CGAL 6.1 - 3D Simplicial Mesh Data Structures

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CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex > Class Template Reference
Reference Manual » Classes

`#include <CGAL/Mesh_complex_3_in_triangulation_3.h>`

## Definition

template<typename Tr, typename CornerIndex, typename CurveIndex>
class CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >

A data structure to represent and maintain a 3D complex embedded in a 3D triangulation.

The class `Mesh_complex_3_in_triangulation_3` implements a data structure to store the 3D restricted Delaunay triangulation used by a mesh generation process.

This class is a model of the concept `MeshComplexWithFeatures_3InTriangulation_3`.

Template Parameters

  Tr | can be instantiated with any 3D triangulation of CGAL provided that its vertex and cell base class are models of the concepts `SimplicialMeshVertexBase_3` and `SimplicialMeshCellBase_3`, respectively.
  CornerIndex | Type of indices for corners (i.e. \( 0\)–dimensional features) of the discretized geometric domain. It must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and `LessThanComparable`. It must match the `Corner_index` of the model of the `MeshDomainWithFeatures_3` concept when used for mesh generation.
  CurveIndex | Type of indices for curves (i.e. \( 1\)-dimensional features) of the discretized geometric domain. It must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and `LessThanComparable`. The default constructed value must be the value for an edge which does not approximate a 1-dimensional feature of the geometric domain. It must match the `Curve_index` types of the model of the `MeshDomainWithFeatures_3` concept when used for mesh generation.

Those two last template parameters default to `int`, so that they can be ignored if the domain used for mesh generation does not include 0 and 1-dimensionnal features (i.e is only a model of the concept `MeshDomain_3`).

Is model of
  `MeshComplexWithFeatures_3InTriangulation_3`

See also
  `CGAL::make_mesh_3()`
  `CGAL::refine_mesh_3()`
  `MeshComplex_3InTriangulation_3`
  `MeshComplexWithFeatures_3InTriangulation_3`
  `SimplicialMeshCellBase_3`,
  `SimplicialMeshVertexBase_3`

Examples
  SMDS_3/c3t3_example.cpp, and SMDS_3/tetrahedron_soup_to_c3t3_example.cpp.

## Public Member Functions
void | remove_isolated_vertices ()
| The tetrahedral mesh generation algorithm implemented in `CGAL::make_mesh_3()` and `CGAL::refine_mesh_3()` does not guarantee that all the points inserted by the algorithm are actually present in the final mesh.
template<typename OutputIterator >
OutputIterator | adjacent_vertices_in_complex (const Vertex_handle &v, OutputIterator out) const
| fills `out` with incident edges (1-dimensional features of `v`).
bool | has_incident_facets_in_complex (const Vertex_handle &v) const
| Returns true if the vertex `v` has is incident to at least a facet of the complex.

## Types
typedef Tr | Triangulation
typedef Tr::size_type | size_type
typedef Tr::Point | Point
typedef Tr::Edge | Edge
typedef Tr::Facet | Facet
typedef Tr::Vertex_handle | Vertex_handle
typedef Tr::Cell_handle | Cell_handle
typedef Tr::Vertex::Index | Index
| Index type.
typedef Tr::Cell::Surface_patch_index | Surface_patch_index
| Surface index type.
typedef Tr::Cell::Subdomain_index | Subdomain_index
| Subdomain index type.
typedef CornerIndex | Corner_index
| Corner index type.
typedef CurveIndex | Curve_index
| Curve index type.

