprVec3Cross(dir, &v2v1, &v3v1);
b3MprVec3Normalize(dir);
}
inline int portalEncapsulesOrigin(const b3MprSimplex_t *portal,
const b3Float4 *dir)
{
float dot;
dot = b3MprVec3Dot(dir, &b3MprSimplexPoint(portal, 1)->v);
return b3MprIsZero(dot) || dot > 0.f;
}
inline int portalReachTolerance(const b3MprSimplex_t *portal,
const b3MprSupport_t *v4,
const b3Float4 *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 = b3MprVec3Dot(&b3MprSimplexPoint(portal, 1)->v, dir);
dv2 = b3MprVec3Dot(&b3MprSimplexPoint(portal, 2)->v, dir);
dv3 = b3MprVec3Dot(&b3MprSimplexPoint(portal, 3)->v, dir);
dv4 = b3MprVec3Dot(&v4->v, dir);
dot1 = dv4 - dv1;
dot2 = dv4 - dv2;
dot3 = dv4 - dv3;
dot1 = B3_MPR_FMIN(dot1, dot2);
dot1 = B3_MPR_FMIN(dot1, dot3);
return b3MprEq(dot1, B3_MPR_TOLERANCE) || dot1 < B3_MPR_TOLERANCE;
}
inline int portalCanEncapsuleOrigin(const b3MprSimplex_t *portal,
const b3MprSupport_t *v4,
const b3Float4 *dir)
{
float dot;
dot = b3MprVec3Dot(&v4->v, dir);
return b3MprIsZero(dot) || dot > 0.f;
}
inline void b3ExpandPortal(b3MprSimplex_t *portal,
const b3MprSupport_t *v4)
{
float dot;
b3Float4 v4v0;
b3MprVec3Cross(&v4v0, &v4->v, &b3MprSimplexPoint(portal, 0)->v);
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 1)->v, &v4v0);
if (dot > 0.f)
{
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 2)->v, &v4v0);
if (dot > 0.f)
{
b3MprSimplexSet(portal, 1, v4);
}
else
{
b3MprSimplexSet(portal, 3, v4);
}
}
else
{
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 3)->v, &v4v0);
if (dot > 0.f)
{
b3MprSimplexSet(portal, 2, v4);
}
else
{
b3MprSimplexSet(portal, 1, v4);
}
}
}
B3_STATIC int b3DiscoverPortal(int pairIndex, int bodyIndexA, int bodyIndexB, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
__global int *hasSepAxis,
b3MprSimplex_t *portal)
{
b3Float4 dir, va, vb;
float dot;
int cont;
// vertex 0 is center of portal
b3FindOrigin(bodyIndexA, bodyIndexB, cpuBodyBuf, b3MprSimplexPointW(portal, 0));
// vertex 0 is center of portal
b3MprSimplexSetSize(portal, 1);
b3Float4 zero = b3MakeFloat4(0, 0, 0, 0);
b3Float4 *b3mpr_vec3_origin = &zero;
if (b3MprVec3Eq(&b3MprSimplexPoint(portal, 0)->v, b3mpr_vec3_origin))
{
// 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...
b3MprVec3Set(&va, FLT_EPSILON * 10.f, 0.f, 0.f);
b3MprVec3Add(&b3MprSimplexPointW(portal, 0)->v, &va);
}
// vertex 1 = support in direction of origin
b3MprVec3Copy(&dir, &b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Scale(&dir, -1.f);
b3MprVec3Normalize(&dir);
b3MprSupport(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, b3MprSimplexPointW(portal, 1));
b3MprSimplexSetSize(portal, 2);
// test if origin isn't outside of v1
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 1)->v, &dir);
if (b3MprIsZero(dot) || dot < 0.f)
return -1;
// vertex 2
b3MprVec3Cross(&dir, &b3MprSimplexPoint(portal, 0)->v,
&b3MprSimplexPoint(portal, 1)->v);
if (b3MprIsZero(b3MprVec3Len2(&dir)))
{
if (b3MprVec3Eq(&b3MprSimplexPoint(portal, 1)->v, b3mpr_vec3_origin))
{
// origin lies on v1
return 1;
}
else
{
// origin lies on v0-v1 segment
return 2;
}
}
b3MprVec3Normalize(&dir);
b3MprSupport(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, b3MprSimplexPointW(portal, 2));
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 2)->v, &dir);
if (b3MprIsZero(dot) || dot < 0.f)
return -1;
b3MprSimplexSetSize(portal, 3);
// vertex 3 direction
