CGAL: Identify convex hull facets when iterating over finite facets

Question

I would like to know if there is any method to identify the facets that are in the convex hull while iterating over finite facets of a Delaunay 3D triangulation

Answer 1

Here is some example code to do identify faces on the convex hull from all the finite faces. Each facet it is a cell-vertex pair and the mirror_facet function provides the other cell-vertex pair that identifies the same facet. Then you can check if either cell (or either vertices) is infinite to decide if the facet is on the convex hull.

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_3.h>

#include <fstream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;

typedef CGAL::Delaunay_triangulation_3<K>  Triangulation;
typedef Triangulation::Point               Point;

int main( )
{
  // read some points from a file
  std::ifstream in("data/threed.cin");
  std::istream_iterator<Point> begin(in);
  std::istream_iterator<Point> end;

  // form the Delaunay triangulation of the points
  Triangulation T;
  T.insert(begin, end);

  // check each finite face to identify those on the convex hull    
  for (auto facet: T.finite_facets())
  {
    if (T.is_infinite(facet.first) ||
        T.is_infinite(T.mirror_facet(facet).first))
    {
      // this facet is on the convex hull
    }
    else
    {
      // this facet is not on the convex hull
    }
  }

  return 0;
}