CGAL 6.1 - 3D Isosurfacing

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Isosurfacing_3/marching_cubes.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/Isosurfacing_3/Cartesian_grid_3.h>
#include <CGAL/Isosurfacing_3/Value_function_3.h>
#include <CGAL/Isosurfacing_3/marching_cubes_3.h>
#include <CGAL/Isosurfacing_3/Marching_cubes_domain_3.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/IO/polygon_mesh_io.h>
#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>
#include <CGAL/Polygon_mesh_processing/remesh.h>
#include <cmath>
#include <iostream>
#include <vector>
using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using FT = typename Kernel::FT;
using Point = typename Kernel::Point_3;
using Vector = typename Kernel::Vector_3;
using Grid = CGAL::Isosurfacing::Cartesian_grid_3<Kernel>;
using Values = CGAL::Isosurfacing::Value_function_3<Grid>;
using Domain = CGAL::Isosurfacing::Marching_cubes_domain_3<Grid, Values>;
using Point_range = std::vector<Point>;
using Polygon_range = std::vector<std::vector<std::size_t> >;
using Mesh = CGAL::Surface_mesh<Point>;
auto value_fn = [](const Point& p) -> FT
{
const FT& x = p.x(), y = p.y(), z = p.z();
// "Klein Bottle" - https://www-sop.inria.fr/galaad/surface/
return -1-4*y*z*z*x*x-2*y+6*z*z*x*x*y*y-16*x*z+16*x*z*y*y+3*x*x+7*y*y+11*z*z-11*z*z*z*z+z*z*z*z*z*z-3*x*x*x*x-7*y*y*y*y+x*x*x*x*x*x+y*y*y*y*y*y-14*z*z*x*x-18*z*z*y*y+3*z*z*z*z*x*x+3*z*z*z*z*y*y-10*x*x*y*y-4*y*y*y*z*z+3*z*z*x*x*x*x+3*z*z*y*y*y*y+16*x*x*x*z+3*x*x*x*x*y*y+3*x*x*y*y*y*y+4*x*x*y-12*z*z*y-2*x*x*x*x*y-4*x*x*y*y*y-2*z*z*z*z*y+16*x*z*z*z+12*y*y*y-2*y*y*y*y*y-32*x*z*y;
};
int main(int argc, char** argv)
{
const FT isovalue = (argc > 1) ? std::stod(argv[1]) : 0.1;
const FT box_c = (argc > 2) ? std::abs(std::stod(argv[2])) : 5.;
const std::size_t grid_n = (argc > 3) ? std::stoi(argv[3]) : 50;
// create bounding box and grid
const CGAL::Bbox_3 bbox { -box_c, -box_c, -box_c, box_c, box_c, box_c };
Grid grid { bbox, CGAL::make_array<std::size_t>(grid_n, grid_n, grid_n) };
std::cout << "Span: " << grid.span() << std::endl;
std::cout << "Cell dimensions: " << grid.spacing()[0] << " " << grid.spacing()[1] << " " << grid.spacing()[2] << std::endl;
std::cout << "Cell #: " << grid.xdim() << ", " << grid.ydim() << ", " << grid.zdim() << std::endl;
// fill up values
Values values { value_fn, grid };
// Below is equivalent to:
// Domain domain { grid, values };
Domain domain = CGAL::Isosurfacing::create_marching_cubes_domain_3(grid, values);
Point_range points;
Polygon_range triangles;
// run marching cubes isosurfacing
std::cout << "Running Marching Cubes with isovalue = " << isovalue << std::endl;
CGAL::Isosurfacing::marching_cubes<CGAL::Parallel_if_available_tag>(domain, isovalue, points, triangles,
CGAL::parameters::use_topologically_correct_marching_cubes(true));
std::cout << "Soup #vertices: " << points.size() << std::endl;
std::cout << "Soup #triangles: " << triangles.size() << std::endl;
if(!CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh(triangles)) {
std::cerr << "Warning: the soup is not a 2-manifold surface, non-manifoldness?..." << std::endl;
return EXIT_FAILURE;
}
std::cout << "Convert the soup to a triangle mesh..." << std::endl;
Mesh mesh;
CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh(points, triangles, mesh);
CGAL::IO::write_polygon_mesh("marching_cubes.off", mesh, CGAL::parameters::stream_precision(17));
// Let's remesh it to something nicer looking
std::cout << "Remeshing..." << std::endl;
const FT target_edge_length = box_c / 50;
CGAL::Polygon_mesh_processing::isotropic_remeshing(faces(mesh), target_edge_length, mesh,
CGAL::parameters::number_of_iterations(5)
.number_of_relaxation_steps(5));
CGAL::IO::write_polygon_mesh("marching_cubes-remeshed.off", mesh, CGAL::parameters::stream_precision(17));
std::cout << "Done" << std::endl;
return EXIT_SUCCESS;
}
CGAL::Bbox_3
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Isosurfacing::Cartesian_grid_3
The class Cartesian_grid_3 represents a 3D Cartesian grid, that is the partition of an iso-cuboid int...
Definition: Cartesian_grid_3.h:148
CGAL::Isosurfacing::Marching_cubes_domain_3
A domain that can be used with the Marching Cubes algorithm.
Definition: Marching_cubes_domain_3.h:50
CGAL::Isosurfacing::Value_function_3
The class Value_function_3 represents a field of scalars computed using a user-provided unary functio...
Definition: Value_function_3.h:40
Kernel::Point_3
Kernel::Vector_3
CGAL::Isosurfacing::create_marching_cubes_domain_3
Marching_cubes_domain_3< Partition, ValueField, EdgeIntersectionOracle > create_marching_cubes_domain_3(const Partition &partition, const ValueField &values, const EdgeIntersectionOracle &intersection_oracle=EdgeIntersectionOracle())
creates a new instance of a domain that can be used with the Marching Cubes algorithm.
Definition: Marching_cubes_domain_3.h:92
CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh
void polygon_soup_to_polygon_mesh(const PointRange &points, const PolygonRange &polygons, PolygonMesh &out, const NamedParameters_PS &np_ps=parameters::default_values(), const NamedParameters_PM &np_pm=parameters::default_values())
CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh
bool is_polygon_soup_a_polygon_mesh(const PolygonRange &polygons)
CGAL::Polygon_mesh_processing::isotropic_remeshing
void isotropic_remeshing(const FaceRange &faces, SizingFunction &sizing, PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
CGAL::IO::write_polygon_mesh
bool write_polygon_mesh(const std::string &fname, Graph &g, const NamedParameters &np=parameters::default_values())
CGAL::Polygon_mesh_processing::bbox
CGAL::Bbox_3 bbox(const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
Kernel