Definition

ParameterizationMesh_3 is a concept for a 3D surface mesh. Its main purpose is to allow the parameterization methods to access meshes in a uniform manner.

A ParameterizationMesh_3 surface consists of vertices, facets and an incidence relation on them. No notion of edge is requested. Vertices represent points in 3d-space. Facets are planar polygons without holes defined by the circular sequence of vertices along their border. The surface itself can have holes. The vertices along the border of a hole are called border vertices. A surface is closed if it contains no border vertices.

The surface must be an oriented 2-manifold with border vertices, i.e. the neighborhood of each point on the surface is either homeomorphic to a disc or to a half disc, except for vertices where many holes and surfaces with border can join.

ParameterizationMesh_3 defines the types, data and methods that a mesh must implement to allow surface parameterization. Among other things, this concept defines accessors to fields specific to parameterizations methods: index, u, v, is_parameterized.

ParameterizationMesh_3 meshes can have any genus, arity or number of components. On the other hand, as parameterization methods deal only with topological disks, ParameterizationMesh_3 defines an interface oriented towards topological disks.

Design Pattern

ParameterizationMesh_3 is an Adaptor [6] : it changes the interface of a 3D mesh to match the interface expected by the parameterization methods.

Creation

Construction and destruction are undefined.

We provide 2 models of this concept:

Has Models:

CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron_3_>

CGAL::Parameterization_mesh_patch_3<ParameterizationPatchableMesh_3>

See Also: ParameterizationPatchableMesh_3

Examples:: Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp.

Types
The following mutable handles, iterators, and circulators have appropriate non-mutable counterparts, i.e. `const_handle`, `const_iterator`, and `const_circulator`. The mutable types are assignable to their non-mutable counterparts. Both circulators are assignable to the `Vertex_iterator`. The iterators are assignable to the respective handle types. Wherever the handles appear in function parameter lists, the corresponding iterators can be used as well.
typedef unspecified_type	NT
	Number type to represent coordinates.

typedef unspecified_type	Point_2
	2D point that represents (u, v) coordinates computed by parameterization methods. More...

typedef unspecified_type	Point_3
	3D point that represents vertices coordinates. More...

typedef unspecified_type	Vector_2
	2D vector. More...

typedef unspecified_type	Vector_3
	3D vector. More...

typedef unspecified_type	Facet
	Opaque type representing a facet of the 3D mesh. More...

typedef unspecified_type	Facet_handle
	Handle to a facet. More...

typedef unspecified_type	Facet_const_handle

typedef unspecified_type	Facet_iterator
	Iterator over all mesh facets. More...

typedef unspecified_type	Facet_const_iterator

typedef unspecified_type	Vertex
	Opaque type representing a vertex of the 3D mesh. More...

typedef unspecified_type	Vertex_handle
	Handle to a vertex. More...

typedef unspecified_type	Vertex_const_handle

typedef unspecified_type	Vertex_iterator
	Iterator over all vertices of a mesh. More...

typedef unspecified_type	Vertex_const_iterator

typedef unspecified_type	Border_vertex_iterator
	Iterator over vertices of the mesh main border. More...

typedef unspecified_type	Border_vertex_const_iterator

typedef unspecified_type	Vertex_around_facet_circulator
	Counter-clockwise circulator over a facet's vertices. More...

typedef unspecified_type	Vertex_around_facet_const_circulator

typedef unspecified_type	Vertex_around_vertex_circulator
	Clockwise circulator over the vertices incident to a vertex. More...

typedef unspecified_type	Vertex_around_vertex_const_circulator

Operations
The following mutable methods returning a handle, iterator, or circulator have appropriate non-mutable counterpart methods, i.e. `const`, returning a `const_handle`, `const_iterator`, or `const_circulator`.
bool	is_valid () const
	Indicate if the mesh matches the `ParameterizationMesh_3` concept.

Vertex_iterator	mesh_vertices_begin ()
	Get iterator over first vertex of mesh.

Vertex_const_iterator	mesh_vertices_begin () const

Vertex_iterator	mesh_vertices_end ()
	Get iterator over past-the-end vertex of mesh.

Vertex_const_iterator	mesh_vertices_end () const

int	count_mesh_vertices () const
	Count the number of vertices of the mesh.

void	index_mesh_vertices ()
	Index vertices of the mesh from 0 to `count_mesh_vertices`()-1.

Border_vertex_iterator	mesh_main_border_vertices_begin ()
	Get iterator over first vertex of mesh's main border.

Border_vertex_const_iterator	mesh_main_border_vertices_begin () const

Border_vertex_iterator	mesh_main_border_vertices_end ()
	Get iterator over past-the-end vertex of mesh's main border.

Border_vertex_const_iterator	mesh_main_border_vertices_end () const

std::list< Vertex_handle >	get_border (Vertex_handle seed_vertex)
	Return the border containing `seed_vertex`. More...

Facet_iterator	mesh_facets_begin ()
	Get iterator over first facet of mesh.

Facet_const_iterator	mesh_facets_begin () const

Facet_iterator	mesh_facets_end ()
	Get iterator over past-the-end facet of mesh.

