CGAL::Subdivision_method_3

Definition

A subdivision method recursively refines a coarse mesh and generates an ever closer approximation to a smooth surface. Subdivision_method_3 consists of four subdivision methods and their refinement hosts. Each refinement host is a template function of a polyhedron class and a geometry policy class. It refines the connectivity of the control mesh and computes the geometry of the refined mesh. The geometry computation is dedicated to the custom geometry policy. A geometry policy consists of functions that compute the new point based on the subdivision stencil. A stencil defines the footprint (a submesh of the control mesh) of a new point.

The four supported refinement hosts are the primal quadrilateral quadrisection (PQQ), the primal triangle quadrisection (PTQ), the dual quadrilateral quadrisection (DQQ), and the $$sqrt(3) triangulation. These refinements are respectively used in Catmull-Clark, Loop, Doo-Sabin and $$sqrt(3) subdivision.

#include <CGAL/Subdivision_method_3.h>

Refinement Host

template <class Polyhedron_3, template <typename> class Mask>
void	PQQ ( Polyhedron_3& p, Mask<Polyhedron_3> mask, int step = 1)
		applies the PQQ refinement on the control mesh p step times. The geometry of the refined mesh is computed by the geometry policy mask. This function overwrites the control mesh p with the refined mesh.
template <class Polyhedron_3, template <typename> class Mask>
void	PTQ ( Polyhedron_3& p, Mask<Polyhedron_3> mask, int step = 1)
		applies the PTQ refinement on the control mesh p step times, where p contains only triangle facets. The geometry of the refined mesh is computed by the geometry policy mask. This function overwrites the control mesh p with the refined mesh. The result of a non-triangle mesh p is undefined.
template <class Polyhedron_3, template <typename> class Mask>
void	DQQ ( Polyhedron_3& p, Mask<Polyhedron_3> mask, int step = 1)
		applies the DQQ refinement on the control mesh p step times. The geometry of the refined mesh is computed by the geometry policy mask. This function overwrites the control mesh p with the refined mesh.
template <class Polyhedron_3, template <typename> class Mask>
void	Sqrt3 ( Polyhedron_3& p, Mask<Polyhedron_3> mask, int step = 1)
		applies the $$sqrt(3) triangulation on the control mesh p step times, where p contains only triangle facets. The geometry of the refined mesh is computed by the geometry policy mask. This function overwrites the control mesh p with the refined mesh. The result of a non-triangle mesh p is undefined.

Subdivision Method

template <class Polyhedron_3>
void	CatmullClark_subdivision ( Polyhedron_3& p, int step = 1)
		applies Catmull-Clark subdivision step times on the control mesh p. This function overwrites the control mesh p with the subdivided mesh.
template <class Polyhedron_3>
void	Loop_subdivision ( Polyhedron_3& p, int step = 1)
		applies Loop subdivision step times on the control mesh p. This function overwrites the control mesh p with the subdivided mesh.
template <class Polyhedron_3>
void	DooSabin_subdivision ( Polyhedron_3& p, int step = 1)
		applies Doo-Sabin subdivision step times on the control mesh p. This function overwrites the control mesh p with the subdivided mesh.
template <class Polyhedron_3>
void	Sqrt3_subdivision ( Polyhedron_3& p, int step = 1)
		applies $$sqrt(3) subdivision step times on the control mesh p. This function overwrites the control mesh p with the subdivided mesh.

See Also

CGAL::CatmullClark_mask_3<Polyhedron_3>
CGAL::Loop_mask_3<Polyhedron_3>
CGAL::Sqrt3_mask_3<Polyhedron_3>

Example

This example program subdivides a polyhedral mesh with Catmull-Clark subdivision.

// file: examples/Subdivision_method_3/CatmullClark_subdivision.C

#include <CGAL/Cartesian.h>
#include <CGAL/Subdivision_method_3.h>
#include <iostream>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/IO/Polyhedron_iostream.h>

typedef CGAL::Cartesian<double>            Kernel;
typedef CGAL::Polyhedron_3<Kernel>         Polyhedron;

using namespace std;
using namespace CGAL;

int main(int argc, char** argv) {
  if (argc != 2) { 
    cout << "Usage: CatmullClark_subdivision d < filename" << endl; 
    cout << "       d: the depth of the subdivision (0 < d < 10)" << endl; 
    cout << "       filename: the input mesh (.off)" << endl; 
    return 0;
  }

  int d = argv[1][0] - '0';

  Polyhedron P;
  cin >> P; // read the .off

  Subdivision_method_3::CatmullClark_subdivision(P,d);

  cout << P; // write the .off
  
  return 0;
}