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

CGAL 4.8 - 3D Mesh Generation

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Mesh_3/mesh_two_implicit_spheres_with_balls.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/Mesh_domain_with_polyline_features_3.h>
#include <CGAL/make_mesh_3.h>
// Kernel
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
// Domain
typedef K::FT FT;
typedef K::Point_3 Point;
typedef FT (Function)(const Point&);
typedef CGAL::Mesh_domain_with_polyline_features_3<
CGAL::Implicit_mesh_domain_3<Function,K> > Mesh_domain;
// Polyline
typedef std::vector<Point> Polyline_3;
typedef std::list<Polyline_3> Polylines;
// Triangulation
#ifdef CGAL_CONCURRENT_MESH_3
typedef CGAL::Mesh_triangulation_3<
Mesh_domain,
CGAL::Kernel_traits<Mesh_domain>::Kernel, // Same as sequential
CGAL::Parallel_tag // Tag to activate parallelism
>::type Tr;
#else
typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
#endif
typedef CGAL::Mesh_complex_3_in_triangulation_3<
Tr,Mesh_domain::Corner_index,Mesh_domain::Curve_segment_index> C3t3;
// Criteria
typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
// To avoid verbose function and named parameters call
using namespace CGAL::parameters;
// Function
FT sphere_function1 (const Point& p)
{ return CGAL::squared_distance(p, Point(CGAL::ORIGIN))-2; }
FT sphere_function2 (const Point& p)
{ return CGAL::squared_distance(p, Point(2, 0, 0))-2; }
FT sphere_function (const Point& p)
{
if(sphere_function1(p) < 0 || sphere_function2(p) < 0)
return -1;
else
return 1;
}
#include <cmath>
int main()
{
// Domain (Warning: Sphere_3 constructor uses squared radius !)
Mesh_domain domain(sphere_function,
K::Sphere_3(Point(1, 0, 0), 6.));
// Mesh criteria
Mesh_criteria criteria(edge_size = 0.15,
facet_angle = 25, facet_size = 0.15,
cell_radius_edge_ratio = 2, cell_size = 0.15);
// Create edge that we want to preserve
Polylines polylines (1);
Polyline_3& polyline = polylines.front();
for(int i = 0; i < 360; ++i)
{
Point p (1, std::cos(i*CGAL_PI/180), std::sin(i*CGAL_PI/180));
polyline.push_back(p);
}
polyline.push_back(polyline.front()); // close the line
// Insert edge in domain
domain.add_features(polylines.begin(), polylines.end());
// Mesh generation without feature preservation
C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
CGAL::parameters::no_features());
std::ofstream medit_file("out-no-protection.mesh");
c3t3.output_to_medit(medit_file);
medit_file.close();
c3t3.clear();
// Mesh generation with feature preservation
c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);
// Output
medit_file.open("out-with-protection.mesh");
c3t3.output_to_medit(medit_file);
medit_file.close();
return 0;
}