CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d > Class Template Reference

#include <CGAL/Fixed_border_parameterizer_3.h>

Inherits from

CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >.

Inherited by 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 >, and CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >.

Definition

template<class ParameterizationMesh_3, class BorderParameterizer_3 = Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >>
class CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >

The class Fixed_border_parameterizer_3 is the base class of fixed border parameterization methods (Tutte, Floater, ...).

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

This class is a pure virtual class, thus cannot be instantiated. Anyway, it implements most of the parameterization algorithm parameterize(). Subclasses are Strategies that modify the behavior of this algorithm:

• They provide BorderParameterizer_3 and SparseLinearAlgebraTraits_d template parameters.
• They implement compute_w_ij() to compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i.
• They may implement an optimized version of is_one_to_one_mapping().from the linear systems in order to have a symmetric positive definite matrix for Tutte Barycentric Mapping and Discrete Conformal Map algorithms.

Is Model Of:

ParameterizerTraits_3

See Also

CGAL::Parameterizer_traits_3<ParameterizationMesh_3>

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::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

Public Types
typedef BorderParameterizer_3	Border_param
	Export BorderParameterizer_3 template parameter.
typedef SparseLinearAlgebraTraits_d	Sparse_LA
	Export SparseLinearAlgebraTraits_d 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
	Fixed_border_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.

Protected Member Functions
virtual Error_code	check_parameterize_preconditions (Adaptor &mesh)
	Check parameterize() preconditions: More...
void	initialize_system_from_mesh_border (Matrix &A, Vector &Bu, Vector &Bv, const Adaptor &mesh)
	Initialize A, Bu and Bv after border parameterization. More...
virtual NT	compute_w_ij (const Adaptor &mesh, Vertex_const_handle main_vertex_v_i, Vertex_around_vertex_const_circulator neighbor_vertex_v_j)=0
	Compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i. More...
virtual Error_code	setup_inner_vertex_relations (Matrix &A, Vector &Bu, Vector &Bv, const Adaptor &mesh, Vertex_const_handle vertex)
	Compute the line i of matrix A for i inner vertex: More...
void	set_mesh_uv_from_system (Adaptor &mesh, const Vector &Xu, const Vector &Xv)
	Copy Xu and Xv coordinates into the (u,v) pair of each surface vertex.
virtual Error_code	check_parameterize_postconditions (const Adaptor &mesh, const Matrix &A, const Vector &Bu, const Vector &Bv)
	Check parameterize() postconditions: More...
virtual bool	is_one_to_one_mapping (const Adaptor &mesh, const Matrix &A, const Vector &Bu, const Vector &Bv)
	Check if 3D -> 2D mapping is one-to-one. More...
Border_param &	get_border_parameterizer ()
	Get the object that maps the surface's border onto a 2D space.
Sparse_LA &	get_linear_algebra_traits ()
	Get the sparse linear algebra (traits object to access the linear system).

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 = Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >>

CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >::Fixed_border_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 >

Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::Error_code CGAL::Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::check_parameterize_postconditions ( const Adaptor &  mesh, const Matrix &  A, const Vector &  Bu, const Vector &  Bv  )

protectedvirtual

Check parameterize() postconditions:

• 3D -> 2D mapping is one-to-one.

template<class Adaptor , class Border_param , class Sparse_LA >

Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::Error_code CGAL::Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::check_parameterize_preconditions ( Adaptor &  mesh)

protectedvirtual

Check parameterize() preconditions:

• mesh must be a surface with one connected component.
• mesh must be a triangular mesh.
• The mesh border must be mapped onto a convex polygon.

template<class ParameterizationMesh_3 , class BorderParameterizer_3 = Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >>

virtual NT CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >::compute_w_ij ( const Adaptor &  mesh, Vertex_const_handle  main_vertex_v_i, Vertex_around_vertex_const_circulator  neighbor_vertex_v_j  )

protectedpure virtual

Compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i.

Implementation note: Subclasses must at least implement compute_w_ij().

Implemented in CGAL::Discrete_conformal_map_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >, CGAL::Barycentric_mapping_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >, CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >, and CGAL::Discrete_authalic_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >.

template<class Adaptor , class Border_param , class Sparse_LA >

void CGAL::Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::initialize_system_from_mesh_border ( Matrix &  A, Vector &  Bu, Vector &  Bv, const Adaptor &  mesh  )

protected

Initialize A, Bu and Bv after border parameterization.

Fill the border vertices' lines in both linear systems: "u = constant" and "v = constant".

Precondition

Vertices must be indexed.

A, Bu and Bv must be allocated.

Border vertices must be parameterized.

template<class Adaptor , class Border_param , class Sparse_LA >

bool CGAL::Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::is_one_to_one_mapping ( const Adaptor &  mesh, const Matrix &  A, const Vector &  Bu, const Vector &  Bv  )

protectedvirtual

Check if 3D -> 2D mapping is one-to-one.

The default implementation checks each normal.

Reimplemented in CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >, and CGAL::Barycentric_mapping_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >.

template<class Adaptor , class Border_param , class Sparse_LA >

Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::Error_code CGAL::Fixed_border_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.

The mesh border must be mapped onto a convex polygon.

Implements CGAL::Parameterizer_traits_3< ParameterizationMesh_3 >.

template<class Adaptor , class Border_param , class Sparse_LA >

Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::Error_code CGAL::Fixed_border_parameterizer_3< Adaptor, Border_param, Sparse_LA >::setup_inner_vertex_relations ( Matrix &  A, Vector &  Bu, Vector &  Bv, const Adaptor &  mesh, Vertex_const_handle  vertex  )

protectedvirtual

Compute the line i of matrix A for i inner vertex:

• call compute_w_ij() to compute the A coefficient w_ij for each neighbor v_j.
• compute w_ii = - sum of w_ijs.

Precondition

Vertices must be indexed.

Vertex i musn't be already parameterized.

Line i of A must contain only zeros.