\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13 - 3D Periodic Mesh Generation
Periodic_3_mesh_3/mesh_implicit_shape.cpp
#include <CGAL/Periodic_3_mesh_3/config.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/make_periodic_3_mesh_3.h>
#include <CGAL/optimize_periodic_3_mesh_3.h>
#include <CGAL/Periodic_3_mesh_3/IO/File_medit.h>
#include <CGAL/Periodic_3_mesh_triangulation_3.h>
#include <CGAL/Labeled_mesh_domain_3.h>
#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
#include <CGAL/Mesh_criteria_3.h>
#include <CGAL/number_type_config.h> // CGAL_PI
#include <cmath>
#include <iostream>
#include <fstream>
typedef K::FT FT;
typedef K::Point_3 Point;
typedef K::Iso_cuboid_3 Iso_cuboid;
// Domain
typedef FT (Function)(const Point&);
typedef CGAL::Labeled_mesh_domain_3<K> Periodic_mesh_domain;
// Triangulation
// Criteria
typedef CGAL::Mesh_criteria_3<Tr> Periodic_mesh_criteria;
// To avoid verbose function and named parameters call
using namespace CGAL::parameters;
// Implicit function
FT schwarz_p(const Point& p)
{
const FT x2 = std::cos( p.x() * 2 * CGAL_PI ),
y2 = std::cos( p.y() * 2 * CGAL_PI ),
z2 = std::cos( p.z() * 2 * CGAL_PI );
return x2 + y2 + z2;
}
int main(int argc, char** argv)
{
// 'int' because the 'schwarz_p' function is periodic over the domain only if
// the length of the side of the domain is an integer.
int domain_size = (argc > 1) ? atoi(argv[1]) : 1;
int number_of_copies_in_output = (argc > 2) ? atoi(argv[2]) : 4; // can be 1, 2, 4, or 8
Iso_cuboid canonical_cube(0, 0, 0, domain_size, domain_size, domain_size);
Periodic_mesh_domain domain =
Periodic_mesh_domain::create_implicit_mesh_domain(schwarz_p, canonical_cube);
Periodic_mesh_criteria criteria(facet_angle = 30,
facet_size = 0.05 * domain_size,
facet_distance = 0.025 * domain_size,
cell_radius_edge_ratio = 2.,
cell_size = 0.05);
// Mesh generation
C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria);
std::ofstream medit_file("output_implicit_shape.mesh");
CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
std::cout << "EXIT SUCCESS" << std::endl;
return 0;
}