#include <CGAL/Mean_value_coordinates_parameterizer_3.h>

Inherits from

CGAL::Fixed_border_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 = OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>>
class CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >

The class Mean_value_coordinates_parameterizer_3 implements Floater Mean Value Coordinates parameterization.

[5]. This method is sometimes called simply Floater parameterization.

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

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

This class is used by the main parameterization algorithm Fixed_border_parameterizer_3::parameterize().

It provides defaultBorderParameterizer_3 and SparseLinearAlgebraTraits_d template parameters that make sense.
It implements compute_w_ij() to compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i based on Floater Mean Value Coordinates parameterization.
It implements an optimized version of is_one_to_one_mapping().

Is Model Of:: ParameterizerTraits_3

Examples:: Surface_mesh_parameterization/Eigen_parameterization.cpp, and Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp.

Public Member Functions
	Mean_value_coordinates_parameterizer_3 (Border_param border_param=Border_param(), Sparse_LA sparse_la=Sparse_LA())
	Constructor. More...

Public Member Functions inherited from 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. 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 NT	compute_w_ij (const Adaptor &mesh, Vertex_const_handle main_vertex_v_i, Vertex_around_vertex_const_circulator neighbor_vertex_v_j)
	Compute w_ij = (i, j) coefficient of matrix A for j neighbor vertex of i.

virtual bool	is_one_to_one_mapping (const Adaptor &, const Matrix &, const Vector &, const Vector &)
	Check if 3D -> 2D mapping is one-to-one. More...

Protected Member Functions inherited from CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >
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 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...

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
Public Types inherited from CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >
typedef BorderParameterizer_3	Border_param
	Export BorderParameterizer_3 template parameter.

typedef SparseLinearAlgebraTraits_d	Sparse_LA
	Export SparseLinearAlgebraTraits_d template parameter.

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 = OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>>

CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >::Mean_value_coordinates_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 ParameterizationMesh_3 , class BorderParameterizer_3 = Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>, class SparseLinearAlgebraTraits_d = OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>>

virtual bool CGAL::Mean_value_coordinates_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >::is_one_to_one_mapping	(	const Adaptor &	,
		const Matrix &	,
		const Vector &	,
		const Vector &
	)

protectedvirtual

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

Theorem: one-to-one mapping is guaranteed if all w_ij coefficients are > 0 (for j vertex neighbor of i) and if the surface border is mapped onto a 2D convex polygon. Floater formula above implies that w_ij > 0 (for j vertex neighbor of i), thus mapping is guaranteed if the surface border is mapped onto a 2D convex polygon.

Reimplemented from CGAL::Fixed_border_parameterizer_3< ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d >.

Inherits from

Definition

Public Member Functions

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation