/
sphere.cpp
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/
sphere.cpp
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#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/halfspaces_intersection.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/IO/Polyhedron_iostream.h>
#include <iterator>
#include <fstream>
#include <stdlib.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Convex_hull_traits_3<K> Traits;
typedef Traits::Polyhedron_3 Polyhedron;
typedef Polyhedron::Facet_iterator Facet_iterator;
typedef Polyhedron::Halfedge_around_facet_circulator Halfedge_facet_circulator;
typedef K::FT FT;
typedef K::Point_3 Point;
typedef K::Vector_3 Vector;
typedef K::Plane_3 Plane;
double mu = 0.4;
Point
project_back(const Point & p)
{
double sk = p.x() * p.x() + p.y() * p.y() + (p.z() * p.z() / (mu*mu));
return Point(p.x()/sqrt(sk), p.y()/sqrt(sk), p.z()/sqrt(sk));
}
Plane
tangent_plane (Point &p)
{
Vector v (p.x(), p.y(), p.z()/(mu*mu));
v = v/sqrt(v.squared_length());
return Plane(v.x(), v.y(), v.z(), - (p - CGAL::ORIGIN) * v);
}
Point
rescale (Point p)
{
return Point(p.x(), p.y(), mu * p.z());
}
double lloyd_step (std::vector<Point> &points)
{
std::vector<Plane> planes;
for (size_t i = 0; i < points.size(); ++i)
planes.push_back(tangent_plane(points[i]));
Polyhedron P;
CGAL::internal::halfspaces_intersection(planes.begin(),
planes.end(), P, K());
size_t N = points.size();
points.clear();
double totarea = 0.0;
double vararea = 0.0;
for (Polyhedron::Facet_iterator it = P.facets_begin();
it != P.facets_end(); ++it)
{
Polyhedron::Halfedge_around_facet_circulator
h0 = it->facet_begin(), hf = h0--, hs = hf;
hs ++;
double farea = 0.0;
Vector fcentroid (CGAL::NULL_VECTOR);
while(1)
{
const Point &a = h0->vertex()->point(),
&b = hf->vertex()->point(),
&c = hs->vertex()->point();
Vector v =
CGAL::cross_product(b -a, c - a);
double tarea = .5 * sqrt(v.squared_length());
farea += tarea;
fcentroid = fcentroid + (tarea/3.0) * ((a - CGAL::ORIGIN) +
(b - CGAL::ORIGIN) +
(c - CGAL::ORIGIN));
if (hs == h0)
break;
++hs; ++hf;
}
totarea += farea;
vararea += pow(4.0 * M_PI / N - farea, 2.0);
fcentroid = fcentroid/farea;
points.push_back(project_back(CGAL::ORIGIN + fcentroid));
}
std::cerr << "area = " << totarea << ", "
<< "vararea = " << vararea << "\n";
return vararea/totarea;
}
int main(int argc, const char **argv )
{
std::vector<Point> points;
CGAL::Random_points_on_sphere_3<Point> g;
size_t N = 0;
if (argc > 1)
N = atof(argv[1]);
N = std::max(size_t(100), N);
for (size_t i = 0; i < N; ++i)
points.push_back(rescale(*g++));
for (size_t n = 0; n < 100; ++n)
{
std::cerr << "step " << n << ":\n\t";
lloyd_step(points);
}
Polyhedron P;
CGAL::convex_hull_3(points.begin(), points.end(), P);
CGAL::set_ascii_mode( std::cout);
std::cout << "OFF" << std::endl << P.size_of_vertices() << ' '
<< P.size_of_facets() << " 0" << std::endl;
std::copy( P.points_begin(), P.points_end(),
std::ostream_iterator<Point>( std::cout, "\n"));
for ( Facet_iterator i = P.facets_begin(); i != P.facets_end(); ++i) {
Halfedge_facet_circulator j = i->facet_begin();
// Facets in polyhedral surfaces are at least triangles.
CGAL_assertion( CGAL::circulator_size(j) >= 3);
std::cout << CGAL::circulator_size(j) << ' ';
do {
std::cout << ' ' << std::distance(P.vertices_begin(), j->vertex());
} while ( ++j != i->facet_begin());
std::cout << std::endl;
}
std::ofstream os ("test.cloud");
std::copy(points.begin(), points.end(),
std::ostream_iterator<Point>(os, "\n"));
}