b3MprVec3Sub2(&va, &b3MprSimplexPoint(portal, 1)->v,
&b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Sub2(&vb, &b3MprSimplexPoint(portal, 2)->v,
&b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Cross(&dir, &va, &vb);
b3MprVec3Normalize(&dir);
// it is better to form portal faces to be oriented "outside" origin
dot = b3MprVec3Dot(&dir, &b3MprSimplexPoint(portal, 0)->v);
if (dot > 0.f)
{
b3MprSimplexSwap(portal, 1, 2);
b3MprVec3Scale(&dir, -1.f);
}
while (b3MprSimplexSize(portal) < 4)
{
b3MprSupport(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, b3MprSimplexPointW(portal, 3));
dot = b3MprVec3Dot(&b3MprSimplexPoint(portal, 3)->v, &dir);
if (b3MprIsZero(dot) || dot < 0.f)
return -1;
cont = 0;
// test if origin is outside (v1, v0, v3) - set v2 as v3 and
// continue
b3MprVec3Cross(&va, &b3MprSimplexPoint(portal, 1)->v,
&b3MprSimplexPoint(portal, 3)->v);
dot = b3MprVec3Dot(&va, &b3MprSimplexPoint(portal, 0)->v);
if (dot < 0.f && !b3MprIsZero(dot))
{
b3MprSimplexSet(portal, 2, b3MprSimplexPoint(portal, 3));
cont = 1;
}
if (!cont)
{
// test if origin is outside (v3, v0, v2) - set v1 as v3 and
// continue
b3MprVec3Cross(&va, &b3MprSimplexPoint(portal, 3)->v,
&b3MprSimplexPoint(portal, 2)->v);
dot = b3MprVec3Dot(&va, &b3MprSimplexPoint(portal, 0)->v);
if (dot < 0.f && !b3MprIsZero(dot))
{
b3MprSimplexSet(portal, 1, b3MprSimplexPoint(portal, 3));
cont = 1;
}
}
if (cont)
{
b3MprVec3Sub2(&va, &b3MprSimplexPoint(portal, 1)->v,
&b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Sub2(&vb, &b3MprSimplexPoint(portal, 2)->v,
&b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Cross(&dir, &va, &vb);
b3MprVec3Normalize(&dir);
}
else
{
b3MprSimplexSetSize(portal, 4);
}
}
return 0;
}
B3_STATIC int b3RefinePortal(int pairIndex, int bodyIndexA, int bodyIndexB, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
b3MprSimplex_t *portal)
{
b3Float4 dir;
b3MprSupport_t v4;
for (int i = 0; i < B3_MPR_MAX_ITERATIONS; i++)
//while (1)
{
// compute direction outside the portal (from v0 throught v1,v2,v3
// face)
b3PortalDir(portal, &dir);
// test if origin is inside the portal
if (portalEncapsulesOrigin(portal, &dir))
return 0;
// get next support point
b3MprSupport(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &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).
b3ExpandPortal(portal, &v4);
}
return -1;
}
B3_STATIC void b3FindPos(const b3MprSimplex_t *portal, b3Float4 *pos)
{
b3Float4 zero = b3MakeFloat4(0, 0, 0, 0);
b3Float4 *b3mpr_vec3_origin = &zero;
b3Float4 dir;
size_t i;
float b[4], sum, inv;
b3Float4 vec, p1, p2;
b3PortalDir(portal, &dir);
// use barycentric coordinates of tetrahedron to find origin
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 1)->v,
&b3MprSimplexPoint(portal, 2)->v);
b[0] = b3MprVec3Dot(&vec, &b3MprSimplexPoint(portal, 3)->v);
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 3)->v,
&b3MprSimplexPoint(portal, 2)->v);
b[1] = b3MprVec3Dot(&vec, &b3MprSimplexPoint(portal, 0)->v);
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 0)->v,
&b3MprSimplexPoint(portal, 1)->v);
b[2] = b3MprVec3Dot(&vec, &b3MprSimplexPoint(portal, 3)->v);
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 2)->v,
&b3MprSimplexPoint(portal, 1)->v);
b[3] = b3MprVec3Dot(&vec, &b3MprSimplexPoint(portal, 0)->v);
sum = b[0] + b[1] + b[2] + b[3];
if (b3MprIsZero(sum) || sum < 0.f)
{
b[0] = 0.f;
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 2)->v,
&b3MprSimplexPoint(portal, 3)->v);
b[1] = b3MprVec3Dot(&vec, &dir);
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 3)->v,
&b3MprSimplexPoint(portal, 1)->v);
b[2] = b3MprVec3Dot(&vec, &dir);
b3MprVec3Cross(&vec, &b3MprSimplexPoint(portal, 1)->v,
&b3MprSimplexPoint(portal, 2)->v);
b[3] = b3MprVec3Dot(&vec, &dir);
sum = b[1] + b[2] + b[3];
}
inv = 1.f / sum;
b3MprVec3Copy(&p1, b3mpr_vec3_origin);
b3MprVec3Copy(&p2, b3mpr_vec3_origin);
for (i = 0; i < 4; i++)
{
b3MprVec3Copy(&vec, &b3MprSimplexPoint(portal, i)->v1);
b3MprVec3Scale(&vec, b[i]);
b3MprVec3Add(&p1, &vec);
b3MprVec3Copy(&vec, &b3MprSimplexPoint(portal, i)->v2);
b3MprVec3Scale(&vec, b[i]);
b3MprVec3Add(&p2, &vec);
}
b3MprVec3Scale(&p1, inv);
b3MprVec3Scale(&p2, inv);
b3MprVec3Copy(pos, &p1);
b3MprVec3Add(pos, &p2);
b3MprVec3Scale(pos, 0.5);
}
inline float b3MprVec3Dist2(const b3Float4 *a, const b3Float4 *b)
{
b3Float4 ab;
b3MprVec3Sub2(&ab, a, b);
return b3MprVec3Len2(&ab);
}
inline float _b3MprVec3PointSegmentDist2(const b3Float4 *P,
const b3Float4 *x0,
const b3Float4 *b,
b3Float4 *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;
b3Float4 d, a;
// direction of segment
b3MprVec3Sub2(&d, b, x0);
// precompute vector from P to x0
b3MprVec3Sub2(&a, x0, P);
t = -1.f * b3MprVec3Dot(&a, &d);
t /= b3MprVec3Len2(&d);
if (t < 0.f || b3MprIsZero(t))
{
dist = b3MprVec3Dist2(x0, P);
if (witness)
b3MprVec3Copy(witness, x0);
}
else if (t > 1.f || b3MprEq(t, 1.f))
{
dist = b3MprVec3Dist2(b, P);
if (witness)
b3MprVec3Copy(witness, b);
}
else
{
if (witness)
{
b3MprVec3Copy(witness, &d);
b3MprVec3Scale(witness, t);
b3MprVec3Add(witness, x0);
dist = b3MprVec3Dist2(witness, P);
}
else
{
// recycling variables
b3MprVec3Scale(&d, t);
b3MprVec3Add(&d, &a);
dist = b3MprVec3Len2(&d);
}
}
return dist;
}
inline float b3MprVec3PointTriDist2(const b3Float4 *P,
const b3Float4 *x0, const b3Float4 *B,
const b3Float4 *C,
b3Float4 *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.
b3Float4 d1, d2, a;
float u, v, w, p, q, r;
float s, t, dist, dist2;
b3Float4 witness2;
b3MprVec3Sub2(&d1, B, x0);
b3MprVec3Sub2(&d2, C, x0);
b3MprVec3Sub2(&a, x0, P);
u = b3MprVec3Dot(&a, &a);
v = b3MprVec3Dot(&d1, &d1);
w = b3MprVec3Dot(&d2, &d2);
p = b3MprVec3Dot(&a, &d1);
q = b3MprVec3Dot(&a, &d2);
r = b3MprVec3Dot(&d1, &d2);
s = (q * r - w * p) / (w * v - r * r);
t = (-s * r - q) / w;
if ((b3MprIsZero(s) || s > 0.f) && (b3MprEq(s, 1.f) || s < 1.f) && (b3MprIsZero(t) || t > 0.f) && (b3MprEq(t, 1.f) || t < 1.f) && (b3MprEq(t + s, 1.f) || t + s < 1.f))
{
if (witness)
{
b3MprVec3Scale(&d1, s);
b3MprVec3Scale(&d2, t);
b3MprVec3Copy(witness, x0);
b3MprVec3Add(witness, &d1);
b3MprVec3Add(witness, &d2);
dist = b3MprVec3Dist2(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 = _b3MprVec3PointSegmentDist2(P, x0, B, witness);
dist2 = _b3MprVec3PointSegmentDist2(P, x0, C, &witness2);
if (dist2 < dist)
{
dist = dist2;
if (witness)
b3MprVec3Copy(witness, &witness2);
}
dist2 = _b3MprVec3PointSegmentDist2(P, B, C, &witness2);
if (dist2 < dist)
{
dist = dist2;
if (witness)
b3MprVec3Copy(witness, &witness2);
}
}
return dist;
}
B3_STATIC void b3FindPenetr(int pairIndex, int bodyIndexA, int bodyIndexB, b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
b3MprSimplex_t *portal,
float *depth, b3Float4 *pdir, b3Float4 *pos)
{
b3Float4 dir;
b3MprSupport_t v4;
unsigned long iterations;
b3Float4 zero = b3MakeFloat4(0, 0, 0, 0);
b3Float4 *b3mpr_vec3_origin = &zero;
iterations = 1UL;
for (int i = 0; i < B3_MPR_MAX_ITERATIONS; i++)
//while (1)
{
// compute portal direction and obtain next support point
b3PortalDir(portal, &dir);
b3MprSupport(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &dir, &v4);
// reached tolerance -> find penetration info
if (portalReachTolerance(portal, &v4, &dir) || iterations == B3_MPR_MAX_ITERATIONS)
{
*depth = b3MprVec3PointTriDist2(b3mpr_vec3_origin, &b3MprSimplexPoint(portal, 1)->v, &b3MprSimplexPoint(portal, 2)->v, &b3MprSimplexPoint(portal, 3)->v, pdir);
*depth = B3_MPR_SQRT(*depth);
if (b3MprIsZero((*pdir).x) && b3MprIsZero((*pdir).y) && b3MprIsZero((*pdir).z))
{
*pdir = dir;
}
b3MprVec3Normalize(pdir);
// barycentric coordinates:
b3FindPos(portal, pos);
return;
}
b3ExpandPortal(portal, &v4);
iterations++;
}
}
B3_STATIC void b3FindPenetrTouch(b3MprSimplex_t *portal, float *depth, b3Float4 *dir, b3Float4 *pos)
{
// Touching contact on portal's v1 - so depth is zero and direction
// is unimportant and pos can be guessed
*depth = 0.f;
b3Float4 zero = b3MakeFloat4(0, 0, 0, 0);
b3Float4 *b3mpr_vec3_origin = &zero;
b3MprVec3Copy(dir, b3mpr_vec3_origin);
b3MprVec3Copy(pos, &b3MprSimplexPoint(portal, 1)->v1);
b3MprVec3Add(pos, &b3MprSimplexPoint(portal, 1)->v2);
b3MprVec3Scale(pos, 0.5);
}
B3_STATIC void b3FindPenetrSegment(b3MprSimplex_t *portal,
float *depth, b3Float4 *dir, b3Float4 *pos)
{
// Origin lies on v0-v1 segment.
// Depth is distance to v1, direction also and position must be
// computed
b3MprVec3Copy(pos, &b3MprSimplexPoint(portal, 1)->v1);
b3MprVec3Add(pos, &b3MprSimplexPoint(portal, 1)->v2);
b3MprVec3Scale(pos, 0.5f);
b3MprVec3Copy(dir, &b3MprSimplexPoint(portal, 1)->v);
*depth = B3_MPR_SQRT(b3MprVec3Len2(dir));
b3MprVec3Normalize(dir);
}
inline int b3MprPenetration(int pairIndex, int bodyIndexA, int bodyIndexB,
b3ConstArray(b3RigidBodyData_t) cpuBodyBuf,
b3ConstArray(b3ConvexPolyhedronData_t) cpuConvexData,
b3ConstArray(b3Collidable_t) cpuCollidables,
b3ConstArray(b3Float4) cpuVertices,
__global b3Float4 *sepAxis,
__global int *hasSepAxis,
float *depthOut, b3Float4 *dirOut, b3Float4 *posOut)
{
b3MprSimplex_t portal;
// if (!hasSepAxis[pairIndex])
// return -1;
hasSepAxis[pairIndex] = 0;
int res;
// Phase 1: Portal discovery
res = b3DiscoverPortal(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, hasSepAxis, &portal);
//sepAxis[pairIndex] = *pdir;//or -dir?
switch (res)
{
case 0:
{
// Phase 2: Portal refinement
res = b3RefinePortal(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &portal);
if (res < 0)
return -1;
// Phase 3. Penetration info
b3FindPenetr(pairIndex, bodyIndexA, bodyIndexB, cpuBodyBuf, cpuConvexData, cpuCollidables, cpuVertices, sepAxis, &portal, depthOut, dirOut, posOut);
hasSepAxis[pairIndex] = 1;
sepAxis[pairIndex] = -*dirOut;
break;
}
case 1:
{
// Touching contact on portal's v1.
b3FindPenetrTouch(&portal, depthOut, dirOut, posOut);
break;
}
case 2:
{
b3FindPenetrSegment(&portal, depthOut, dirOut, posOut);
break;
}
default:
{
hasSepAxis[pairIndex] = 0;
//if (res < 0)
//{
// Origin isn't inside portal - no collision.
return -1;
//}
}
};
return 0;
};
#endif //B3_MPR_PENETRATION_H
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