\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Halfedge Data Structures

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CGAL::HalfedgeDS_decorator< HDS > Class Template Reference
Decorators

`#include <CGAL/HalfedgeDS_decorator.h>`

## Inherits from

CGAL::HalfedgeDS_items_decorator< HDS >.

## Definition

The class `CGAL::HalfedgeDS_items_decorator<HDS>` provides additional functions for vertices, halfedges, and faces of a halfedge data structure without knowing the containing halfedge data structure.

The class `CGAL::HalfedgeDS_decorator<HDS>` stores a reference to the halfedge data structure and provides functions that modify the halfedge data structure, for example Euler-operators. The class `CGAL::HalfedgeDS_const_decorator<HDS>` stores a const reference to the halfedge data structure. It contains non-modifying functions, for example the test for validness of the data structure.

All these additional functions take care of the different capabilities a halfedge data structure may have or may not have. The functions evaluate the type tags of the halfedge data structure to decide on the actions. If a particular feature is not supported nothing is done. Note that for example the creation of new halfedges is mandatory for all halfedge data structures and will not appear here again.

See Also
  `CGAL::HalfedgeDS_items_decorator<HDS>`
  `CGAL::HalfedgeDS_const_decorator<HDS>`

Example

The following program fragment illustrates the implementation of the Euler operator `split_vertex()` for a simplified polyhedron class.

template <class Traits>
namespace CGAL {
class Polyhedron {
typedef HalfedgeDS_default<Traits> HDS;
HDS hds;
public:
// ...
Halfedge_handle split_vertex( Halfedge_handle h, Halfedge_handle g) {
HalfedgeDS_decorator<HDS> D(hds);
// Stricter preconditions than for HalfedgeDS only.
CGAL_precondition( D.get_vertex(h) == D.get_vertex(g));
CGAL_precondition( h != g);
return D.split_vertex( h, g);
}
};
}

Examples:
  HalfedgeDS/hds_prog_compact.cpp, HalfedgeDS/hds_prog_compact2.cpp, HalfedgeDS/hds_prog_default.cpp, HalfedgeDS/hds_prog_edge_iterator.cpp, HalfedgeDS/hds_prog_graph.cpp, HalfedgeDS/hds_prog_graph2.cpp, HalfedgeDS/hds_prog_halfedge_iterator.cpp, and HalfedgeDS/hds_prog_vector.cpp.

## Creation
| HalfedgeDS_decorator (HDS &hds)
| keeps internally a reference to `hds`.

## Creation of New Items
Vertex_handle | vertices_push_back (const Vertex &v)
| appends a copy of `v` to `hds` if vertices are supported. More...
Face_handle | faces_push_back (const Face &f)
| appends a copy of `f` to `hds` if faces are supported. More...

## Creation of New Composed Items
Halfedge_handle | create_loop ()
| returns handle of a halfedge from a newly created loop in `hds` consisting of a single closed edge, one vertex and two faces (if supported respectively).
Halfedge_handle | create_segment ()
| returns a halfedge from a newly created segment in `hds` consisting of a single open edge, two vertices and one face (if supported respectively).

## Removal of Elements
The following member functions do not update affected incidence relations except if mentioned otherwise.
void | vertices_pop_front ()
| removes the first vertex if vertices are supported. More...
void | vertices_pop_back ()
| removes the last vertex if vertices are supported.
void | vertices_erase (Vertex_handle v)
| removes the vertex `v` if vertices are supported. More...
void | vertices_erase (Vertex_handle first, Vertex_handle last)
| removes the range `[first,last)` if vertices are supported. More...
void | faces_pop_front ()
| removes the first face if faces are supported. More...
void | faces_pop_back ()
| removes the last face if faces are supported.
void | faces_erase (Face_handle f)
| removes the face `f` if faces are supported. More...
void | faces_erase (Face_handle first, Face_handle last)
| removes the range `[first,last)` if faces are supported. More...
void | erase_face (Halfedge_handle h)
| removes the face incident to `h` from `hds` and changes all halfedges incident to the face into border edges or removes them from the halfedge data structure if they were already border edges. More...
void | erase_connected_component (Halfedge_handle h)
| removes the vertices, halfedges, and faces that belong to the connected component of `h`. More...
unsigned int | keep_largest_connected_components (unsigned int nb_components_to_keep)
| Erases the small connected components and the isolated vertices. More...

