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

CGAL 4.8 - CGAL and the Boost Graph Library

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BGL_triangulation_2/emst.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>
#include <boost/graph/kruskal_min_spanning_tree.hpp>
#include <boost/graph/filtered_graph.hpp>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_2 Point;
typedef CGAL::Delaunay_triangulation_2<K> Triangulation;
// As we only consider finite vertices and edges
// we need the following filter
template <typename T>
struct Is_finite {
const T* t_;
Is_finite()
: t_(NULL)
{}
Is_finite(const T& t)
: t_(&t)
{ }
template <typename VertexOrEdge>
bool operator()(const VertexOrEdge& voe) const {
return ! t_->is_infinite(voe);
}
};
typedef Is_finite<Triangulation> Filter;
typedef boost::filtered_graph<Triangulation,Filter,Filter> Finite_triangulation;
typedef boost::graph_traits<Finite_triangulation>::vertex_descriptor vertex_descriptor;
typedef boost::graph_traits<Finite_triangulation>::vertex_iterator vertex_iterator;
typedef boost::graph_traits<Finite_triangulation>::edge_descriptor edge_descriptor;
// The BGL makes use of indices associated to the vertices
// We use a std::map to store the index
typedef std::map<vertex_descriptor,int> VertexIndexMap;
VertexIndexMap vertex_id_map;
// A std::map is not a property map, because it is not lightweight
typedef boost::associative_property_map<VertexIndexMap> VertexIdPropertyMap;
VertexIdPropertyMap vertex_index_pmap(vertex_id_map);
int
main(int,char*[])
{
Triangulation t;
Filter is_finite(t);
Finite_triangulation ft(t, is_finite, is_finite);
Point p ;
while(std::cin >> p){
t.insert(p);
}
vertex_iterator vit, ve;
// Associate indices to the vertices
int index = 0;
// boost::tie assigns the first and second element of the std::pair
// returned by boost::vertices to the variables vit and ve
for(boost::tie(vit,ve)=boost::vertices(ft); vit!=ve; ++vit ){
vertex_descriptor vd = *vit;
vertex_id_map[vd]= index++;
}
// We use the default edge weight which is the squared length of the edge
// This property map is defined in graph_traits_Triangulation_2.h
// In the function call you can see a named parameter: vertex_index_map
std::list<edge_descriptor> mst;
boost::kruskal_minimum_spanning_tree(ft,
std::back_inserter(mst),
vertex_index_map(vertex_index_pmap));
std::cout << "The edges of the Euclidean mimimum spanning tree:" << std::endl;
for(std::list<edge_descriptor>::iterator it = mst.begin(); it != mst.end(); ++it){
edge_descriptor ed = *it;
vertex_descriptor svd = source(ed,t);
vertex_descriptor tvd = target(ed,t);
Triangulation::Vertex_handle sv = svd;
Triangulation::Vertex_handle tv = tvd;
std::cout << "[ " << sv->point() << " | " << tv->point() << " ] " << std::endl;
}
return 0;
}