## Traversal of the complex
typedef unspecified_type | Cells_in_complex_iterator
| Iterator type to visit the cells of the 3D complex.
typedef unspecified_type | Facets_in_complex_iterator
| Iterator type to visit the facets of the 2D complex.
typedef unspecified_type | Edges_in_complex_iterator
| Iterator type to visit the edges of the 1D complex.
typedef unspecified_type | Vertices_in_complex_iterator
| Iterator type to visit the vertices of the 0D complex.
typedef Iterator_range< unspecified_type > | Cells_in_complex
| Range type for iterating over all cells of the 3D complex, with a nested type iterator that has as value type `Cell_handle`.
typedef Iterator_range< unspecified_type > | Facets_in_complex
| Range type for iterating over all facets of the 2D complex, with a nested type iterator that has as value type `Facet`.
typedef Iterator_range< unspecified_type > | Edges_in_complex
| Range type for iterating over all cells of the 1D complex, with a nested type iterator that has as value type `Edge`.
typedef Iterator_range< unspecified_type > | Vertices_in_complex
| Range type for iterating over all vertices of the 0D complex, with a nested type iterator that has as value type `Vertex_handle`.

## Creation
| Mesh_complex_3_in_triangulation_3 ()
| Constructor builds an empty 3D complex.
| Mesh_complex_3_in_triangulation_3 (const Self &rhs)
| Copy constructor.
| Mesh_complex_3_in_triangulation_3 (Self &&rhs)
| Move constructor.
Self & | operator= (Self rhs)
| Assignment operator, also serves as move-assignment.
void | swap (Self &rhs)
| swaps `this` and `rhs`

## Access Functions
const Triangulation & | triangulation () const
| returns a const reference to the triangulation

## Modifiers
void | clear ()
| clears data of the complex
void | set_triangulation (const Triangulation &tr)
| sets the internal triangulation to `tr`
void | set_triangulation (Triangulation &&tr)
| sets the internal triangulation to `tr`
void | add_to_complex (const Cell_handle &cell, const Subdomain_index &index)
| adds cell `cell` to the 3D complex, with subdomain index `index`
void | add_to_complex (const Facet &facet, const Surface_patch_index &index)
| adds facet `facet` to the 2D complex, with surface index `index`
void | add_to_complex (const Cell_handle &cell, const int i, const Surface_patch_index &index)
| adds facet(`cell`, `i`) to the 2D complex, with surface index `index`
void | add_to_complex (const Edge &e, const Curve_index &index)
| adds edge `e` to complex, with curve index `index`
void | add_to_complex (const Vertex_handle &v1, const Vertex_handle &v2, const Curve_index &index)
| adds edge (`v1`, `v2`) to the 1D complex, with `Curve_index` `index`
void | add_to_complex (const Vertex_handle &v, const Corner_index &index)
| marks vertex `v` as a corner of the complex
void | remove_from_complex (const Cell_handle &cell)
| removes cell `cell` from the 3D complex
void | remove_from_complex (const Facet &facet)
| removes facet `facet` from the 2D complex
void | remove_from_complex (const Cell_handle &c, const int i)
| removes facet(`cell`, `i`) from the 2D complex
void | remove_from_complex (const Edge &e)
| removes edge `e` from the 1D complex
void | remove_from_complex (const Vertex_handle &v1, const Vertex_handle &v2)
| removes edge (v1,v2) from the 1D complex
void | remove_from_complex (const Vertex_handle &v)
| removes vertex `v` from the complex
void | set_index (const Vertex_handle &vertex, const Index &index) const
| sets the index of vertex `vertex` to `index`
void | set_surface_patch_index (const Facet &f, const Surface_patch_index &index)
| sets the surface index of facet `facet` to `index`
void | set_surface_patch_index (const Cell_handle &cell, const int i, const Surface_patch_index &index) const
| sets the surface index of facet(`cell`, `i`) to `index`
void | set_subdomain_index (const Cell_handle &cell, const Subdomain_index &index) const
| sets the subdomain index of cell `cell` to `index`
void | set_dimension (const Vertex_handle &vertex, int dimension) const
| sets the dimension of vertex `vertex` to `dimension`