## Modifying Functions (For Border Halfedges)
void | make_hole (Halfedge_handle h)
| removes the face incident to `h` from `hds` and creates a hole. More...
Halfedge_handle | fill_hole (Halfedge_handle h)
| fills the hole incident to `h` with a new face from `hds`. More...
Halfedge_handle | fill_hole (Halfedge_handle h, const Face &f)
| fills the hole incident to `h` with a copy of face `f`. More...
Halfedge_handle | add_face_to_border (Halfedge_handle h, Halfedge_handle g)
| extends the surface with a new face from `hds` into the hole incident to `h` and `g`. More...
Halfedge_handle | add_face_to_border (Halfedge_handle h, Halfedge_handle g, const Face &f)
| extends the surface with a copy of face `f` into the hole incident to `h` and `g`. More...

## Modifying Functions (Euler Operators)
The following Euler operations modify consistently the combinatorial structure of the halfedge data structure. The geometry remains unchanged. Note that well known graph operations are also captured with these Euler operators, for example an edge contraction is equal to a `join_vertex()` operation, or an edge removal to `join_face()`. Given a halfedge data structure `hds` and a halfedge handle `h` four special applications of the Euler operators are worth mentioning: `split_vertex(h,h)` results in an antenna emanating from the tip of `h`; `split_vertex(h,h->next()->opposite())` results in an edge split of the halfedge `h->next` with a new vertex in-between; `split_face(h,h)` results in a loop directly following `h`; and `split_face(h,h->next())` results in a bridge parallel to the halfedge `h->next` with a new face in-between.
Halfedge_handle | split_face (Halfedge_handle h, Halfedge_handle g)
| splits the face incident to `h` and `g` into two faces with a new diagonal between the two vertices denoted by `h` and `g` respectively. More...
Halfedge_handle | join_face (Halfedge_handle h)
| joins the two faces incident to `h`. More...
Halfedge_handle | split_vertex (Halfedge_handle h, Halfedge_handle g)
| splits the vertex incident to `h` and `g` into two vertices and connects them with a new edge. More...
Halfedge_handle | join_vertex (Halfedge_handle h)
| joins the two vertices incident to `h`. More...
Halfedge_handle | create_center_vertex (Halfedge_handle h)
| barycentric triangulation of `h->face()`. More...
Halfedge_handle | erase_center_vertex (Halfedge_handle g)
| reverses `create_center_vertex`. More...
Halfedge_handle | split_loop (Halfedge_handle h, Halfedge_handle i, Halfedge_handle j)
| cuts the halfedge data structure into two parts along the cycle `(h,i,j)`. More...
Halfedge_handle | join_loop (Halfedge_handle h, Halfedge_handle g)
| glues the boundary of the two faces denoted by `h` and `g` together and returns `h`. More...

## Validness Checks
These operations are the same as for `CGAL::HalfedgeDS_const_decorator<HDS>`.
bool | is_valid (bool verbose=false, int level=0) const
bool | normalized_border_is_valid (bool verbose=false) const

