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>
Parameterizer_traits_3<ParameterizationMesh_3>
Model of the ParameterizerTraits_3 concept.
LSCM_parameterizer_3 class is a Strategy [GHJV95]: it implements a strategy of surface parameterization for models of ParameterizationMesh_3.
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;
LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>::Border_param | |
Export BorderParameterizer_3 template parameter.
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LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>::Sparse_LA | |
Export SparseLinearAlgebraTraits_d template parameter.
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Constructor.
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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.
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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>