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>
using namespace std;
using namespace CGAL;
namespace params = CGAL::Polygon_mesh_processing::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 char* in_file = (argc > 2) ? argv[2] : "data/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();
std::cerr << "Done (" << t.time() << " s)" << std::endl;
std::ofstream out(out_file);
out << pmesh;
return 0;
}
- See Also
CGAL::CatmullClark_mask_3<PolygonMesh>
-
CGAL::DooSabin_mask_3<PolygonMesh
-
CGAL::Loop_mask_3<PolygonMesh
-
CGAL::Sqrt3_mask_3<PolygonMesh>
|
template<class PolygonMesh , class NamedParameters > |
void | CGAL::Subdivision_method_3::CatmullClark_subdivision (PolygonMesh &pmesh, const NamedParameters &np) |
| applies Catmull-Clark subdivision several times on the control mesh pmesh . More...
|
|
template<class PolygonMesh , class NamedParameters > |
void | CGAL::Subdivision_method_3::Loop_subdivision (PolygonMesh &pmesh, const NamedParameters &np) |
| applies Loop subdivision several times on the control mesh pmesh . More...
|
|
template<class PolygonMesh , class NamedParameters > |
void | CGAL::Subdivision_method_3::DooSabin_subdivision (PolygonMesh &pmesh, const NamedParameters &np) |
| applies DooSabin subdivision several times on the control mesh pmesh . More...
|
|
template<class PolygonMesh , class NamedParameters > |
void | CGAL::Subdivision_method_3::Sqrt3_subdivision (PolygonMesh &pmesh, const NamedParameters &np) |
| applies \( \sqrt{3}\)-subdivision several times on the control mesh pmesh . More...
|
|
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 . More...
|
|
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 . More...
|
|
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 . More...
|
|
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 . More...
|
|
template<class PolygonMesh , class NamedParameters >
void CGAL::Subdivision_method_3::CatmullClark_subdivision |
( |
PolygonMesh & |
pmesh, |
|
|
const NamedParameters & |
np |
|
) |
| |
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
-
- Parameters
-
pmesh | a polygon mesh |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
- Precondition
pmesh
must be a triangle mesh.
#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>
- Examples:
- Subdivision_method_3/CatmullClark_subdivision.cpp.
template<class PolygonMesh , class NamedParameters >
void CGAL::Subdivision_method_3::DooSabin_subdivision |
( |
PolygonMesh & |
pmesh, |
|
|
const NamedParameters & |
np |
|
) |
| |
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
-
- Parameters
-
pmesh | a polygon mesh |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>
- Examples:
- Subdivision_method_3/DooSabin_subdivision.cpp.
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
.
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
-
- Parameters
-
pmesh | a polygon mesh |
mask | a geometry policy mask |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
- Precondition
pmesh
must be a triangle mesh.
#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>
template<class PolygonMesh , class NamedParameters >
void CGAL::Subdivision_method_3::Loop_subdivision |
( |
PolygonMesh & |
pmesh, |
|
|
const NamedParameters & |
np |
|
) |
| |
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
-
- Parameters
-
pmesh | a polygon mesh |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>
- Examples:
- Subdivision_method_3/Loop_subdivision.cpp.
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
.
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
-
- Parameters
-
pmesh | a polygon mesh |
mask | a geometry policy mask |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>
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
.
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
-
- Parameters
-
pmesh | a polygon mesh |
mask | a geometry policy mask |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>
- Examples:
- Subdivision_method_3/Customized_subdivision.cpp.
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
.
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
-
- Parameters
-
pmesh | a polygon mesh |
mask | a geometry policy mask |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
- Precondition
pmesh
must be a triangle mesh.
#include <CGAL/Subdivision_method_3/subdivision_hosts_3.h>
template<class PolygonMesh , class NamedParameters >
void CGAL::Subdivision_method_3::Sqrt3_subdivision |
( |
PolygonMesh & |
pmesh, |
|
|
const NamedParameters & |
np |
|
) |
| |
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
-
- Parameters
-
pmesh | a polygon mesh |
np | optional sequence of Named Parameters among the ones listed below |
- Named Parameters
vertex_point_map | the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh |
number_of_iterations | the number of subdivision steps, by default 1. |
- Precondition
pmesh
must be a triangle mesh.
#include <CGAL/Subdivision_method_3/subdivision_methods_3.h>
- Examples:
- Subdivision_method_3/Sqrt3_subdivision.cpp.