Do constrained refinement with CGAL isotropic_remeshing

Question

I'd like to do refinement of eg a simple cube (from a .off); there are a few ways but the ones suitable for what I want to do next end up with 'wrinkles', ie the object shape gets distorted.

This way below promises to allow the boundaries (shape?) of the object to be preserved, permitting what you'd expect of refinement, to just add more edges and vertices:

http://doc.cgal.org/latest/Polygon_mesh_processing/Polygon_mesh_processing_2isotropic_remeshing_example_8cpp-example.html

I want an edge constraint map (and if that isn't sufficient then I'll want a vertex constraint map as well) but can't figure out the template abstractions well enough. I tried an OpenMesh Constrained_edge_map from a different CGAL example, but that's too different and won't compile. What I'm asking for is an edge map and maybe a vertex map that I can feed to the call:

PMP::isotropic_remeshing( faces(mesh), target_edge_length, mesh, PMP::parameters::number_of_iterations(nb_iter) .protect_constraints(true)//i.e. protect border, here );

I'm using CGAL 4.8.1, the latest at time of writing. Thanks.

Answer 1

Here is a minimal example to remesh a triangulated cube:

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/boost/graph/graph_traits_Surface_mesh.h>
#include <CGAL/Polygon_mesh_processing/remesh.h>
#include <CGAL/Mesh_3/dihedral_angle_3.h>
#include <boost/foreach.hpp>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Surface_mesh<K::Point_3>               Mesh;
typedef boost::graph_traits<Mesh>::halfedge_descriptor halfedge_descriptor;
typedef boost::graph_traits<Mesh>::edge_descriptor edge_descriptor;

namespace PMP=CGAL::Polygon_mesh_processing;

int main(int, char* argv[])
{
  std::ifstream input(argv[1]);
  Mesh tmesh;
  input >> tmesh;

  double target_edge_length = 0.20;
  unsigned int nb_iter = 10;

  // give each vertex a name, the default is empty
  Mesh::Property_map<edge_descriptor,bool> is_constrained =
    tmesh.add_property_map<edge_descriptor,bool>("e:is_constrained",false).first;

  //detect sharp features
  BOOST_FOREACH(edge_descriptor e, edges(tmesh))
  {
    halfedge_descriptor hd = halfedge(e,tmesh);
    if ( !is_border(e,tmesh) ){
      double angle = CGAL::Mesh_3::dihedral_angle(tmesh.point(source(hd,tmesh)),
                                                  tmesh.point(target(hd,tmesh)),
                                                  tmesh.point(target(next(hd,tmesh),tmesh)),
                                                  tmesh.point(target(next(opposite(hd,tmesh),tmesh),tmesh)));
      if ( CGAL::abs(angle)<100 )
        is_constrained[e]=true;
    }
  }

  //remesh
  PMP::isotropic_remeshing(
      faces(tmesh),
      target_edge_length,
      tmesh,
      PMP::parameters::number_of_iterations(nb_iter)
      .edge_is_constrained_map(is_constrained) );

  std::ofstream out("out.off");
  out << tmesh;
  return 0;
}