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

LSCM_parameterizer_3<Adaptor, Border_param, Sparse_LA>::Error_code
	param.parameterize ( Adaptor& mesh)
		[virtual] 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