CGAL 6.1 - 3D Surface Subdivision Methods

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Functions
Subdivision Methods
Reference Manual

##

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 polygon mesh 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 \( \sqrt{3}\) subdivisions.

Refinement Host

A refinement host is a template function of a polygon mesh class and a geometry mask class. It refines the input polygon mesh, and computes new points through the geometry masks. `Subdivision_method_3` supports four refinement hosts: `PQQ`, `PTQ`, `DQQ` and `Sqrt3`.

Example

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

File Subdivision_method_3/CatmullClark_subdivision.cpp

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/boost/graph/graph_traits_Surface_mesh.h>
#include <CGAL/subdivision_method_3.h>
#include <CGAL/Timer.h>
#include <boost/lexical_cast.hpp>
#include <iostream>
#include <fstream>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef CGAL::Surface_mesh<Kernel::Point_3> PolygonMesh;
using namespace std;
using namespace CGAL;
namespace params = CGAL::parameters;
int main(int argc, char** argv) {
if (argc > 4) {
cerr << "Usage: CatmullClark_subdivision [d] [filename_in] [filename_out] \n";
cerr << " d -- the depth of the subdivision (default: 1) \n";
cerr << " filename_in -- the input mesh (.off) (default: data/quint_tris.off) \n";
cerr << " filename_out -- the output mesh (.off) (default: result.off)" << endl;
return 1;
}
int d = (argc > 1) ? boost::lexical_cast<int>(argv[1]) : 1;
const std::string in_file = (argc > 2) ? argv[2] : CGAL::data_file_path("meshes/quint_tris.off");
const char* out_file = (argc > 3) ? argv[3] : "result.off";
PolygonMesh pmesh;
std::ifstream in(in_file);
if(in.fail()) {
std::cerr << "Could not open input file " << in_file << std::endl;
return 1;
}
in >> pmesh;
Timer t;
t.start();
Subdivision_method_3::CatmullClark_subdivision(pmesh, params::number_of_iterations(d));
std::cerr << "Done (" << t.time() << " s)" << std::endl;
std::ofstream out(out_file);
out << pmesh;
return 0;
}
CGAL::Surface_mesh
CGAL::Subdivision_method_3::CatmullClark_subdivision
void CatmullClark_subdivision(PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
applies Catmull-Clark subdivision several times on the control mesh pmesh.
Definition: subdivision_methods_3.h:132
CGAL
CGAL::parameters
Kernel
std
STL namespace.
CGAL::Simple_cartesian
subdivision_method_3.h
Convenience header file including the headers for all the free functions of this package.

See also
  `CGAL::CatmullClark_mask_3<PolygonMesh>`
  `CGAL::DooSabin_mask_3<PolygonMesh`
  `CGAL::Loop_mask_3<PolygonMesh`
  `CGAL::Sqrt3_mask_3<PolygonMesh>`
  `CGAL::Linear_mask_3<PolygonMesh>`

## Functions
template<class PolygonMesh , class Mask , class NamedParameters >
void | CGAL::Subdivision_method_3::PQQ (PolygonMesh &pmesh, Mask mask, const NamedParameters &np)
| applies the PQQ refinement several times on the control mesh `pmesh`.
template<class PolygonMesh , class Mask , class NamedParameters >
void | CGAL::Subdivision_method_3::PTQ (PolygonMesh &pmesh, Mask mask, const NamedParameters &np)
| applies the PTQ refinement several times on the control mesh `pmesh`.
template<class PolygonMesh , class Mask , class NamedParameters >
void | CGAL::Subdivision_method_3::DQQ (PolygonMesh &pmesh, Mask mask, const NamedParameters &np)
| applies the DQQ refinement several times on the control mesh `pmesh`.
template<class PolygonMesh , class Mask , class NamedParameters >
void | CGAL::Subdivision_method_3::Sqrt3 (PolygonMesh &pmesh, Mask mask, const NamedParameters &np)
| applies the \( \sqrt{3}\) refinement several times on the control mesh `pmesh`.
template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Subdivision_method_3::CatmullClark_subdivision (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
| applies Catmull-Clark subdivision several times on the control mesh `pmesh`.
template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Subdivision_method_3::Loop_subdivision (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
| applies Loop subdivision several times on the control mesh `pmesh`.
template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Subdivision_method_3::DooSabin_subdivision (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
| applies DooSabin subdivision several times on the control mesh `pmesh`.
template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>
void | CGAL::Subdivision_method_3::Sqrt3_subdivision (PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
| applies \( \sqrt{3}\)-subdivision several times on the control mesh `pmesh`.