## Miscellaneous
void | inside_out ()
| reverses face orientations. More...

## Additional Inherited Members
Private Types inherited from CGAL::HalfedgeDS_items_decorator< HDS >
typedef unspecified_type | HalfedgeDS
| halfedge data structure.
typedef unspecified_type | Vertex
| vertex type of `HalfedgeDS`.
typedef unspecified_type | Halfedge
| halfedge type of `HalfedgeDS`.
typedef unspecified_type | Face
| face type of `HalfedgeDS`.
typedef unspecified_type | Vertex_handle
typedef unspecified_type | Halfedge_handle
typedef unspecified_type | Face_handle
typedef unspecified_type | Vertex_iterator
typedef unspecified_type | Halfedge_iterator
typedef unspecified_type | Face_iterator
typedef unspecified_type | size_type
typedef unspecified_type | difference_type
typedef unspecified_type | iterator_category
typedef unspecified_type | Supports_vertex_halfedge
typedef unspecified_type | Supports_halfedge_prev
typedef unspecified_type | Supports_halfedge_vertex
typedef unspecified_type | Supports_halfedge_face
typedef unspecified_type | Supports_face_halfedge
typedef unspecified_type | Supports_removal
Private Member Functions inherited from CGAL::HalfedgeDS_items_decorator< HDS >
| HalfedgeDS_items_decorator ()
| default constructor.
Halfedge_handle | get_vertex_halfedge (Vertex_handle v)
| returns the incident halfedge of `v` if supported, `Halfedge_handle()` otherwise.
Vertex_handle | get_vertex (Halfedge_handle h)
| returns the incident vertex of `h` if supported, `Vertex_handle()` otherwise.
Halfedge_handle | get_prev (Halfedge_handle h)
| returns the previous halfedge of `h` if supported, `Halfedge_handle()` otherwise.
Halfedge_handle | find_prev (Halfedge_handle h)
| returns the previous halfedge of `h`. More...
Halfedge_handle | find_prev_around_vertex (Halfedge_handle h)
| returns the previous halfedge of `h`. More...
Face_handle | get_face (Halfedge_handle h)
| returns the incident face of `h` if supported, `Face_handle()` otherwise.
Halfedge_handle | get_face_halfedge (Face_handle f)
| returns the incident halfedge of `f` if supported, `Halfedge_handle()` otherwise.
void | close_tip (Halfedge_handle h) const
| makes `h->opposite()` the successor of `h`.
void | close_tip (Halfedge_handle h, Vertex_handle v) const
| makes `h->opposite()` the successor of `h` and sets the incident vertex of `h` to `v`.
void | insert_tip (Halfedge_handle h, Halfedge_handle v) const
| inserts the tip of the edge `h` into the halfedges around the vertex pointed to by `v`. More...
void | remove_tip (Halfedge_handle h) const
| removes the edge `h->next()->opposite()` from the halfedge circle around the vertex referred to by `h`. More...
void | insert_halfedge (Halfedge_handle h, Halfedge_handle f) const
| inserts the halfedge `h` between `f` and `f->next()`. More...
void | remove_halfedge (Halfedge_handle h) const
| removes edge `h->next()` from the halfedge circle around the face referred to by `h`. More...
void | set_vertex_in_vertex_loop (Halfedge_handle h, Vertex_handle v) const
| loops around the vertex incident to `h` and sets all vertex pointers to `v`. More...
void | set_face_in_face_loop (Halfedge_handle h, Face_handle f) const
| loops around the face incident to `h` and sets all face pointers to `f`. More...
Halfedge_handle | flip_edge (Halfedge_handle h) const
| performs an edge flip. More...
void | set_vertex_halfedge (Vertex_handle v, Halfedge_handle g) const
| sets the incident halfedge of `v` to `g`.
void | set_vertex_halfedge (Halfedge_handle h) const
| sets the incident halfedge of the vertex `v` to `h`.
void | set_vertex (Halfedge_handle h, Vertex_handle v) const
| sets the incident vertex of `h` to `v`.
void | set_prev (Halfedge_handle h, Halfedge_handle g) const
| sets the previous link of `h` to `g`.
void | set_face (Halfedge_handle h, Face_handle f) const
| sets the incident face of `h` to `f`.
void | set_face_halfedge (Face_handle f, Halfedge_handle g) const
| sets the incident halfedge of `f` to `g`.
void | set_face_halfedge (Halfedge_handle h) const
| sets the incident halfedge of the face `f` to `h`.

## Member Function Documentation

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::add_face_to_border | ( | Halfedge_handle | h,
|  | Halfedge_handle | g
| ) |  |

extends the surface with a new face from `hds` into the hole incident to `h` and `g`.

It creates a new edge connecting the vertex denoted by `g` with the vertex denoted by `h` and fills this separated part of the hole with a new face, such that the new face is incident to `g`. Returns the new halfedge that is incident to the new face.

