static void findPenetrSegment(const void *obj1, const void *obj2, const ccd_t *ccd,
ccd_simplex_t *portal,
ccd_real_t *depth, ccd_vec3_t *dir, ccd_vec3_t *pos)
{
(void)(obj1);
(void)(obj2);
(void)(ccd);
/*
ccd_vec3_t vec;
ccd_real_t k;
*/
/* Origin lies on v0-v1 segment.*/
/* Depth is distance to v1, direction also and position must be*/
/* computed*/
ccdVec3Copy(pos, &ccdSimplexPoint(portal, 1)->v1);
ccdVec3Add(pos, &ccdSimplexPoint(portal, 1)->v2);
ccdVec3Scale(pos, CCD_REAL(0.5));
/*
ccdVec3Sub2(&vec, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 0)->v);
k = CCD_SQRT(ccdVec3Len2(&ccdSimplexPoint(portal, 0)->v));
k /= CCD_SQRT(ccdVec3Len2(&vec));
ccdVec3Scale(&vec, -k);
ccdVec3Add(pos, &vec);
*/
ccdVec3Copy(dir, &ccdSimplexPoint(portal, 1)->v);
*depth = CCD_SQRT(ccdVec3Len2(dir));
ccdVec3Normalize(dir);
}
_ccd_inline ccd_real_t __ccdVec3PointSegmentDist2(const ccd_vec3_t *P,
const ccd_vec3_t *x0,
const ccd_vec3_t *b,
ccd_vec3_t *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.
ccd_real_t dist, t;
ccd_vec3_t d, a;
// direction of segment
ccdVec3Sub2(&d, b, x0);
// precompute vector from P to x0
ccdVec3Sub2(&a, x0, P);
t = -CCD_REAL(1.) * ccdVec3Dot(&a, &d);
t /= ccdVec3Len2(&d);
if (t < CCD_ZERO || ccdIsZero(t)){
dist = ccdVec3Dist2(x0, P);
if (witness)
ccdVec3Copy(witness, x0);
}else if (t > CCD_ONE || ccdEq(t, CCD_ONE)){
dist = ccdVec3Dist2(b, P);
if (witness)
ccdVec3Copy(witness, b);
}else{
if (witness){
ccdVec3Copy(witness, &d);
ccdVec3Scale(witness, t);
ccdVec3Add(witness, x0);
dist = ccdVec3Dist2(witness, P);
}else{
// recycling variables
ccdVec3Scale(&d, t);
ccdVec3Add(&d, &a);
dist = ccdVec3Len2(&d);
}
}
return dist;
}
static void findPenetrTouch(const void *obj1, const void *obj2, const ccd_t *ccd,
ccd_simplex_t *portal,
ccd_real_t *depth, ccd_vec3_t *dir, ccd_vec3_t *pos)
{
// Touching contact on portal's v1 - so depth is zero and direction
// is unimportant and pos can be guessed
*depth = CCD_REAL(0.);
ccdVec3Copy(dir, ccd_vec3_origin);
ccdVec3Copy(pos, &ccdSimplexPoint(portal, 1)->v1);
ccdVec3Add(pos, &ccdSimplexPoint(portal, 1)->v2);
ccdVec3Scale(pos, 0.5);
}
static void findPos(const void *obj1, const void *obj2, const ccd_t *ccd,
const ccd_simplex_t *portal, ccd_vec3_t *pos)
{
ccd_vec3_t dir;
size_t i;
ccd_real_t b[4], sum, inv;
ccd_vec3_t vec, p1, p2;
(void)(obj1);
(void)(obj2);
(void)(ccd);
(void)(portal);
