CGAL::LSCM_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d > Class Template Reference

#include <CGAL/LSCM_parameterizer_3.h>

Inherits from

CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >.

Definition

template<class ParameterizationMesh_3, class BorderParameterizer_3 = Two_vertices_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = Eigen_solver_traits<Eigen::SimplicialLDLT<Eigen_sparse_symmetric_matrix<double>::EigenType> >>
class CGAL::LSCM_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >

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

[7].

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

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

Note that his parametrization method has no template parameter for changing the sparse solver.

Is Model Of:

ParameterizerTraits_3

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::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

Examples:

Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp.

Public Types
typedef BorderParameterizer_3	Border_param
	Export BorderParameterizer_3 template parameter.
Public Types inherited from CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >
enum	Error_code {   OK, ERROR_EMPTY_MESH, ERROR_NON_TRIANGULAR_MESH, ERROR_NO_TOPOLOGICAL_DISC,   ERROR_BORDER_TOO_SHORT, ERROR_NON_CONVEX_BORDER, ERROR_CANNOT_SOLVE_LINEAR_SYSTEM, ERROR_NO_1_TO_1_MAPPING,   ERROR_OUT_OF_MEMORY, ERROR_WRONG_PARAMETER }
	List of errors detected by this package. More...
typedef ParameterizationMesh_3	Adaptor
	Export ParameterizationMesh_3 template parameter.

Public Member Functions
	LSCM_parameterizer_3 (Border_param border_param=Border_param(), Sparse_LA sparse_la=Sparse_LA())
	Constructor. More...
virtual Error_code	parameterize (Adaptor &mesh)
	Compute a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space. More...
Public Member Functions inherited from CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >
virtual	~Parameterizer_traits_3 ()
	Destructor of base class should be virtual.

Additional Inherited Members
Static Public Member Functions inherited from CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >
static const char *	get_error_message (int error_code)
	Get message corresponding to an error code. More...
Protected Types inherited from CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >
typedef Adaptor::NT	NT
typedef Adaptor::Point_2	Point_2
typedef Adaptor::Point_3	Point_3
typedef Adaptor::Vector_2	Vector_2
typedef Adaptor::Vector_3	Vector_3
typedef Adaptor::Facet	Facet
typedef Adaptor::Facet_handle	Facet_handle
typedef Adaptor::Facet_const_handle	Facet_const_handle
typedef Adaptor::Facet_iterator	Facet_iterator
typedef Adaptor::Facet_const_iterator	Facet_const_iterator
typedef Adaptor::Vertex	Vertex
typedef Adaptor::Vertex_handle	Vertex_handle
typedef Adaptor::Vertex_const_handle	Vertex_const_handle
typedef Adaptor::Vertex_iterator	Vertex_iterator
typedef Adaptor::Vertex_const_iterator	Vertex_const_iterator
typedef Adaptor::Border_vertex_iterator	Border_vertex_iterator
typedef Adaptor::Border_vertex_const_iterator	Border_vertex_const_iterator
typedef Adaptor::Vertex_around_facet_circulator	Vertex_around_facet_circulator
typedef Adaptor::Vertex_around_facet_const_circulator	Vertex_around_facet_const_circulator
typedef Adaptor::Vertex_around_vertex_circulator	Vertex_around_vertex_circulator
typedef Adaptor::Vertex_around_vertex_const_circulator	Vertex_around_vertex_const_circulator

Constructor & Destructor Documentation

template<class ParameterizationMesh_3 , class BorderParameterizer_3 = Two_vertices_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = Eigen_solver_traits<Eigen::SimplicialLDLT<Eigen_sparse_symmetric_matrix<double>::EigenType> >>

CGAL::LSCM_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >::LSCM_parameterizer_3	(	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

Member Function Documentation

template<class Adaptor , class Border_param , class Sparse_LA >

LSCM_parameterizer_3< Adaptor, Border_param, Sparse_LA >::Error_code CGAL::LSCM_parameterizer_3< Adaptor, Border_param, Sparse_LA >::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.

Precondition

mesh must be a surface with one connected component.

mesh must be a triangular mesh.

Implements CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >.