CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ > Class Template Reference

#include <CGAL/Surface_mesh_parameterization/Fixed_border_parameterizer_3.h>

Definition

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>
class CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >

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

A one-to-one mapping is guaranteed if the border of the surface is mapped onto a convex polygon.

This class is a pure virtual class and thus cannot be instantiated. Nevertheless, it implements most of the parameterization algorithm parameterize(). Subclasses are Strategies [5] that modify the behavior of this algorithm:

• They provide the template parameters BorderParameterizer_ and SolverTraits_.
• They implement compute_w_ij() to compute w_ij, the (i,j)-coefficient of matrix A for j neighbor vertex of i.

  Is Model Of:

  Parameterizer_3

Template Parameters

TriangleMesh_	must be a model of FaceGraph.
BorderParameterizer_	is a Strategy to parameterize the surface border and must be a model of Parameterizer_3. Default: Circular_border_arc_length_parameterizer_3<TriangleMesh_>
SolverTraits_	must be a model of SparseLinearAlgebraTraits_d. Note that the system is not symmetric because Fixed_border_parameterizer_3 does not remove border vertices from the system. Default: If Eigen 3.1 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then an overload of Eigen_solver_traits is provided as default parameter: CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >

See also

CGAL::Surface_mesh_parameterization::Barycentric_mapping_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>

CGAL::Surface_mesh_parameterization::Discrete_authalic_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>

CGAL::Surface_mesh_parameterization::Discrete_conformal_map_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>

CGAL::Surface_mesh_parameterization::Mean_value_coordinates_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>

Public Types
typedef Border_parameterizer_	Border_parameterizer
	Border parameterizer type.
typedef SolverTraits_	Solver_traits
	Solver traits type.
typedef TriangleMesh_	Triangle_mesh
	Triangle mesh type.
typedef boost::graph_traits< Triangle_mesh >::vertex_descriptor	vertex_descriptor
	Mesh vertex type.
typedef boost::graph_traits< Triangle_mesh >::halfedge_descriptor	halfedge_descriptor
	Mesh halfedge type.
typedef Solver_traits::Vector	Vector
	Solver vector type.
typedef Solver_traits::Matrix	Matrix
	Solver matrix type.

Public Member Functions
	Fixed_border_parameterizer_3 (Border_parameterizer border_param=Border_parameterizer(), Solver_traits sparse_la=Solver_traits())
	Constructor. More...
virtual	~Fixed_border_parameterizer_3 ()
	Destructor of base class should be virtual.
template<typename VertexUVmap , typename VertexIndexMap , typename VertexParameterizedMap >
Error_code	parameterize (Triangle_mesh &mesh, halfedge_descriptor bhd, VertexUVmap uvmap, VertexIndexMap vimap, VertexParameterizedMap vpmap)
	computes a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space. More...

Protected Member Functions
template<typename VertexUVmap , typename VertexIndexMap >
void	initialize_system_from_mesh_border (Matrix &A, Vector &Bu, Vector &Bv, const Triangle_mesh &mesh, halfedge_descriptor bhd, VertexUVmap uvmap, VertexIndexMap vimap) const
	initializes A, Bu and Bv after border parameterization. More...
virtual NT	compute_w_ij (const Triangle_mesh &mesh, vertex_descriptor main_vertex_v_i, Vertex_around_target_circulator< Triangle_mesh > neighbor_vertex_v_j) const =0
	computes w_ij, coefficient of matrix A for j neighbor vertex of i. More...
template<typename VertexIndexMap >
Error_code	setup_inner_vertex_relations (Matrix &A, Vector &, Vector &, const Triangle_mesh &mesh, vertex_descriptor vertex, VertexIndexMap vimap) const
	Compute the line i of matrix A for i inner vertex: More...
Border_parameterizer &	get_border_parameterizer ()
	Get the object that maps the surface's border onto a 2D space.
Solver_traits &	get_linear_algebra_traits ()
	Get the sparse linear algebra (traits object to access the linear system).