portalDir(portal, &dir);
/* use barycentric coordinates of tetrahedron to find origin*/
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 2)->v);
b[0] = ccdVec3Dot(&vec, &ccdSimplexPoint(portal, 3)->v);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 3)->v,
&ccdSimplexPoint(portal, 2)->v);
b[1] = ccdVec3Dot(&vec, &ccdSimplexPoint(portal, 0)->v);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 0)->v,
&ccdSimplexPoint(portal, 1)->v);
b[2] = ccdVec3Dot(&vec, &ccdSimplexPoint(portal, 3)->v);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 2)->v,
&ccdSimplexPoint(portal, 1)->v);
b[3] = ccdVec3Dot(&vec, &ccdSimplexPoint(portal, 0)->v);
sum = b[0] + b[1] + b[2] + b[3];
if (ccdIsZero(sum) || sum < CCD_ZERO) {
b[0] = CCD_REAL(0.);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 2)->v,
&ccdSimplexPoint(portal, 3)->v);
b[1] = ccdVec3Dot(&vec, &dir);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 3)->v,
&ccdSimplexPoint(portal, 1)->v);
b[2] = ccdVec3Dot(&vec, &dir);
ccdVec3Cross(&vec, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 2)->v);
b[3] = ccdVec3Dot(&vec, &dir);
sum = b[1] + b[2] + b[3];
}
inv = CCD_REAL(1.) / sum;
ccdVec3Copy(&p1, ccd_vec3_origin);
ccdVec3Copy(&p2, ccd_vec3_origin);
for (i = 0; i < 4; i++) {
ccdVec3Copy(&vec, &ccdSimplexPoint(portal, i)->v1);
ccdVec3Scale(&vec, b[i]);
ccdVec3Add(&p1, &vec);
ccdVec3Copy(&vec, &ccdSimplexPoint(portal, i)->v2);
ccdVec3Scale(&vec, b[i]);
ccdVec3Add(&p2, &vec);
}
ccdVec3Scale(&p1, inv);
ccdVec3Scale(&p2, inv);
ccdVec3Copy(pos, &p1);
ccdVec3Add(pos, &p2);
ccdVec3Scale(pos, 0.5);
}
static int discoverPortal(const void *obj1, const void *obj2,
const ccd_t *ccd, ccd_simplex_t *portal)
{
ccd_vec3_t dir, va, vb;
ccd_real_t dot;
int cont;
/* vertex 0 is center of portal*/
findOrigin(obj1, obj2, ccd, ccdSimplexPointW(portal, 0));
ccdSimplexSetSize(portal, 1);
if (ccdVec3Eq(&ccdSimplexPoint(portal, 0)->v, ccd_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...*/
ccdVec3Set(&va, CCD_EPS * CCD_REAL(10.), CCD_ZERO, CCD_ZERO);
ccdVec3Add(&ccdSimplexPointW(portal, 0)->v, &va);
}
/* vertex 1 = support in direction of origin*/
ccdVec3Copy(&dir, &ccdSimplexPoint(portal, 0)->v);
ccdVec3Scale(&dir, CCD_REAL(-1.));
ccdVec3Normalize(&dir);
__ccdSupport(obj1, obj2, &dir, ccd, ccdSimplexPointW(portal, 1));
ccdSimplexSetSize(portal, 2);
/* test if origin isn't outside of v1*/
dot = ccdVec3Dot(&ccdSimplexPoint(portal, 1)->v, &dir);
if (ccdIsZero(dot) || dot < CCD_ZERO)
return -1;
/* vertex 2*/
ccdVec3Cross(&dir, &ccdSimplexPoint(portal, 0)->v,
&ccdSimplexPoint(portal, 1)->v);
if (ccdIsZero(ccdVec3Len2(&dir))) {
if (ccdVec3Eq(&ccdSimplexPoint(portal, 1)->v, ccd_vec3_origin)) {
/* origin lies on v1*/
return 1;
} else {
/* origin lies on v0-v1 segment*/
return 2;
}
}
ccdVec3Normalize(&dir);
__ccdSupport(obj1, obj2, &dir, ccd, ccdSimplexPointW(portal, 2));
dot = ccdVec3Dot(&ccdSimplexPoint(portal, 2)->v, &dir);
if (ccdIsZero(dot) || dot < CCD_ZERO)
return -1;
ccdSimplexSetSize(portal, 3);
/* vertex 3 direction*/
ccdVec3Sub2(&va, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 0)->v);
ccdVec3Sub2(&vb, &ccdSimplexPoint(portal, 2)->v,
&ccdSimplexPoint(portal, 0)->v);
ccdVec3Cross(&dir, &va, &vb);
ccdVec3Normalize(&dir);
/* it is better to form portal faces to be oriented "outside" origin*/
dot = ccdVec3Dot(&dir, &ccdSimplexPoint(portal, 0)->v);
if (dot > CCD_ZERO) {
ccdSimplexSwap(portal, 1, 2);
ccdVec3Scale(&dir, CCD_REAL(-1.));
}
while (ccdSimplexSize(portal) < 4) {
__ccdSupport(obj1, obj2, &dir, ccd, ccdSimplexPointW(portal, 3));
dot = ccdVec3Dot(&ccdSimplexPoint(portal, 3)->v, &dir);
if (ccdIsZero(dot) || dot < CCD_ZERO)
return -1;
cont = 0;
/* test if origin is outside (v1, v0, v3) - set v2 as v3 and*/
/* continue*/
ccdVec3Cross(&va, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 3)->v);
dot = ccdVec3Dot(&va, &ccdSimplexPoint(portal, 0)->v);
if (dot < CCD_ZERO && !ccdIsZero(dot)) {
ccdSimplexSet(portal, 2, ccdSimplexPoint(portal, 3));
cont = 1;
}
if (!cont) {
/* test if origin is outside (v3, v0, v2) - set v1 as v3 and*/
/* continue*/
ccdVec3Cross(&va, &ccdSimplexPoint(portal, 3)->v,
&ccdSimplexPoint(portal, 2)->v);
dot = ccdVec3Dot(&va, &ccdSimplexPoint(portal, 0)->v);
if (dot < CCD_ZERO && !ccdIsZero(dot)) {
ccdSimplexSet(portal, 1, ccdSimplexPoint(portal, 3));
cont = 1;
}
}
if (cont) {
ccdVec3Sub2(&va, &ccdSimplexPoint(portal, 1)->v,
&ccdSimplexPoint(portal, 0)->v);
ccdVec3Sub2(&vb, &ccdSimplexPoint(portal, 2)->v,
&ccdSimplexPoint(portal, 0)->v);
ccdVec3Cross(&dir, &va, &vb);
ccdVec3Normalize(&dir);
} else {
ccdSimplexSetSize(portal, 4);
}
}
return 0;
}
ccd_real_t ccdVec3PointTriDist2(const ccd_vec3_t *P,
const ccd_vec3_t *x0, const ccd_vec3_t *B,
const ccd_vec3_t *C,
ccd_vec3_t *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.
