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

CGAL 4.3 - 3D Mesh Generation

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Mesh_3/mesh_implicit_ellipsoid.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_mesh_domain_3.h>
#include <CGAL/make_mesh_3.h>
#include <CGAL/perturb_mesh_3.h>
#include <CGAL/exude_mesh_3.h>
// Domain
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::FT FT;
typedef K::Point_3 Point;
typedef FT (Function)(const Point&);
typedef CGAL::Implicit_mesh_domain_3<Function,K> Mesh_domain;
// Triangulation
typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
// Criteria
typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
typedef Mesh_criteria::Facet_criteria Facet_criteria;
typedef Mesh_criteria::Cell_criteria Cell_criteria;
// Function
FT ellipsoid_function (const Point& p)
{
const FT x2=p.x()*p.x();
const FT y2=p.y()*p.y();
const FT z2=p.z()*p.z();
return x2+2*y2+4*z2-1;
}
// To avoid verbose function and named parameters call
using namespace CGAL::parameters;
int main()
{
// Domain (Warning: Sphere_3 constructor uses square radius !)
Mesh_domain domain(ellipsoid_function, K::Sphere_3(CGAL::ORIGIN, 2.));
// Criteria
Facet_criteria facet_criteria(30, 0.08, 0.025); // angle, size, approximation
Cell_criteria cell_criteria(2, 0.1); // radius-edge ratio, size
Mesh_criteria criteria(facet_criteria, cell_criteria);
// Mesh generation (without optimization)
C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, no_perturb(), no_exude());
// Output
std::ofstream medit_file("out_wo.mesh");
c3t3.output_to_medit(medit_file);
medit_file.close();
// Perturbation (5s, 12degree)
CGAL::perturb_mesh_3(c3t3, domain, time_limit=5, sliver_bound=12);
// Exudation
CGAL::exude_mesh_3(c3t3);
// Output
medit_file.open("out_optimized.mesh");
c3t3.output_to_medit(medit_file);
return 0;
}