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

CGAL 4.8 - 3D Mesh Generation

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Mesh_3/mesh_implicit_domains.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Mesh_triangulation_3.h>
#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
#include <CGAL/Mesh_criteria_3.h>
#include <CGAL/Implicit_to_labeling_function_wrapper.h>
#include <CGAL/Labeled_mesh_domain_3.h>
#include <CGAL/make_mesh_3.h>
#include "implicit_functions.h"
// IO
#include <CGAL/IO/File_medit.h>
using namespace CGAL::parameters;
// Domain
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef FT_to_point_function_wrapper<K::FT, K::Point_3> Function;
typedef CGAL::Implicit_multi_domain_to_labeling_function_wrapper<Function>
Function_wrapper;
typedef Function_wrapper::Function_vector Function_vector;
typedef CGAL::Labeled_mesh_domain_3<Function_wrapper, K> Mesh_domain;
// Triangulation
typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
// Mesh Criteria
typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
typedef Mesh_criteria::Facet_criteria Facet_criteria;
typedef Mesh_criteria::Cell_criteria Cell_criteria;
int main()
{
// Define functions
Function f1(&torus_function);
Function f2(&sphere_function<3>);
Function_vector v;
v.push_back(f1);
v.push_back(f2);
// Domain (Warning: Sphere_3 constructor uses square radius !)
Mesh_domain domain(v, K::Sphere_3(CGAL::ORIGIN, 5.*5.), 1e-6);
// Set mesh criteria
Facet_criteria facet_criteria(30, 0.2, 0.02); // angle, size, approximation
Cell_criteria cell_criteria(2., 0.4); // radius-edge ratio, size
Mesh_criteria criteria(facet_criteria, cell_criteria);
// Mesh generation
C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, no_exude(), no_perturb());
// Perturbation (maximum cpu time: 10s, targeted dihedral angle: default)
CGAL::perturb_mesh_3(c3t3, domain, time_limit = 10);
// Exudation
CGAL::exude_mesh_3(c3t3,12);
// Output
std::ofstream medit_file("out.mesh");
CGAL::output_to_medit(medit_file, c3t3);
return 0;
}