CGAL 6.1.1 - 3D Periodic Mesh Generation

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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 CGAL::Exact_predicates_inexact_constructions_kernel K;
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
typedef CGAL::Periodic_3_mesh_triangulation_3<Periodic_mesh_domain>::type Tr;
typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
// Criteria
typedef CGAL::Mesh_criteria_3<Tr> Periodic_mesh_criteria;
// To avoid verbose function and named parameters call
namespace params = 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)
{
// 'atoi' because the 'schwarz_p' function is periodic over the domain
// only if the length of the side of the domain is an integer.
const int x_span = (argc > 1) ? atoi(argv[1]) : 1;
const int y_span = (argc > 2) ? atoi(argv[2]) : x_span;
const int z_span = (argc > 3) ? atoi(argv[3]) : x_span;
const int min_span = (std::min)({x_span, y_span, z_span});
const int number_of_copies_in_output = (argc > 4) ? atoi(argv[4]) : 4; // can be 1, 2, 4, or 8
const Iso_cuboid canonical_cube(0, 0, 0, x_span, y_span, z_span);
const Periodic_mesh_domain domain =
Periodic_mesh_domain::create_implicit_mesh_domain(schwarz_p, canonical_cube);
Periodic_mesh_criteria criteria(params::facet_angle(30)
.facet_size(0.035 * min_span)
.facet_distance(0.025 * min_span)
.cell_radius_edge_ratio(2.)
.cell_size(0.05 * min_span));
// Mesh generation
C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria);
std::cout << "Created mesh with " << c3t3.number_of_vertices_in_complex() << " vertices"
<< " and " << c3t3.number_of_cells_in_complex() << " cells" << std::endl;
std::ofstream medit_file("output_implicit_shape.mesh");
CGAL::IO::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
std::cout << "EXIT SUCCESS" << std::endl;
return 0;
}
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Labeled_mesh_domain_3
CGAL::Mesh_criteria_3
unspecified_type
CGAL::parameters