CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

Definition

The class Discrete_conformal_map_parameterizer_3 implements the Discrete Conformal Map (DCM) parameterization [EDD$$⁺95]. This algorithm is also called Discrete Conformal Parameterization (DCP), Discrete Harmonic Map or Fixed Conformal Parameterization by other authors.

This is a conformal parameterization, i.e. it attempts to preserve angles.

One-to-one mapping is guaranteed if surface's border is mapped onto a convex polygon.

This class is a Strategy [GHJV95] called by the main parameterization algorithm Fixed_border_parameterizer_3::parameterize(). Discrete_conformal_map_parameterizer_3:

• provides default BorderParameterizer_3 and SparseLinearAlgebraTraits_d template parameters that make sense.
• implements compute_w_ij() to compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i based on Discrete Conformal Map method.

#include <CGAL/Discrete_conformal_map_parameterizer_3.h>

Is Model for the Concepts

Model of the ParameterizerTraits_3 concept.

Design Pattern

Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, ...> class is a Strategy [GHJV95]: it implements a strategy of surface parameterization for models of ParameterizationMesh_3.

Parameters

The full template declaration is:

template$$<
class ParameterizationMesh_3,
class BorderParameterizer_3 = Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
class SparseLinearAlgebraTraits_d = OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>$$>
class Discrete_conformal_map_parameterizer_3;

Parameters:

ParameterizationMesh_3

3D surface mesh.

BorderParameterizer_3

Strategy to parameterize the surface border.

SparseLinearAlgebraTraits_d

Traits class to solve a sparse linear system. Note: the system is NOT symmetric because Fixed_border_parameterizer_3 does not remove (yet) border vertices from the system.

Types

Creation

Parameters:

border_param

Object that maps the surface's border to 2D space.

sparse_la

Traits object to access a sparse linear system.

Operations

See Also

CGAL::Parameterizer_traits_3<ParameterizationMesh_3>
CGAL::Fixed_border_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>
CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>
CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>
CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>
CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>