ccd_vec3_t d1, d2, a;
ccd_real_t u, v, w, p, q, r, d;
ccd_real_t s, t, dist, dist2;
ccd_vec3_t witness2;
ccdVec3Sub2(&d1, B, x0);
ccdVec3Sub2(&d2, C, x0);
ccdVec3Sub2(&a, x0, P);
u = ccdVec3Dot(&a, &a);
v = ccdVec3Dot(&d1, &d1);
w = ccdVec3Dot(&d2, &d2);
p = ccdVec3Dot(&a, &d1);
q = ccdVec3Dot(&a, &d2);
r = ccdVec3Dot(&d1, &d2);
d = w * v - r * r;
if (ccdIsZero(d)){
// To avoid division by zero for zero (or near zero) area triangles
s = t = -1.;
}else{
s = (q * r - w * p) / d;
t = (-s * r - q) / w;
}
if ((ccdIsZero(s) || s > CCD_ZERO)
&& (ccdEq(s, CCD_ONE) || s < CCD_ONE)
&& (ccdIsZero(t) || t > CCD_ZERO)
&& (ccdEq(t, CCD_ONE) || t < CCD_ONE)
&& (ccdEq(t + s, CCD_ONE) || t + s < CCD_ONE)){
if (witness){
ccdVec3Scale(&d1, s);
ccdVec3Scale(&d2, t);
ccdVec3Copy(witness, x0);
ccdVec3Add(witness, &d1);
ccdVec3Add(witness, &d2);
dist = ccdVec3Dist2(witness, P);
}else{
dist = s * s * v;
dist += t * t * w;
dist += CCD_REAL(2.) * s * t * r;
dist += CCD_REAL(2.) * s * p;
dist += CCD_REAL(2.) * t * q;
dist += u;
}
}else{
dist = __ccdVec3PointSegmentDist2(P, x0, B, witness);
dist2 = __ccdVec3PointSegmentDist2(P, x0, C, &witness2);
if (dist2 < dist){
dist = dist2;
if (witness)
ccdVec3Copy(witness, &witness2);
}
dist2 = __ccdVec3PointSegmentDist2(P, B, C, &witness2);
if (dist2 < dist){
dist = dist2;
if (witness)
ccdVec3Copy(witness, &witness2);
}
}
return dist;
}
* <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.
*/
#include <stdio.h>
#include <ccd/vec3.h>
#include "dbg.h"
static CCD_VEC3(__ccd_vec3_origin, CCD_ZERO, CCD_ZERO, CCD_ZERO);
ccd_vec3_t *ccd_vec3_origin = &__ccd_vec3_origin;
static ccd_vec3_t points_on_sphere[] = {
CCD_VEC3_STATIC(CCD_REAL( 0.000000), CCD_REAL(-0.000000), CCD_REAL(-1.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.723608), CCD_REAL(-0.525725), CCD_REAL(-0.447219)),
CCD_VEC3_STATIC(CCD_REAL(-0.276388), CCD_REAL(-0.850649), CCD_REAL(-0.447219)),
CCD_VEC3_STATIC(CCD_REAL(-0.894426), CCD_REAL(-0.000000), CCD_REAL(-0.447216)),
CCD_VEC3_STATIC(CCD_REAL(-0.276388), CCD_REAL( 0.850649), CCD_REAL(-0.447220)),
CCD_VEC3_STATIC(CCD_REAL( 0.723608), CCD_REAL( 0.525725), CCD_REAL(-0.447219)),
CCD_VEC3_STATIC(CCD_REAL( 0.276388), CCD_REAL(-0.850649), CCD_REAL( 0.447220)),
CCD_VEC3_STATIC(CCD_REAL(-0.723608), CCD_REAL(-0.525725), CCD_REAL( 0.447219)),
CCD_VEC3_STATIC(CCD_REAL(-0.723608), CCD_REAL( 0.525725), CCD_REAL( 0.447219)),
CCD_VEC3_STATIC(CCD_REAL( 0.276388), CCD_REAL( 0.850649), CCD_REAL( 0.447219)),
CCD_VEC3_STATIC(CCD_REAL( 0.894426), CCD_REAL( 0.000000), CCD_REAL( 0.447216)),
CCD_VEC3_STATIC(CCD_REAL(-0.000000), CCD_REAL( 0.000000), CCD_REAL( 1.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.425323), CCD_REAL(-0.309011), CCD_REAL(-0.850654)),
CCD_VEC3_STATIC(CCD_REAL(-0.162456), CCD_REAL(-0.499995), CCD_REAL(-0.850654)),
CCD_VEC3_STATIC(CCD_REAL( 0.262869), CCD_REAL(-0.809012), CCD_REAL(-0.525738)),
CCD_VEC3_STATIC(CCD_REAL( 0.425323), CCD_REAL( 0.309011), CCD_REAL(-0.850654)),
