CGAL 5.5.2 - Planar Parameterization of Triangulated Surface Meshes

The central functions, main entry point of the package.

## Functions

template<class TriangleMesh , class Parameterizer , class HD , class VertexUVmap >
Error_code CGAL::Surface_mesh_parameterization::parameterize (TriangleMesh &mesh, Parameterizer parameterizer, HD bhd, VertexUVmap uvmap)
computes a one-to-one mapping from a 3D triangle surface mesh to a simple 2D domain. More...

template<class TriangleMesh , class HD , class VertexUVmap >
Error_code CGAL::Surface_mesh_parameterization::parameterize (TriangleMesh &mesh, HD bhd, VertexUVmap uvmap)
computes a one-to-one mapping from a 3D triangle surface mesh to a 2D circle, using Floater Mean Value Coordinates algorithm. More...

## ◆ parameterize() [1/2]

template<class TriangleMesh , class Parameterizer , class HD , class VertexUVmap >
 Error_code CGAL::Surface_mesh_parameterization::parameterize ( TriangleMesh & mesh, Parameterizer parameterizer, HD bhd, VertexUVmap uvmap )

#include <CGAL/Surface_mesh_parameterization/parameterize.h>

computes a one-to-one mapping from a 3D triangle surface mesh to a simple 2D domain.

The mapping is piecewise linear on the triangle mesh. The result is a pair (u,v) of parameter coordinates for each vertex of the input mesh.

A one-to-one mapping may be guaranteed or not, depending on the chosen Parameterizer algorithm.

Template Parameters
 TriangleMesh must be a model of FaceGraph. Parameterizer must be a model of Parameterizer_3. HD must be the halfedge_descriptor type corresponding to the graph traits of TriangleMesh. VertexUVmap must be a model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_2 (type deduced from TriangleMesh using Kernel_traits) as value type.
Parameters
 mesh a triangulated surface. parameterizer a parameterizer. bhd a halfedge descriptor on the boundary of mesh. uvmap an instanciation of the class VertexUVmap.
Precondition
mesh must be a triangular mesh.
The mesh border must be mapped onto a convex polygon (for fixed border parameterizations).
The vertices must be indexed (vimap must be initialized).
Examples:
Surface_mesh_parameterization/ARAP_parameterization.cpp, Surface_mesh_parameterization/discrete_authalic.cpp, Surface_mesh_parameterization/lscm.cpp, Surface_mesh_parameterization/seam_Polyhedron_3.cpp, Surface_mesh_parameterization/simple_parameterization.cpp, and Surface_mesh_parameterization/square_border_parameterizer.cpp.

## ◆ parameterize() [2/2]

template<class TriangleMesh , class HD , class VertexUVmap >
 Error_code CGAL::Surface_mesh_parameterization::parameterize ( TriangleMesh & mesh, HD bhd, VertexUVmap uvmap )

#include <CGAL/Surface_mesh_parameterization/parameterize.h>

computes a one-to-one mapping from a 3D triangle surface mesh to a 2D circle, using Floater Mean Value Coordinates algorithm.

A one-to-one mapping is guaranteed.

The mapping is piecewise linear on the input mesh triangles. The result is a (u,v) pair of parameter coordinates for each vertex of the input mesh.

Template Parameters
 TriangleMesh must be a model of FaceGraph. HD must be the halfedge_descriptor type corresponding to the graph traits of TriangleMesh. VertexUVmap must be a model of ReadWritePropertyMap with boost::graph_traits::vertex_descriptor as key type and Point_2 (type deduced from TriangleMesh using Kernel_traits) as value type.
Parameters
 mesh a triangulated surface. bhd a halfedge descriptor on the boundary of mesh. uvmap an instanciation of the class VertexUVmap.
Precondition
mesh must be a triangular mesh.
The vertices must be indexed (vimap must be initialized).