## Queries on the identifier of the face complex including triangulation cells, facets, and vertices.
Index | index (const Vertex_handle &v) const
| returns the index of vertex `v`
Subdomain_index | subdomain_index (const Cell_handle &cell) const
| returns the subdomain index of cell `cell`
Surface_patch_index | surface_patch_index (const Facet &f) const
| returns the surface index of facet `f`
Surface_patch_index | surface_patch_index (const Cell_handle &cell, const int i) const
| returns the surface index of facet(`cell`, `i`)
int | in_dimension (const Vertex_handle &v) const
| returns the dimension of the lowest dimensional face of the input 3D complex that contains the vertex
Curve_index | curve_index (const Edge &e) const
| returns the curve index of edge `e`
Curve_index | curve_index (const Vertex_handle &v1, const Vertex_handle &v2) const
| returns the curve index of the edge formed by `v1` and `v2`
Corner_index | corner_index (const Vertex_handle &v) const
| returns the corner index of vertex `v`

## Queries on the faces of the embedded complex
size_type | number_of_cells_in_complex () const
| returns the number of cells which belong to the 3D complex
size_type | number_of_cells () const
| returns the number of cells which belong to the 3D complex
size_type | number_of_facets_in_complex () const
| returns the number of surface facets of the complex
size_type | number_of_facets () const
| returns the number of surface facets of the complex
size_type | number_of_edges_in_complex () const
| returns the number of edges of the complex
size_type | number_of_edges () const
| returns the number of edges of the complex
size_type | number_of_vertices_in_complex () const
| returns the number of corners of the complex
size_type | number_of_corners () const
| returns the number of corners of the complex
bool | is_in_complex (const Cell_handle &cell) const
| returns `true` if cell `cell` belongs to the 3D complex
bool | is_in_complex (const Facet &facet) const
| returns true if facet `facet` belongs to the 2D complex
bool | is_in_complex (const Cell_handle &cell, const int i) const
| returns true if facet (`cell`, `i`) belongs to the 2D complex
bool | is_in_complex (const Edge &e) const
| returns true if edge `e` belongs to the 1D complex
bool | is_in_complex (const Vertex_handle &v1, const Vertex_handle &v2) const
| returns true if edge (v1,v2) belongs to the 1D complex
bool | is_in_complex (const Vertex_handle &v) const
| returns true if `v` is a 0-dimensionnal feature in the complex

## I/O Functions
std::ostream & | output_boundary_to_off (std::ostream &out) const
| outputs the outer boundary of the entire domain, with facets oriented outward.
std::ostream & | output_boundary_to_off (std::ostream &out, Subdomain_index subdomain) const
| outputs the outer boundary of the selected subdomain, with facets oriented outward.
std::ostream & | output_facets_in_complex_to_off (std::ostream &out) const
| outputs the surface facets, with a consistent orientation at the interface of two subdomains.
void | output_to_medit (std::ostream &os) const
| outputs the mesh to `os` in Medit format.
void | output_to_maya (std::ostream &os, bool surfaceOnly=true) const

## Iterators
Cells_in_complex_iterator | cells_in_complex_begin () const
| returns a `Cells_in_complex_iterator` to the first cell of the 3D complex
Cells_in_complex_iterator | cells_in_complex_begin (const Subdomain_index &index) const
| returns a `Cells_in_complex_iterator` to the first cell of the 3D complex
Cells_in_complex_iterator | cells_in_complex_end () const
| returns the past-the-end iterator for the cells of the 3D complex
Facets_in_complex_iterator | facets_in_complex_begin () const
| returns a `Facets_in_complex_iterator` to the first facet of the 2D complex
Facets_in_complex_iterator | facets_in_complex_begin (const Surface_patch_index &index) const
| returns a `Facets_in_complex_iterator` to the first facet of the 2D complex
Facets_in_complex_iterator | facets_in_complex_end (const Surface_patch_index=Surface_patch_index()) const
| returns past-the-end iterator on facet of the 2D complex
Edges_in_complex_iterator | edges_in_complex_begin () const
| returns a `Edges_in_complex_iterator` to the first edge of the 1D complex
Edges_in_complex_iterator | edges_in_complex_begin (const Curve_index &index) const
| returns a `Edges_in_complex_iterator` to the first edge of the 1D complex
Edges_in_complex_iterator | edges_in_complex_end (const Curve_index &=Curve_index()) const
| returns past-the-end iterator on edges of the 1D complex
Vertices_in_complex_iterator | vertices_in_complex_begin () const
| returns a `Vertices_in_complex_iterator` to the first vertex of the 0D complex
Vertices_in_complex_iterator | vertices_in_complex_begin (const Corner_index &index) const
| returns a `Vertices_in_complex_iterator` to the first vertex of the 0D complex
Vertices_in_complex_iterator | vertices_in_complex_end () const
| returns past-the-end iterator on vertices of the 0D complex
Vertices_in_complex | vertices_in_complex () const
| returns a range of iterators over vertices of the 0D complex
Edges_in_complex | edges_in_complex () const
| returns a range of iterators over the edges of the 1D complex, starting at an arbitrary edge.
Facets_in_complex | facets_in_complex () const
| returns a range of iterators over the facets of the 2D complex, starting at an arbitrary facet.
Cells_in_complex | cells_in_complex () const
| returns a range of iterators over cells of the 3D complex.

