CGAL 6.1 - 3D Periodic Mesh Generation

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Periodic_3_mesh_3/mesh_implicit_shape_with_features.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/Periodic_3_mesh_3/IO/File_medit.h>
#include <CGAL/Periodic_3_mesh_triangulation_3.h>
#include <CGAL/Periodic_3_function_wrapper.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/Mesh_domain_with_polyline_features_3.h>
#include <algorithm>
#include <cmath>
#include <fstream>
#include <iostream>
#include <list>
#include <vector>
// Kernel
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
// Domain
typedef K::FT FT;
typedef K::Point_3 Point;
typedef K::Iso_cuboid_3 Iso_cuboid;
typedef FT (Function)(const Point&);
typedef CGAL::Periodic_3_function_wrapper<Function, K> Periodic_function;
typedef CGAL::Mesh_domain_with_polyline_features_3<CGAL::Labeled_mesh_domain_3<K> > Periodic_mesh_domain;
// Polyline
typedef std::vector<Point> Polyline_3;
typedef std::list<Polyline_3> Polylines;
// Triangulation
typedef CGAL::Periodic_3_mesh_triangulation_3<Periodic_mesh_domain>::type Tr;
typedef CGAL::Mesh_complex_3_in_triangulation_3<
Tr, Periodic_mesh_domain::Corner_index, Periodic_mesh_domain::Curve_index> 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
static const FT cx = 0.51, cy = 0.51, cz = 0.5;
static const FT scale = 0.9;
FT cone_function(const Point& p)
{
const FT x = p.x(), y = p.y(), z = p.z();
if (((x-cx)*(x-cx) + (y-cy)*(y-cy)) > scale * (z-cz)*(z-cz))
return 1; // outside
else
return -1; // inside
}
// To obtain a good looking mesh at the base of the cone, we protect the base circle
void cone_polylines(Polylines& polylines)
{
const FT z = 0.;
const FT radius_at_z = CGAL::sqrt(scale * cz * cz);
Polyline_3 polyline;
for(int i=0; i<360; ++i)
{
polyline.push_back(Point(cx + radius_at_z * std::sin(i*CGAL_PI/180),
cy + radius_at_z * std::cos(i*CGAL_PI/180),
z));
}
polyline.push_back(polyline.front()); // close the line
polylines.push_back(polyline);
}
int main(int argc, char** argv)
{
int number_of_copies_in_output = (argc > 1) ? atoi(argv[1]) : 8; // can be 1, 2, 4, or 8
// Domain
const int domain_size = 1;
Iso_cuboid canonical_cube(0, 0, 0, domain_size, domain_size, domain_size);
Periodic_mesh_domain domain =
Periodic_mesh_domain::create_implicit_mesh_domain(
Periodic_function(cone_function, canonical_cube), canonical_cube);
// Mesh criteria
Periodic_mesh_criteria criteria(params::edge_size(0.02 * domain_size)
.facet_angle(30)
.facet_size(0.02 * domain_size)
.cell_radius_edge_ratio(2)
.cell_size(0.5 * domain_size));
// Create the features that we want to preserve
Polylines polylines;
cone_polylines(polylines);
// Insert the features in the domain
domain.add_features(polylines.begin(), polylines.end());
// Insert a corner to make sure the apex of the cone is present in the mesh
domain.add_corner(Point(0.51, 0.51, 0.5));
// Mesh generation WITHOUT feature preservation (and no optimizers)
C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria,
params::no_features().
no_exude().
no_perturb());
std::ofstream medit_file("output_implicit_shape_without_protection.mesh");
CGAL::IO::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
// Mesh generation WITH feature preservation (and no optimizers)
C3t3 c3t3_bis = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria,
params::features().
no_exude().
no_perturb());
std::ofstream medit_file_bis("output_implicit_shape_with_protection.mesh");
CGAL::IO::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis, number_of_copies_in_output);
std::cout << "EXIT SUCCESS" << std::endl;
return 0;
}
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Mesh_criteria_3
CGAL::Mesh_domain_with_polyline_features_3
CGAL::Periodic_3_function_wrapper
The class Periodic_3_function_wrapper is a helper class designed to wrap an (a priori non-periodic) i...
Definition: Periodic_3_function_wrapper.h:72
unspecified_type
CGAL::parameters::no_perturb
unspecified_type no_perturb()
CGAL::parameters::no_exude
unspecified_type no_exude()
CGAL::parameters