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

CGAL 4.8 - CGAL and the Boost Graph Library

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BGL_polyhedron_3/kruskal.cpp
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/IO/Polyhedron_iostream.h>
#include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
#include <iostream>
#include <list>
#include <boost/graph/kruskal_min_spanning_tree.hpp>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::Vector_3 Vector;
typedef Kernel::Point_3 Point;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
typedef boost::graph_traits<Polyhedron>::vertex_descriptor vertex_descriptor;
typedef boost::graph_traits<Polyhedron>::vertex_iterator vertex_iterator;
typedef boost::graph_traits<Polyhedron>::edge_descriptor edge_descriptor;
// The BGL makes heavy use of indices associated to the vertices
// We use a std::map to store the index
typedef std::map<vertex_descriptor,int> Vertex_index_map;
Vertex_index_map vertex_index_map;
// A std::map is not a property map, because it is not lightweight
typedef boost::associative_property_map<Vertex_index_map> Vertex_index_pmap;
Vertex_index_pmap vertex_index_pmap(vertex_index_map);
void
kruskal(const Polyhedron& P)
{
// associate indices to the vertices
vertex_iterator vb, ve;
int index = 0;
// boost::tie assigns the first and second element of the std::pair
// returned by boost::vertices to the variables vb and ve
for(boost::tie(vb, ve)=vertices(P); vb!=ve; ++vb){
vertex_index_pmap[*vb]= index++;
}
// We use the default edge weight which is the squared length of the edge
// This property map is defined in graph_traits_Polyhedron_3.h
// In the function call you can see a named parameter: vertex_index_map
std::list<edge_descriptor> mst;
boost::kruskal_minimum_spanning_tree(P,
std::back_inserter(mst),
boost::vertex_index_map(vertex_index_pmap));
std::cout << "#VRML V2.0 utf8\n"
"Shape {\n"
" appearance Appearance {\n"
" material Material { emissiveColor 1 0 0}}\n"
" geometry\n"
" IndexedLineSet {\n"
" coord Coordinate {\n"
" point [ \n";
for(boost::tie(vb, ve) = vertices(P); vb!=ve; ++vb){
std::cout << " " << (*vb)->point() << "\n";
}
std::cout << " ]\n"
" }\n"
" coordIndex [\n";
for(std::list<edge_descriptor>::iterator it = mst.begin(); it != mst.end(); ++it)
{
edge_descriptor e = *it ;
vertex_descriptor s = source(e,P);
vertex_descriptor t = target(e,P);
std::cout << " " << vertex_index_pmap[s] << ", " << vertex_index_pmap[t] << ", -1\n";
}
std::cout << "]\n"
" }#IndexedLineSet\n"
"}# Shape\n";
}
int main() {
Polyhedron P;
Point a(1,0,0);
Point b(0,1,0);
Point c(0,0,1);
Point d(0,0,0);
P.make_tetrahedron(a,b,c,d);
kruskal(P);
return 0;
}