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vec3.c
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vec3.c
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/***
* libccd
* ---------------------------------
* Copyright (c)2010 Daniel Fiser <[email protected]>
*
*
* This file is part of libccd.
*
* Distributed under the OSI-approved BSD License (the "License");
* see accompanying file BDS-LICENSE for details or 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.
*/
#include <stdio.h>
#include "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)),
CCD_VEC3_STATIC(CCD_REAL( 0.850648), CCD_REAL(-0.000000), CCD_REAL(-0.525736)),
CCD_VEC3_STATIC(CCD_REAL(-0.525730), CCD_REAL(-0.000000), CCD_REAL(-0.850652)),
CCD_VEC3_STATIC(CCD_REAL(-0.688190), CCD_REAL(-0.499997), CCD_REAL(-0.525736)),
CCD_VEC3_STATIC(CCD_REAL(-0.162456), CCD_REAL( 0.499995), CCD_REAL(-0.850654)),
CCD_VEC3_STATIC(CCD_REAL(-0.688190), CCD_REAL( 0.499997), CCD_REAL(-0.525736)),
CCD_VEC3_STATIC(CCD_REAL( 0.262869), CCD_REAL( 0.809012), CCD_REAL(-0.525738)),
CCD_VEC3_STATIC(CCD_REAL( 0.951058), CCD_REAL( 0.309013), CCD_REAL( 0.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.951058), CCD_REAL(-0.309013), CCD_REAL( 0.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.587786), CCD_REAL(-0.809017), CCD_REAL( 0.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.000000), CCD_REAL(-1.000000), CCD_REAL( 0.000000)),
CCD_VEC3_STATIC(CCD_REAL(-0.587786), CCD_REAL(-0.809017), CCD_REAL( 0.000000)),
CCD_VEC3_STATIC(CCD_REAL(-0.951058), CCD_REAL(-0.309013), CCD_REAL(-0.000000)),
CCD_VEC3_STATIC(CCD_REAL(-0.951058), CCD_REAL( 0.309013), CCD_REAL(-0.000000)),
CCD_VEC3_STATIC(CCD_REAL(-0.587786), CCD_REAL( 0.809017), CCD_REAL(-0.000000)),
CCD_VEC3_STATIC(CCD_REAL(-0.000000), CCD_REAL( 1.000000), CCD_REAL(-0.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.587786), CCD_REAL( 0.809017), CCD_REAL(-0.000000)),
CCD_VEC3_STATIC(CCD_REAL( 0.688190), CCD_REAL(-0.499997), CCD_REAL( 0.525736)),
CCD_VEC3_STATIC(CCD_REAL(-0.262869), CCD_REAL(-0.809012), CCD_REAL( 0.525738)),
CCD_VEC3_STATIC(CCD_REAL(-0.850648), CCD_REAL( 0.000000), CCD_REAL( 0.525736)),
CCD_VEC3_STATIC(CCD_REAL(-0.262869), CCD_REAL( 0.809012), CCD_REAL( 0.525738)),
CCD_VEC3_STATIC(CCD_REAL( 0.688190), CCD_REAL( 0.499997), CCD_REAL( 0.525736)),
CCD_VEC3_STATIC(CCD_REAL( 0.525730), CCD_REAL( 0.000000), CCD_REAL( 0.850652)),
CCD_VEC3_STATIC(CCD_REAL( 0.162456), CCD_REAL(-0.499995), CCD_REAL( 0.850654)),
CCD_VEC3_STATIC(CCD_REAL(-0.425323), CCD_REAL(-0.309011), CCD_REAL( 0.850654)),
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_t *ccd_points_on_sphere = points_on_sphere;
size_t ccd_points_on_sphere_len = sizeof(points_on_sphere) / sizeof(ccd_vec3_t);
_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;
}
ccd_real_t ccdVec3PointSegmentDist2(const ccd_vec3_t *P,
const ccd_vec3_t *x0, const ccd_vec3_t *b,
ccd_vec3_t *witness)
{
return __ccdVec3PointSegmentDist2(P, x0, b, witness);
}
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;
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);
s = (q * r - w * p) / (w * v - r * r);
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;
}