LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits

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CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

Definition

The class LSCM_parameterizer_3 implements the Least Squares Conformal Maps (LSCM) parameterization [LPRM02].

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

This is a free border parameterization. No need to map the surface's border onto a convex polygon (only two pinned vertices are needed to ensure a unique solution), but one-to-one mapping is not guaranteed.

#include <CGAL/LSCM_parameterizer_3.h>

Inherits From

Parameterizer_traits_3<ParameterizationMesh_3>

Is Model for the Concepts

Model of the ParameterizerTraits_3 concept.

Design Pattern

LSCM_parameterizer_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 = Two_vertices_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = OpenNL::SymmetricLinearSolverTraits<typename ParameterizationMesh_3::NT>>
class LSCM_parameterizer_3;

Types

LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>::Border_param
	Export BorderParameterizer_3 template parameter.
LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>::Sparse_LA
	Export SparseLinearAlgebraTraits_d template parameter.

Creation

LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d> param ( Border_param border_param = Border_param(),
Sparse_LA sparse_la = Sparse_LA());

Constructor.

Parameters:

border_param: Object that maps the surface's border to 2D space. sparse_la: Traits object to access a sparse linear system.

Operations

Error_code

param.parameterize ( Adaptor& mesh)

Compute a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space. The mapping is linear by pieces (linear in each triangle). The result is the (u, v) pair image of each vertex of the 3D surface.

Preconditions:

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

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::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>
CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

Next: SparseLinearAlgebraTraits_d::Matrix