Constructor & Destructor Documentation

Fixed_border_parameterizer_3()

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>

CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::Fixed_border_parameterizer_3	(	Border_parameterizer	border_param = Border_parameterizer(),
		Solver_traits	sparse_la = Solver_traits()
	)

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

compute_w_ij()

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>

virtual NT CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::compute_w_ij ( const Triangle_mesh &  mesh, vertex_descriptor  main_vertex_v_i, Vertex_around_target_circulator< Triangle_mesh >  neighbor_vertex_v_j  ) const

protectedpure virtual

computes w_ij, coefficient of matrix A for j neighbor vertex of i.

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

Parameters

mesh	a triangulated surface.
main_vertex_v_i	the vertex of mesh with index i
neighbor_vertex_v_j	the vertex of mesh with index j

Implemented in CGAL::Surface_mesh_parameterization::Mean_value_coordinates_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >, CGAL::Surface_mesh_parameterization::Barycentric_mapping_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >, CGAL::Surface_mesh_parameterization::Discrete_authalic_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >, and CGAL::Surface_mesh_parameterization::Discrete_conformal_map_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >.

initialize_system_from_mesh_border()

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>

template<typename VertexUVmap , typename VertexIndexMap >

void CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::initialize_system_from_mesh_border ( Matrix &  A, Vector &  Bu, Vector &  Bv, const Triangle_mesh &  mesh, halfedge_descriptor  bhd, VertexUVmap  uvmap, VertexIndexMap  vimap  ) const

protected

initializes A, Bu and Bv after border parameterization.

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

Template Parameters

VertexUVmap	must be a model of ReadWritePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and Point_2 (type deduced from Triangle_mesh using Kernel_traits) as value type.
VertexIndexMap	must be a model of ReadablePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and a unique integer as value type.

Parameters

A	the matrix in both linear system
Bu	the right hand side vector in the linear system of x coordinates
Bv	the right hand side vector in the linear system of y coordinates
mesh	a triangulated surface.
bhd	a halfedge descriptor on the boundary of mesh.
uvmap	an instanciation of the class VertexUVmap.
vimap	an instanciation of the class VertexIndexMap.

Precondition

Vertices must be indexed (vimap must be initialized).

A, Bu, and Bv must be allocated.

Border vertices must be parameterized.

parameterize()

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>

template<typename VertexUVmap , typename VertexIndexMap , typename VertexParameterizedMap >

Error_code CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::parameterize	(	Triangle_mesh &	mesh,
		halfedge_descriptor	bhd,
		VertexUVmap	uvmap,
		VertexIndexMap	vimap,
		VertexParameterizedMap	vpmap
	)

computes a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space.

The mapping is piecewise linear (linear in each triangle). The result is the (u,v) pair image of each vertex of the 3D surface.

Template Parameters

VertexUVmap	must be a model of ReadWritePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and Point_2 (type deduced from Triangle_mesh using Kernel_traits) as value type.
VertexIndexMap	must be a model of ReadablePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and a unique integer as value type.
VertexParameterizedMap	must be a model of ReadWritePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and a Boolean as value type.

Parameters

mesh	a triangulated surface.
bhd	a halfedge descriptor on the boundary of mesh.
uvmap	an instanciation of the class VertexUVmap.
vimap	an instanciation of the class VertexIndexMap.
vpmap	an instanciation of the class VertexParameterizedMap.

Precondition

mesh must be a triangular mesh.

The mesh border must be mapped onto a convex polygon.

The vertices must be indexed (vimap must be initialized)

setup_inner_vertex_relations()

template<typename TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>

template<typename VertexIndexMap >

Error_code CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::setup_inner_vertex_relations ( Matrix &  A, Vector &  , Vector &  , const Triangle_mesh &  mesh, vertex_descriptor  vertex, VertexIndexMap  vimap  ) const

protected

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.