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geometry.c
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Sun, May 25, 03:49

geometry.c
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/*
* dot dot product
* cross cross product
* determinant determinant of matrix built from three vectors
* pdist distance from point towards origin
* ppdist distance between two points
* plinproj projection of point onto line spanned by two points
* ptriproj projection of point onto plane spanned by three points
* ltrisect intersection of line with plane spanned by three points
* lmoutr compute la/mu parameters for projection on triangle
* routlm compute projection on triangle from la/mu parameters
* ptriside determines on which side of a triangle a point lies
* solang computes solid angle of triangle as seen from origin
*
* (c) 2002 Robert Oostenveld
*
*/
#include <math.h>
#include "geometry.h"
/****************************************************************************/
double dot(double* a, double* b)
{
double ss=0;
ss += a[0]*b[0];
ss += a[1]*b[1];
ss += a[2]*b[2];
return ss;
}
/****************************************************************************/
void cross(double* a, double* b, double* r)
{
r[0] = a[1]*b[2] - a[2]*b[1];
r[1] = a[2]*b[0] - a[0]*b[2];
r[2] = a[0]*b[1] - a[1]*b[0];
return;
}
/****************************************************************************/
double determinant(double* a, double* b, double* c)
{
return a[0]*(b[1]*c[2]-c[1]*b[2]) - a[1]*(b[0]*c[2]-c[0]*b[2]) + a[2]*(b[0]*c[1]-c[0]*b[1]);
}
/****************************************************************************/
double pdist(double* v1)
{
double ss=0;
ss += v1[0]*v1[0];
ss += v1[1]*v1[1];
ss += v1[2]*v1[2];
return sqrt(ss);
}
/****************************************************************************/
double ppdist(double* v1, double* v2)
{
double ss=0;
ss += (v1[0]-v2[0])*(v1[0]-v2[0]);
ss += (v1[1]-v2[1])*(v1[1]-v2[1]);
ss += (v1[2]-v2[2])*(v1[2]-v2[2]);
return sqrt(ss);
}
/****************************************************************************/
double plinproj(double* l1, double* l2, double* r, double *proj, int flag)
{
double l12[3], l1r[3];
double l12_l=0, l1r_l=0, la=0;
int k;
for (k=0; k<3; k++)
{
l12[k]=l2[k]-l1[k];
l1r[k]=r[k]-l1[k];
l12_l += l12[k]*l12[k];
l1r_l += l1r[k]*l1r[k];
}
l12_l = sqrt(l12_l);
l1r_l = sqrt(l1r_l);
if (l12_l==0)
{
/* begin and endpoint of linepiece are the same */
proj[0] = l1[0];
proj[1] = l1[1];
proj[2] = l1[2];
return l1r_l;
}
if (l1r_l==0)
{
/* point lies exactly at beginpoint of linepiece */
proj[0] = l1[0];
proj[1] = l1[1];
proj[2] = l1[2];
return 0;
}
/* compute relative distance along linepiece */
la = dot(l12,l1r)/(l12_l*l12_l);
if (flag && la<0)
/* intended projection point would lie before begin of linepiece */
la=0;
else if (flag && la>1)
/* intended projection point would lie after end of linepiece */
la=1;
/* compute projection point along line through l1 and l2 */
proj[0] = l1[0] + la*l12[0];
proj[1] = l1[1] + la*l12[1];
proj[2] = l1[2] + la*l12[2];
return ppdist(proj,r);
}
/****************************************************************************/
double ptriproj(double* v1, double* v2, double* v3, double* r, double* proj, int flag)
{
double la, mu, d;
lmoutr(v1, v2, v3, r, &la, &mu, &d);
if (flag)
{
/* projection of r on triangle */
if (la>=0 && mu>=0 && (la+mu)<=1)
routlm(v1, v2, v3, la, mu, proj);
else if (la<0)
d = plinproj(v1, v3, r, proj, flag);
else if (mu<0)
d = plinproj(v1, v2, r, proj, flag);
else
d = plinproj(v2, v3, r, proj, flag);
}
else
{
/* projection of r on plane */
routlm(v1, v2, v3, la, mu, proj);
}
return d;
}
/****************************************************************************/
void ltrisect(double* v1, double* v2, double* v3, double* l1, double* l2, double* proj)
{
double la1, mu1, d1;
double la2, mu2, d2;
double p1[3];
double p2[3];
int s1, s2;
char str[256];