## Function Documentation

## ◆ CatmullClark_subdivision()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Subdivision_method_3::CatmullClark_subdivision | ( | PolygonMesh & | pmesh,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>`

applies Catmull-Clark subdivision several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy mask `CatmullClark_mask_3`. This function overwrites the control mesh `pmesh` with the subdivided mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |
  if set to `true`, the geometry of the mesh will not be modified Type: Boolean Default: `false` Extra: If `pmesh` is in fact a triangle mesh, this named parameter is also available in Loop subdivision and will create better shaped elements. |

Examples
  Subdivision_method_3/Linear_subdivision.cpp.

## ◆ DooSabin_subdivision()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Subdivision_method_3::DooSabin_subdivision | ( | PolygonMesh & | pmesh,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>`

applies DooSabin subdivision several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy mask `DooSabin_mask_3`. This function overwrites the control mesh `pmesh` with the subdivided mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

## ◆ DQQ()

template<class PolygonMesh , class Mask , class NamedParameters >

void CGAL::Subdivision_method_3::DQQ | ( | PolygonMesh & | pmesh,
|  | Mask | mask,
|  | const NamedParameters & | np
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>`

applies the DQQ refinement several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy `mask`. This function overwrites the control mesh `pmesh` with the refined mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  Mask | a model of `DQQMask_3`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  mask | a geometry policy mask
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

Precondition
  `pmesh` must be a triangle mesh.

## ◆ Loop_subdivision()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Subdivision_method_3::Loop_subdivision | ( | PolygonMesh & | pmesh,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>`

applies Loop subdivision several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy mask `Loop_mask_3`. This function overwrites the control mesh `pmesh` with the subdivided mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |
  if set to `true`, the geometry of the mesh will not be modified Type: Boolean Default: `false` Extra: This named parameter is also available in Catmull-Clark subdivision for non-triangle meshes. |

Precondition
  `pmesh` must be a triangle mesh.

## ◆ PQQ()

template<class PolygonMesh , class Mask , class NamedParameters >

void CGAL::Subdivision_method_3::PQQ | ( | PolygonMesh & | pmesh,
|  | Mask | mask,
|  | const NamedParameters & | np
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>`

applies the PQQ refinement several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy `mask`. This function overwrites the control mesh `pmesh` with the refined mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  Mask | a model of `PQQMask_3`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  mask | a geometry policy mask
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

## ◆ PTQ()

template<class PolygonMesh , class Mask , class NamedParameters >

void CGAL::Subdivision_method_3::PTQ | ( | PolygonMesh & | pmesh,
|  | Mask | mask,
|  | const NamedParameters & | np
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>`

applies the PTQ refinement several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy `mask`. This function overwrites the control mesh `pmesh` with the refined mesh.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  Mask | a model of `PTQMask_3`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  mask | a geometry policy mask
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

## ◆ Sqrt3()

template<class PolygonMesh , class Mask , class NamedParameters >

void CGAL::Subdivision_method_3::Sqrt3 | ( | PolygonMesh & | pmesh,
|  | Mask | mask,
|  | const NamedParameters & | np
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>`

applies the \( \sqrt{3}\) refinement several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy `mask`. This function overwrites the control mesh `pmesh` with the refined mesh.

Attention
  The border subdivision only happens every second subdivision step during a single call of this function.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  Mask | a model of `Sqrt3Mask_3`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  mask | a geometry policy mask
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

Precondition
  `pmesh` must be a triangle mesh.

## ◆ Sqrt3_subdivision()

template<class PolygonMesh , class NamedParameters = parameters::Default_named_parameters>

void CGAL::Subdivision_method_3::Sqrt3_subdivision | ( | PolygonMesh & | pmesh,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>`

applies \( \sqrt{3}\)-subdivision several times on the control mesh `pmesh`.

The geometry of the refined mesh is computed by the geometry policy mask `Sqrt3_mask_3`. This function overwrites the control mesh `pmesh` with the subdivided mesh.

Attention
  The border subdivision only happens every second subdivision step during a single call of this function.

Template Parameters

  PolygonMesh | a model of `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  pmesh | a polygon mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a property map associating points to the vertices of `pmesh` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `Point_3` as value type Default: `boost::get(CGAL::vertex_point, pmesh)` Extra: If this parameter is omitted, an internal property map for `CGAL::vertex_point_t` should be available for the vertices of `pmesh`. |
  the number of subdivision steps Type: unsigned int Default: `1` |

Precondition
  `pmesh` must be a triangle mesh.