Facet_const_iterator	mesh_facets_end () const

int	count_mesh_facets () const
	Count the number of facets of the mesh.

bool	is_mesh_triangular () const
	Return true of all mesh's facets are triangles.

int	count_mesh_halfedges () const
	Count the number of halfedges of the mesh.

Vertex_around_facet_circulator	facet_vertices_begin (Facet_handle facet)
	Get circulator over facet's vertices.

Vertex_around_facet_const_circulator	facet_vertices_begin (Facet_const_handle facet) const

int	count_facet_vertices (Facet_const_handle facet) const
	Count the number of vertices of a facet.

Point_3	get_vertex_position (Vertex_const_handle vertex) const
	Get the 3D position of a vertex.

Point_2	get_vertex_uv (Vertex_const_handle vertex) const
	Get/set the 2D position (u/v pair) of a vertex. More...

void	set_vertex_uv (Vertex_handle vertex, const Point_2 &uv)

bool	is_vertex_parameterized (Vertex_const_handle vertex) const
	Get/set is parameterized field of vertex. More...

void	set_vertex_parameterized (Vertex_handle vertex, bool parameterized)

int	get_vertex_index (Vertex_const_handle vertex) const
	Get/set vertex index. More...

void	set_vertex_index (Vertex_handle vertex, int index)

int	get_vertex_tag (Vertex_const_handle vertex) const
	Get/set vertex' all purpose tag. More...

void	set_vertex_tag (Vertex_handle vertex, int tag)

bool	is_vertex_on_border (Vertex_const_handle vertex) const
	Return true if a vertex belongs to ANY mesh's border.

bool	is_vertex_on_main_border (Vertex_const_handle vertex) const
	Return true if a vertex belongs to the UNIQUE mesh's main border.

Vertex_around_vertex_circulator	vertices_around_vertex_begin (Vertex_handle vertex, Vertex_handle start_position=Vertex_handle())
	Get circulator over the vertices incident to `vertex`. More...

Vertex_around_vertex_const_circulator	vertices_around_vertex_begin (Vertex_const_handle vertex, Vertex_const_handle start_position=Vertex_const_handle()) const

Member Typedef Documentation

typedef unspecified_type ParameterizationMesh_3::Border_vertex_iterator

Iterator over vertices of the mesh main border.

Model of the ForwardIterator concept.

typedef unspecified_type ParameterizationMesh_3::Facet

Opaque type representing a facet of the 3D mesh.

No methods are expected.

typedef unspecified_type ParameterizationMesh_3::Facet_handle

Handle to a facet.

Model of the Handle concept.

typedef unspecified_type ParameterizationMesh_3::Facet_iterator

Iterator over all mesh facets.

Model of the ForwardIterator concept.

typedef unspecified_type ParameterizationMesh_3::Point_2

2D point that represents (u, v) coordinates computed by parameterization methods.

Must provide x() and y() methods.

typedef unspecified_type ParameterizationMesh_3::Point_3

3D point that represents vertices coordinates.

Must provide x(), y() and z() methods.

typedef unspecified_type ParameterizationMesh_3::Vector_2

2D vector.

Must provide x() and y() methods.

typedef unspecified_type ParameterizationMesh_3::Vector_3

3D vector.

Must provide x(), y() and z() methods.

typedef unspecified_type ParameterizationMesh_3::Vertex

Opaque type representing a vertex of the 3D mesh.

No methods are expected.

typedef unspecified_type ParameterizationMesh_3::Vertex_around_facet_circulator

Counter-clockwise circulator over a facet's vertices.

Model of the BidirectionalCirculator concept.

typedef unspecified_type ParameterizationMesh_3::Vertex_around_vertex_circulator

Clockwise circulator over the vertices incident to a vertex.

Model of the BidirectionalCirculator concept.

typedef unspecified_type ParameterizationMesh_3::Vertex_handle

Handle to a vertex.

Model of the Handle concept.

typedef unspecified_type ParameterizationMesh_3::Vertex_iterator

Iterator over all vertices of a mesh.

Model of the ForwardIterator concept.

Member Function Documentation

std::list<Vertex_handle> ParameterizationMesh_3::get_border ( Vertex_handle seed_vertex)

Return the border containing seed_vertex.

Return an empty list if not found.

int ParameterizationMesh_3::get_vertex_index ( Vertex_const_handle vertex) const

Get/set vertex index.

Default value is undefined.

int ParameterizationMesh_3::get_vertex_tag ( Vertex_const_handle vertex) const

Get/set vertex' all purpose tag.

Default value is undefined.

Point_2 ParameterizationMesh_3::get_vertex_uv ( Vertex_const_handle vertex) const

Get/set the 2D position (u/v pair) of a vertex.

Default value is undefined.

bool ParameterizationMesh_3::is_vertex_parameterized ( Vertex_const_handle vertex) const

Get/set is parameterized field of vertex.

Default value is undefined.

Vertex_around_vertex_circulator ParameterizationMesh_3::vertices_around_vertex_begin	(	Vertex_handle	vertex,
		Vertex_handle	start_position = `Vertex_handle()`
	)

Get circulator over the vertices incident to vertex.

start_position defines the optional initial position of the circulator.

Definition

Design Pattern

Creation

Types

Operations

Member Typedef Documentation

Member Function Documentation