parameterize

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CGAL::parameterize

Definition

CGAL::parameterize() is the main entry-point of the Surface_mesh_parameterization package.

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

The CGAL::parameterize() function exists in two flavors, to provide a default parameterization algorithm of Floater Mean Value Coordinates.

#include <CGAL/parameterize.h>

Parameterizer_traits_3<ParameterizationMesh_3>::Error_code
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. Preconditions:

'mesh' must be a surface with one connected component.
'mesh' must be a triangular mesh.

Parameters:

mesh: 3D mesh, model of ParameterizationMesh_3 concept

Parameterizer_traits_3<ParameterizationMesh_3>::Error_code

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. Preconditions:

'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:

mesh: 3D mesh, model of ParameterizationMesh_3
parameterizer: Parameterization method for 'mesh'

Parameters

The full template declarations are:

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

template<
class ParameterizationMesh_3,
class ParameterizerTraits_3>
Parameterizer_traits_3<ParameterizationMesh_3>::Error_code
parameterize (ParameterizationMesh_3 &mesh, ParameterizerTraits_3 parameterizer);

Example

See Simple_parameterization.C example.

Implementation

This function simply calls the parameterize() method of the parameterization algorithm chosen.

Next: ParameterizerTraits_3