CGAL 6.1.2 - 3D Isosurfacing

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Isosurfacing_3/contouring_implicit_data.cpp
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Isosurfacing_3/Cartesian_grid_3.h>
#include <CGAL/Isosurfacing_3/dual_contouring_3.h>
#include <CGAL/Isosurfacing_3/Dual_contouring_domain_3.h>
#include <CGAL/Isosurfacing_3/Value_function_3.h>
#include <CGAL/Isosurfacing_3/Gradient_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/Real_timer.h>
#include <CGAL/IO/polygon_soup_io.h>
#include <array>
#include <vector>
using Kernel = CGAL::Simple_cartesian<double>;
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, CGAL::Isosurfacing::Do_not_cache_vertex_locations>;
using Grid = CGAL::Isosurfacing::Cartesian_grid_3<Kernel, CGAL::Isosurfacing::Cache_vertex_locations>;
using Values = CGAL::Isosurfacing::Value_function_3<Grid>;
using Gradients = CGAL::Isosurfacing::Gradient_function_3<Grid>;
using Point_range = std::vector<Point>;
using Polygon_range = std::vector<std::vector<std::size_t> >;
// ---
const FT alpha = 5.01;
auto iwp_value = [](const Point& point)
{
const FT x = alpha * (point.x() + FT(1.0)) * CGAL_PI;
const FT y = alpha * (point.y() + FT(1.0)) * CGAL_PI;
const FT z = alpha * (point.z() + FT(1.0)) * CGAL_PI;
return cos(x)*cos(y) + cos(y)*cos(z) + cos(z)*cos(x) - cos(x)*cos(y)*cos(z); // isovalue = 0
};
auto iwp_gradient = [](const Point& point)
{
const FT x = alpha * (point.x() + FT(1.0)) * CGAL_PI;
const FT y = alpha * (point.y() + FT(1.0)) * CGAL_PI;
const FT z = alpha * (point.z() + FT(1.0)) * CGAL_PI;
const FT gx = CGAL_PI * alpha * sin(x) * (cos(y) * (cos(z) - FT(1.0)) - cos(z));
const FT gy = CGAL_PI * alpha * sin(y) * (cos(x) * (cos(z) - FT(1.0)) - cos(z));
const FT gz = CGAL_PI * alpha * sin(z) * (cos(x) * (cos(y) - FT(1.0)) - cos(y));
return Vector(gx, gy, gz);
};
void run_marching_cubes(const Grid& grid,
const FT isovalue)
{
using Domain = CGAL::Isosurfacing::Marching_cubes_domain_3<Grid, Values>;
std::cout << "\n ---- " << std::endl;
std::cout << "Running Marching Cubes with isovalue = " << isovalue << std::endl;
CGAL::Real_timer timer;
timer.start();
// fill up values
Values values { iwp_value, grid };
Domain domain { grid, values };
// output containers
Point_range points;
Polygon_range triangles;
// run Marching Cubes
CGAL::Isosurfacing::marching_cubes<CGAL::Parallel_if_available_tag>(domain, isovalue, points, triangles);
timer.stop();
std::cout << "Output #vertices (MC): " << points.size() << std::endl;
std::cout << "Output #triangles (MC): " << triangles.size() << std::endl;
std::cout << "Elapsed time: " << timer.time() << " seconds" << std::endl;
CGAL::IO::write_polygon_soup("marching_cubes_implicit.off", points, triangles);
}
void run_dual_contouring(const Grid& grid,
const FT isovalue)
{
using Domain = CGAL::Isosurfacing::Dual_contouring_domain_3<Grid, Values, Gradients>;
std::cout << "\n ---- " << std::endl;
std::cout << "Running Dual Contouring with isovalue = " << isovalue << std::endl;
CGAL::Real_timer timer;
timer.start();
// fill up values and gradients
Values values { iwp_value, grid };
Gradients gradients { iwp_gradient, grid };
Domain domain { grid, values, gradients };
// output containers
Point_range points;
Polygon_range triangles;
// run Dual Contouring
CGAL::Isosurfacing::dual_contouring<CGAL::Parallel_if_available_tag>(domain, isovalue, points, triangles,
CGAL::parameters::do_not_triangulate_faces(true));
timer.stop();
std::cout << "Output #vertices (DC): " << points.size() << std::endl;
std::cout << "Output #triangles (DC): " << triangles.size() << std::endl;
std::cout << "Elapsed time: " << timer.time() << " seconds" << std::endl;
CGAL::IO::write_polygon_soup("dual_contouring_implicit.off", points, triangles);
}
int main(int argc, char** argv)
{
const FT isovalue = (argc > 1) ? std::stod(argv[1]) : 0.;
const CGAL::Bbox_3 bbox{-1, -1, -1, 1, 1, 1};
const FT step = 0.02;
const Vector spacing { step, step, step };
Grid grid { bbox, spacing };
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;
run_marching_cubes(grid, isovalue);
run_dual_contouring(grid, isovalue);
std::cout << "Done" << std::endl;
return EXIT_SUCCESS;
}
CGAL::Bbox_3
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::Dual_contouring_domain_3
A domain that can be used as input in the Dual Contouring algorithm.
Definition: Dual_contouring_domain_3.h:52
CGAL::Isosurfacing::Gradient_function_3
The class Gradient_function_3 represents a field of vectors computed using a user-provided unary func...
Definition: Gradient_function_3.h:39
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::IO::write_polygon_soup
bool write_polygon_soup(const std::string &fname, const PointRange &points, const PolygonRange &polygons, 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
CGAL::Simple_cartesian