## Member Function Documentation

## ◆ adjacent_vertices_in_complex()

template<typename Tr , typename CI_ , typename CSI_ >
template<typename OutputIterator >

OutputIterator CGAL::Mesh_complex_3_in_triangulation_3< Tr, CI_, CSI_ >::adjacent_vertices_in_complex | ( | const Vertex_handle & | v,
|  | OutputIterator | out
| ) |  | const

fills `out` with incident edges (1-dimensional features of `v`).

OutputIterator value type is std::pair<Vertex_handle,Curve_index>

Precondition
  v->in_dimension() < 2

## ◆ cells_in_complex()

template<typename Tr , typename CornerIndex , typename CurveIndex >

Cells_in_complex CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >::cells_in_complex | ( |  | ) | const

returns a range of iterators over cells of the 3D complex.

Returns an empty range when `triangulation().number_of_cells() == 0` or complex is empty.

Note
  The value type of `Cells_in_complex::iterator` is `Cell_handle`.

## ◆ edges_in_complex()

template<typename Tr , typename CornerIndex , typename CurveIndex >

Edges_in_complex CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >::edges_in_complex | ( |  | ) | const

returns a range of iterators over the edges of the 1D complex, starting at an arbitrary edge.

Returns an empty range when `t.dimension() < 2`.

## ◆ facets_in_complex()

template<typename Tr , typename CornerIndex , typename CurveIndex >

Facets_in_complex CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >::facets_in_complex | ( |  | ) | const

returns a range of iterators over the facets of the 2D complex, starting at an arbitrary facet.

Returns an empty range when `t.dimension() < 2`.

## ◆ remove_isolated_vertices()

template<typename Tr , typename CornerIndex , typename CurveIndex >

void CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >::remove_isolated_vertices | ( |  | ) |

The tetrahedral mesh generation algorithm implemented in `CGAL::make_mesh_3()` and `CGAL::refine_mesh_3()` does not guarantee that all the points inserted by the algorithm are actually present in the final mesh.

In most cases, all points are used, but if the geometry of the object has small features compared to the size of the simplices (triangles and tetrahedra), it might be that the Delaunay facets that are selected in the restricted Delaunay triangulation miss some vertices of the triangulation. The concurrent version of the tetrahedral mesh generation algorithm also inserts a small set of auxiliary vertices that belong to the triangulation but are isolated from the complex at the end of the meshing process.

This function removes these so-called isolated vertices, that belong to the triangulation but not to any simplex of the `C3T3`, from the triangulation.

## ◆ vertices_in_complex()

template<typename Tr , typename CornerIndex , typename CurveIndex >

Vertices_in_complex CGAL::Mesh_complex_3_in_triangulation_3< Tr, CornerIndex, CurveIndex >::vertices_in_complex | ( |  | ) | const

returns a range of iterators over vertices of the 0D complex

Note
  The value type of `Vertices_in_complex::iterator` is `Vertex_handle`.