\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - Planar Parameterization of Triangulated Surface Meshes
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Main Function
Planar Parameterization of Triangulated Surface Meshes Reference

Functions

template<class ParameterizationMesh_3 >
Parameterizer_traits_3
< ParameterizationMesh_3 >
::Error_code 		CGAL::parameterize (ParameterizationMesh_3 &mesh)
 Compute a one-to-one mapping from a 3D triangle surface mesh to a 2D circle, using Floater Mean Value Coordinates algorithm. More...
 
template<class ParameterizationMesh_3 , class ParameterizerTraits_3 >
Parameterizer_traits_3
< ParameterizationMesh_3 >
::Error_code 		CGAL::parameterize (ParameterizationMesh_3 &mesh, ParameterizerTraits_3 parameterizer)
 Compute a one-to-one mapping from a 3D triangle surface mesh to a simple 2D domain. More...
 

Function Documentation

template<class ParameterizationMesh_3 >
Parameterizer_traits_3<ParameterizationMesh_3>::Error_code CGAL::parameterize ( ParameterizationMesh_3 &  mesh)

Compute 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.

Precondition
mesh must be a surface with one connected component.
mesh must be a triangular mesh.
Parameters
mesh3D mesh, model of ParameterizationMesh_3 concept

#include <CGAL/parameterize.h>

Examples:
Surface_mesh_parameterization/Complete_parameterization_example.cpp, Surface_mesh_parameterization/Eigen_parameterization.cpp, Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp, Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp, and Surface_mesh_parameterization/Simple_parameterization.cpp.
template<class ParameterizationMesh_3 , class ParameterizerTraits_3 >
Parameterizer_traits_3<ParameterizationMesh_3>::Error_code CGAL::parameterize ( ParameterizationMesh_3 &  mesh,
ParameterizerTraits_3  parameterizer 
)

Compute 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.

One-to-one mapping may be guaranteed or not, depending on the chosen ParametizerTraits_3 algorithm.

Precondition
mesh must be a surface with one connected component.
mesh must be a triangular mesh.
The mesh border must be mapped onto a convex polygon (for fixed border parameterizations).
Parameters
mesh3D mesh, model of ParameterizationMesh_3
parameterizerParameterization method for mesh

#include <CGAL/parameterize.h>