s1 = ptriside(v1, v2, v3, l1);
s2 = ptriside(v1, v2, v3, l2);
if (s1==0)
{
/* point l1 lies on plane spanned by triangle */
proj[0] = l1[0];
proj[1] = l1[1];
proj[2] = l1[2];
return;
}
else if (s2==0)
{
/* point l2 lies on plane spanned by triangle */
proj[0] = l2[0];
proj[1] = l2[1];
proj[2] = l2[2];
return;
}
lmoutr(v1, v2, v3, l1, &la1, &mu1, &d1);
lmoutr(v1, v2, v3, l2, &la2, &mu2, &d2);
routlm(v1, v2, v3, la1, mu1, p1); /* projection of l1 on plane */
routlm(v1, v2, v3, la2, mu2, p2); /* projection of l2 on plane */
/* d1 and d2 are the distances from l1 and l2 to the plane spanned by v1, v2, v3 */
/* these are used to weigh both projected points to their weighed geometric mean */
d1 *= s1;
d2 *= s2;
if (d1==d2)
{
/* the line is parallel to the plane and does not intersect */
proj[0] = mxGetNaN();
proj[1] = mxGetNaN();
proj[2] = mxGetNaN();
return;
}
proj[0] = (d1*p2[0] - d2*p1[0])/(d1-d2);
proj[1] = (d1*p2[1] - d2*p1[1])/(d1-d2);
proj[2] = (d1*p2[2] - d2*p1[2])/(d1-d2);
return;
}
/****************************************************************************/
void lmoutr(double* v1, double* v2, double* v3, double* r, double *la, double *mu, double *ze)
{
double a[3], b[3], c[3], d[3];
double a_l=0, b_l=0, c_l=0, d_l=0;
double det, det_la, det_mu, det_ze;
int k;
for (k=0; k<3; k++)
{
a[k] = r[k]-v1[k];
b[k] = v2[k]-v1[k];
c[k] = v3[k]-v1[k];
a_l += a[k]*a[k];
b_l += b[k]*b[k];
c_l += c[k]*c[k];
}
a_l = sqrt(a_l);
b_l = sqrt(b_l);
c_l = sqrt(c_l);
if (a_l==0)
{
/* point lies exactly on the first vertex */
*la = 0;
*mu = 0;
*ze = 0;
return;
}
else if (b_l==0 || c_l==0)
{
/* this is a degenerate triangle, not possible to compute la/mu */
*la = mxGetNaN();
*mu = mxGetNaN();
*ze = mxGetNaN();
return;
}
else
{
/* compute vector d orthogonal to the triangle */
cross(b, c, d);
d_l = pdist(d);
/* normalize vector d */
d[0] = d[0]/d_l;
d[1] = d[1]/d_l;
d[2] = d[2]/d_l;
/* solve the system of equations using Cramer's method (method of determinants) */
/* c = la*a + mu*b + ze*o */
det = determinant(b, c, d);
det_la = determinant(a, c, d);
det_mu = determinant(b, a, d);
det_ze = determinant(b, c, a);
*la = det_la/det;
*mu = det_mu/det;
*ze = det_ze/det;
/* since d is an orthonormal vector to the plane, the distance of r */
/* to the plane equals the absolume value of parameter ze */
*ze = ((*ze)<0 ? -(*ze) : +(*ze));
}
return;
}
/****************************************************************************/
void routlm(double* v1, double* v2, double* v3, double la, double mu, double* r)
{
r[0] = (1-la-mu)*v1[0]+la*v2[0]+mu*v3[0];
r[1] = (1-la-mu)*v1[1]+la*v2[1]+mu*v3[1];
r[2] = (1-la-mu)*v1[2]+la*v2[2]+mu*v3[2];
return;
}
/****************************************************************************/
int ptriside(double* v1, double* v2, double* v3, double *r)
{
double val;
double a[3], b[3], c[3], d[3];
int k;
for (k=0; k<3; k++)
{
a[k] = r[k]-v1[k];
b[k] = v2[k]-v1[k];
c[k] = v3[k]-v1[k];
}
cross(b, c, d);
val = dot(a, d);
if (val>0)
return 1;
else if (val<0)
return -1;
else
return 0;
}
/****************************************************************************/
double solang(double *r1, double *r2, double *r3, int *on_triangle)
{
double cp23_x,cp23_y,cp23_z,n1,n2,n3,ip12,ip23,ip13,nom,den;
*on_triangle=0;
cp23_x = r2[1] * r3[2] - r2[2] * r3[1];
cp23_y = r2[2] * r3[0] - r2[0] * r3[2];
cp23_z = r2[0] * r3[1] - r2[1] * r3[0];
nom = cp23_x*r1[0] + cp23_y*r1[1] + cp23_z*r1[2];
n1 = sqrt(r1[0]*r1[0] + r1[1]*r1[1] + r1[2]*r1[2]);
n2 = sqrt(r2[0]*r2[0] + r2[1]*r2[1] + r2[2]*r2[2]);
n3 = sqrt(r3[0]*r3[0] + r3[1]*r3[1] + r3[2]*r3[2]);
ip12 = r1[0]*r2[0] + r1[1]*r2[1] + r1[2]*r2[2];
ip23 = r2[0]*r3[0] + r2[1]*r3[1] + r2[2]*r3[2];
ip13 = r1[0]*r3[0] + r1[1]*r3[1] + r1[2]*r3[2];
den = n1*n2*n3 + ip12*n3 + ip23*n1 + ip13*n2;
if (nom==0 & den<=0)
{
*on_triangle=1;
return 0;
}
return -2.*atan2 (nom,den);
}

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