void CModel::FacetHarmonics(int fh, int bw, double r, gsl_complex *coeff){
int i, j, sign;
gsl_complex err;
Triangle_3 tr;
tr = Triangle_3(plist[flist[fh*3+0]],plist[flist[fh*3+1]],plist[flist[fh*3+2]]);
Tetrahedron_3 tetr;
tetr = Tetrahedron_3(Point_3(0.0, 0.0, 0.0),plist[flist[fh*3+0]],plist[flist[fh*3+1]],plist[flist[fh*3+2]]);
if(tetr.is_degenerate()) return;
sign = (tetr.volume()<0 ? -1 : 1);
for(i=0; i<bw; i++){
for(j=0; j<=i; j++){
Integrate(i, j, r, tetr, &coeff[i*bw+j], &err);
coeff[i*bw+j] = gsl_complex_mul_real(coeff[i*bw+j], (double)sign);
}
}
}
bool
does_intersect_convex_polygon_segment_3_in_3d(const vector<Point>& conv_poly,
const Segment& s)
{
// dissect the polygon into a set of triangles with common apex at the centroid.
Vector centroid = CGAL::NULL_VECTOR;
vector<Triangle_3> t;
for(int i = 0; i < (int)conv_poly.size(); i ++)
centroid = centroid + (conv_poly[i] - CGAL::ORIGIN);
centroid = (1./(int)conv_poly.size()) * centroid;
for(int i = 0; i < (int)conv_poly.size(); i ++)
t.push_back(Triangle_3(CGAL::ORIGIN + centroid,
conv_poly[i], conv_poly[(i+1)%((int)conv_poly.size())]));
//CGAL::Failure_function old_ff = CGAL::set_error_handler(failure_func);
//CGAL::Failure_behaviour old_fb = CGAL::set_error_behaviour(CGAL::CONTINUE);
// Now for every triangle in t check if the Delaunay edge e intersects it.
// use CGAL routine.
bool is_degenerate_poly = true;
for(int i = 0; i < (int)t.size(); i ++)
{
cgal_failed = false;
bool intersect_result = CGAL::do_intersect(t[i], s);
if(cgal_failed) continue;
is_degenerate_poly = false;
if(intersect_result)
{
//CGAL::set_error_handler(old_ff);
//CGAL::set_error_behaviour(old_fb);
is_degenerate_poly = false;
return true;
}
}
//CGAL::set_error_handler(old_ff);
//CGAL::set_error_behaviour(old_fb);
if(is_degenerate_poly) cerr << "+";
return false;
}
// -------------------------------------------------------------
// dg_voronoi_point
// -------------------------------------------------------------
// This function computes a voronoi point when some degeneracies
// have been discovered about the four points of a tetrahedron.
//
// In this function we assume that the degeneracies occured
// because of the coplanarity. We approximate the circumcenter
// of the tetrahedron by the circumcenter of one of the triangular
// facets.
// -------------------------------------------------------------
Point
dg_voronoi_point(const Point &a,
const Point &b,
const Point &c,
const Point &d,
bool &is_correct_computation)
{
// First, we check if our assumption is correct.
// This is more of a debugging purpose than of
// actual computation.
Tetrahedron t = Tetrahedron(a,b,c,d);
if( ! t.is_degenerate() )
{
// cerr << "error in the assumption of coplanarity." << endl;
/*
// debug
cout << "{OFF " << endl;
cout << "4 4 0" << endl;
cout << a << "\n" << b << "\n" << c << "\n" << d << endl;
cout << "3\t0 1 2" << endl;
cout << "3\t0 2 3" << endl;
cout << "3\t0 3 1" << endl;
cout << "3\t1 2 3" << endl;
cout << "}" << endl;
// end debug
*/
}
// Approximate the circumcenter of the tetrahedron with that of
// one of its triangular facets. The facet should not be collinear.
// The following boolean variable will keep track if we have found
// a valid circumcenter (of a triangle) to replace that of a
// tetrahedron.
Point cc = CGAL::ORIGIN;
is_correct_computation = false;
Point p[4] = {a,b,c,d};
for(int i = 0; i < 4; i ++)
{
// first check if the facet is degenerate or not.
Triangle_3 t = Triangle_3(p[(i+1)%4], p[(i+2)%4], p[(i+3)%4]);
if( t.is_degenerate() ) continue;
// since we found a non-degenerate triangle we can now compute
// its circumcenter and we will be done.
cc = nondg_cc_tr_3(p[(i+1)%4], p[(i+2)%4], p[(i+3)%4], is_correct_computation);
if( is_correct_computation )
break;
}
if( is_correct_computation )
{
if(cc == CGAL::ORIGIN) cerr << "<dg_vp : returning cc as ORIGIN>" << endl;
return cc;
}
cerr << "four points are colinear. " << endl;
// for the time being, I just average the four points. What should be
// the circumcenter of a tetrahedron whose four points are collinear ?
cc = CGAL::ORIGIN +
( 0.25*Vector
(
a[0]+b[0]+c[0]+d[0],
a[1]+b[1]+c[1]+d[1],
a[2]+b[2]+c[2]+d[2]
)
);
if(cc == CGAL::ORIGIN) cerr << "<dg_vp : returning cc as ORIGIN>" << endl;
return cc;
}