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

CGAL 4.8 - 3D Alpha Shapes

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Alpha_shapes_3/ex_fixed_weighted_alpha_shapes_3.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_3.h>
#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
#include <CGAL/Fixed_alpha_shape_3.h>
#include <CGAL/Fixed_alpha_shape_vertex_base_3.h>
#include <CGAL/Fixed_alpha_shape_cell_base_3.h>
#include <list>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_euclidean_traits_3<K> Gt;
typedef CGAL::Fixed_alpha_shape_vertex_base_3<Gt> Vb;
typedef CGAL::Fixed_alpha_shape_cell_base_3<Gt> Fb;
typedef CGAL::Triangulation_data_structure_3<Vb,Fb> Tds;
typedef CGAL::Regular_triangulation_3<Gt,Tds> Triangulation_3;
typedef CGAL::Fixed_alpha_shape_3<Triangulation_3> Fixed_alpha_shape_3;
typedef Fixed_alpha_shape_3::Cell_handle Cell_handle;
typedef Fixed_alpha_shape_3::Vertex_handle Vertex_handle;
typedef Fixed_alpha_shape_3::Facet Facet;
typedef Fixed_alpha_shape_3::Edge Edge;
typedef Gt::Weighted_point Weighted_point;
typedef Gt::Bare_point Bare_point;
int main()
{
std::list<Weighted_point> lwp;
//input : a small molecule
lwp.push_back(Weighted_point(Bare_point( 1, -1, -1), 4));
lwp.push_back(Weighted_point(Bare_point(-1, 1, -1), 4));
lwp.push_back(Weighted_point(Bare_point(-1, -1, 1), 4));
lwp.push_back(Weighted_point(Bare_point( 1, 1, 1), 4));
lwp.push_back(Weighted_point(Bare_point( 2, 2, 2), 1));
//build one alpha_shape with alpha=0
Fixed_alpha_shape_3 as(lwp.begin(), lwp.end(), 0);
//explore the 0-shape - It is dual to the boundary of the union.
std::list<Cell_handle> cells;
std::list<Facet> facets;
std::list<Edge> edges;
as.get_alpha_shape_cells(std::back_inserter(cells),
Fixed_alpha_shape_3::INTERIOR);
as.get_alpha_shape_facets(std::back_inserter(facets),
Fixed_alpha_shape_3::REGULAR);
as.get_alpha_shape_facets(std::back_inserter(facets),
Fixed_alpha_shape_3::SINGULAR);
as.get_alpha_shape_edges(std::back_inserter(edges),
Fixed_alpha_shape_3::SINGULAR);
std::cout << " The 0-shape has : " << std::endl;
std::cout << cells.size() << " interior tetrahedra" << std::endl;
std::cout << facets.size() << " boundary facets" << std::endl;
std::cout << edges.size() << " singular edges" << std::endl;
return 0;
}