CGAL 4.7 - 3D Envelopes: Envelope_3/envelope_spheres.cpp

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 3D Envelopes

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Envelope_3/envelope_spheres.cpp
// Constructing the lower envelope of a set of spheres read from a file.
#include <CGAL/basic.h>
#ifndef CGAL_USE_CORE
#include <iostream>
int main()
{
std::cout << "Sorry, this example needs CORE ..." << std::endl;
return 0;
}
#else
#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_conic_traits_2.h>
#include <CGAL/Env_sphere_traits_3.h>
#include <CGAL/envelope_3.h>
#include <CGAL/Timer.h>
#include <iostream>
#include <list>
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
typedef Nt_traits::Rational Rational;
typedef Nt_traits::Algebraic Algebraic;
typedef CGAL::Cartesian<Rational> Rat_kernel;
typedef Rat_kernel::Point_3 Rat_point_3;
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
typedef CGAL::Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>
Conic_traits_2;
typedef CGAL::Env_sphere_traits_3<Conic_traits_2> Traits_3;
typedef Traits_3::Surface_3 Sphere_3;
typedef CGAL::Envelope_diagram_2<Traits_3> Envelope_diagram_2;
int main(int argc, char **argv)
{
// Get the name of the input file from the command line, or use the default
// fan_grids.dat file if no command-line parameters are given.
const char * filename = (argc > 1) ? argv[1] : "spheres.dat";
// Open the input file.
std::ifstream in_file(filename);
if (! in_file.is_open())
{
std::cerr << "Failed to open " << filename << " ..." << std::endl;
return 1;
}
// Read the spheres from the file.
// The input file format should be (all coordinate values are integers):
// <n> // number of spheres.
// <x_1> <y_1> <x_1> <R_1> // center and squared radious of sphere #1.
// <x_2> <y_2> <x_2> <R_2> // center and squared radious of sphere #2.
// : : : :
// <x_n> <y_n> <x_n> <R_n> // center and squared radious of sphere #n.
int n = 0;
std::list<Sphere_3> spheres;
int x = 0, y = 0, z = 0, sqr_r = 0;
int i;
in_file >> n;
for (i = 0; i < n; ++i)
{
in_file >> x >> y >> z >> sqr_r;
spheres.push_back(Sphere_3(Rat_point_3(x, y, z), Rational(sqr_r)));
}
in_file.close();
// Compute the lower envelope.
Envelope_diagram_2 min_diag;
CGAL::Timer timer;
std::cout << "Constructing the lower envelope of "
<< n << " spheres." << std::endl;
timer.start();
CGAL::lower_envelope_3(spheres.begin(), spheres.end(), min_diag);
timer.stop();
// Print the dimensions of the minimization diagram.
std::cout << "V = " << min_diag.number_of_vertices()
<< ", E = " << min_diag.number_of_edges()
<< ", F = " << min_diag.number_of_faces() << std::endl;
std::cout << "Construction took " << timer.time()
<< " seconds." << std::endl;
return 0;
}
#endif