Precondition
  `h != Halfedge_handle()`, `g != Halfedge_handle()`, `h->is_border()`, `g->is_border()` and `g` can be reached along the hole starting with `h`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::add_face_to_border | ( | Halfedge_handle | h,
|  | Halfedge_handle | g,
|  | const Face & | f
| ) |  |

extends the surface with a copy of face `f` into the hole incident to `h` and `g`.

It creates a new edge connecting the tip of `g` with the tip of `h` and fills this separated part of the hole with a copy of face `f`, such that the new face is incident to `g`. Returns the new halfedge that is incident to the new face.

Precondition
  `h != Halfedge_handle()`, `g != Halfedge_handle()`, `h->is_border()`, `g->is_border()` and `g` can be reached along the hole starting with `h`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::create_center_vertex | ( | Halfedge_handle | h) |  |

barycentric triangulation of `h->face()`.

Creates a new vertex, a copy of `h->vertex()`, and connects it to each vertex incident to `h->face()` splitting `h->face()` into triangles. `h` remains incident to the original face, all other triangles are copies of this face. Returns the halfedge `h->next()` after the operation, i.e., a halfedge pointing to the new vertex. The time is proportional to the size of the face.

Precondition
  `h` is not a border halfedge.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::erase_center_vertex | ( | Halfedge_handle | g) |  |

reverses `create_center_vertex`.

Erases the vertex pointed to by `g` and all incident halfedges thereby merging all incident faces. Only `g->face()` remains. The neighborhood of `g->vertex()` may not be triangulated, it can have larger faces. Returns the halfedge `g->prev()`. Thus, the invariant `h == erase_center_vertex( create_center_vertex(h))` holds if `h` is not a border halfedge. The time is proportional to the sum of the size of all incident faces.

Precondition
  None of the incident faces of `g->vertex()` is a hole. There are at least two distinct faces incident to the faces that are incident to `g->vertex()`. (This prevents the operation from collapsing a volume into two faces glued together with opposite orientations, such as would happen with any vertex of a tetrahedron.)

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::erase_connected_component | ( | Halfedge_handle | h) |  |

removes the vertices, halfedges, and faces that belong to the connected component of `h`.

Precondition
  For all halfedges `g` in the connected component `g.next() != Halfedge_handle()`.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::erase_face | ( | Halfedge_handle | h) |  |

removes the face incident to `h` from `hds` and changes all halfedges incident to the face into border edges or removes them from the halfedge data structure if they were already border edges.

If this creates isolated vertices they get removed as well. See `make_hole()` for a more specialized variant.

Precondition
  `h->is_border() == false`.

If faces are supported, `Supports_removal`must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::faces_erase | ( | Face_handle | f) |  |

removes the face `f` if faces are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::faces_erase | ( | Face_handle | first,
|  | Face_handle | last
| ) |  |

removes the range `[first,last)` if faces are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::faces_pop_front | ( | ) |  |

removes the first face if faces are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

Face_handle CGAL::HalfedgeDS_decorator< HDS >::faces_push_back | ( | const Face & | f) |  |

appends a copy of `f` to `hds` if faces are supported.

Returns a handle of the new face, or `Face_handle()` otherwise.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::fill_hole | ( | Halfedge_handle | h) |  |

fills the hole incident to `h` with a new face from `hds`.

Returns `h`.

Precondition
  `h != Halfedge_handle()` and `h->is_border()`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::fill_hole | ( | Halfedge_handle | h,
|  | const Face & | f
| ) |  |

fills the hole incident to `h` with a copy of face `f`.

Returns `h`.

Precondition
  `h != Halfedge_handle()` and `h->is_border()`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::inside_out | ( | ) |  |

reverses face orientations.

Precondition
  `is_valid()` of level three.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::join_face | ( | Halfedge_handle | h) |  |

joins the two faces incident to `h`.

The face incident to `h->opposite()` gets removed from `hds`. Both faces might be holes. Returns the predecessor of `h` around the face. The invariant `join_face( split_face( h, g))` returns `h` and keeps the data structure unchanged. The time is proportional to the size of the face removed and the time to compute `h->prev()`.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::join_loop | ( | Halfedge_handle | h,
|  | Halfedge_handle | g
| ) |  |

glues the boundary of the two faces denoted by `h` and `g` together and returns `h`.

Both faces and the vertices along the face denoted by `g` gets removed. Both faces may be holes. The invariant `join_loop( h, split_loop( h, i, j))` returns `h` and keeps the data structure unchanged.

Precondition
  The faces denoted by `h` and `g` are different and have equal degree (i.e., number of edges).

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::join_vertex | ( | Halfedge_handle | h) |  |

joins the two vertices incident to `h`.

The vertex denoted by `h->opposite()` gets removed by `hds`. Returns the predecessor of `h` around the vertex, i.e., `h->opposite()->prev()`. The invariant `join_vertex( split_vertex( h, g))` returns `h` and keeps the polyhedron unchanged. The time is proportional to the degree of the vertex removed and the time to compute `h->prev()` and `h->opposite()->prev()`.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

unsigned int CGAL::HalfedgeDS_decorator< HDS >::keep_largest_connected_components | ( | unsigned int | nb_components_to_keep) |  |

Erases the small connected components and the isolated vertices.

Keep `nb_components_to_keep` largest connected components. Returns the number of connected components erased (ignoring isolated vertices).

`Supports_removal` must be `CGAL::Tag_true`, `Supports_vertex_halfedge` must be `CGAL::Tag_true` and `Supports_halfedge_vertex` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::make_hole | ( | Halfedge_handle | h) |  |

removes the face incident to `h` from `hds` and creates a hole.

Precondition
  `h != Halfedge_handle()` and `!(h->is_border())`.

If faces are supported, `Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::split_face | ( | Halfedge_handle | h,
|  | Halfedge_handle | g
| ) |  |

splits the face incident to `h` and `g` into two faces with a new diagonal between the two vertices denoted by `h` and `g` respectively.

The second (new) face obtained from `hds` is a copy of the first face. Returns `h->next()` after the operation, i.e., the new diagonal. The new face is to the right of the new diagonal, the old face is to the left. The time is proportional to the distance from `h` to `g` around the face.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::split_loop | ( | Halfedge_handle | h,
|  | Halfedge_handle | i,
|  | Halfedge_handle | j
| ) |  |

cuts the halfedge data structure into two parts along the cycle `(h,i,j)`.

Three new vertices (one copy for each vertex in the cycle) and three new halfedges (one copy for each halfedge in the cycle), and two new triangles are created. `h,i,j` will be incident to the first new triangle. The return value will be the halfedge incident to the second new triangle which is the copy of `h-opposite()`.

Precondition
  `h,i,j` denote distinct, consecutive vertices of the halfedge data structure and form a cycle: i.e., `h->vertex() == i->opposite()->vertex()`, \(\ldots\) , `j->vertex() == h->opposite()->vertex()`.

template<typename HDS >

Halfedge_handle CGAL::HalfedgeDS_decorator< HDS >::split_vertex | ( | Halfedge_handle | h,
|  | Halfedge_handle | g
| ) |  |

splits the vertex incident to `h` and `g` into two vertices and connects them with a new edge.

The second (new) vertex obtained from `hds` is a copy of the first vertex. Returns `h->next()->opposite()` after the operation, i.e., the new edge in the orientation towards the new vertex. The time is proportional to the distance from `h` to `g` around the vertex.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::vertices_erase | ( | Vertex_handle | v) |  |

removes the vertex `v` if vertices are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::vertices_erase | ( | Vertex_handle | first,
|  | Vertex_handle | last
| ) |  |

removes the range `[first,last)` if vertices are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

void CGAL::HalfedgeDS_decorator< HDS >::vertices_pop_front | ( | ) |  |

removes the first vertex if vertices are supported.

`Supports_removal` must be `CGAL::Tag_true`.

template<typename HDS >

Vertex_handle CGAL::HalfedgeDS_decorator< HDS >::vertices_push_back | ( | const Vertex & | v) |  |

appends a copy of `v` to `hds` if vertices are supported.

Returns a handle of the new vertex, or `Vertex_handle()` otherwise.