CGAL 6.1.1 - Surface Mesh Topology

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CGAL::Surface_mesh_topology::Path_on_surface< Mesh > Class Template Reference
Reference Manual » Classes

`#include <CGAL/Path_on_surface.h>`

## Definition

template<typename Mesh>
class CGAL::Surface_mesh_topology::Path_on_surface< Mesh >

The class `Path_on_surface` represents a walk in a mesh which is either a model of `CombinatorialMap`, a model of `GeneralizedMap` or a model of a `FaceGraph`.

Each object of this class is constructed from an external mesh on which the path should lie. A path is represented as a sequence of darts or halfedges, each one representing an oriented edge in the path. The class `Path_on_surface` behaves as a container for this sequence of darts/halfedges. Elements are added in the path one at a time to the path thanks to the `push_back()` method.

Template Parameters

  Mesh | a model of `CombinatorialMap`, `GeneralizedMap` or of `FaceGraph`

Examples
  Surface_mesh_topology/edgewidth_surface_mesh.cpp, Surface_mesh_topology/open_path_homotopy.cpp, Surface_mesh_topology/path_homotopy_double_torus.cpp, Surface_mesh_topology/path_homotopy_with_symbols.cpp, Surface_mesh_topology/path_homotopy_with_symbols_2.cpp, Surface_mesh_topology/path_simplicity_double_torus.cpp, Surface_mesh_topology/path_simplicity_double_torus_2.cpp, and Surface_mesh_topology/shortest_noncontractible_cycle.cpp.

## Public Types
typedef unspecified_type | halfedge_descriptor
| A handle to `Dart` for combinatorial/generalized maps, or a halfedge descriptor for models of the `FaceGraph` concept.

## Public Member Functions
| Path_on_surface (const Mesh &amesh)
| creates an empty path object which lies on `amesh`.
bool | is_empty () const
| returns `true` iff this path is empty
bool | is_closed () const
| returns `true` iff this path is closed.
bool | is_simple () const
| returns `true` iff this path does not pass twice through a same edge or a same vertex.
std::size_t | length () const
| returns the length of the path, i.e. its number of edges.
halfedge_descriptor | operator[] (std::size_t i) const
| returns the ith dart of the path.
void | clear ()
| clears this path.
bool | can_be_pushed (halfedge_descriptor hd, bool flip=false) const
| returns `true` iff `hd` can be added at the end of this path. If `flip` is true, the direction of `hd` is reversed before checking
void | push_back (halfedge_descriptor hd, bool flip=false)
| adds `hd` at the end of this path.
bool | can_be_pushed_by_index (std::size_t i) const
| returns `true` iff the dart/halfedge with index `i` can be added at the end of this path.
void | push_back_by_index (std::size_t i)
| adds the dart/halfedge with index `i` at the end of this path.
void | push_back_by_index (std::initializer_list< std::size_t > l)
| adds successively all dart/halfedges in `l` (a sequence of indices), at the end of the path.
void | extend_positive_turn (std::size_t nb)
| adds the dart/halfedge obtained by turning `nb` times around the target vertex of the last dart/halfedge in this path, in the positive circular order.
void | extend_negative_turn (std::size_t nb)
| adds the dart/halfedge obtained by turning `nb` times around the target vertex of the last dart/halfedge in this path, in the negative circular order.
bool | can_be_pushed_by_label (const std::string &l) const
| returns `true` iff the dart/halfedge with label `l` can be added at the end of this path.
void | push_back_by_label (const std::string &s)
| adds successively all darts/halfedges in `s` (a sequence of labels separated by spaces) at the end of this path.
Self & | operator+= (const Self &other)
| concatenates `other` to this path.
void | reverse ()
| reverses this path (i.e. negates its orientation).
void | generate_random_path (std::size_t length, Random &random=get_default_random())
| creates a random open path with `length` darts/halfedges.
void | generate_random_closed_path (std::size_t length, Random &random=get_default_random())
| creates a random closed path with at least `length` darts/halfedges.

## Member Function Documentation

## ◆ can_be_pushed_by_index()

template<typename Mesh >

bool CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::can_be_pushed_by_index | ( | std::size_t | i | ) | const

returns `true` iff the dart/halfedge with index `i` can be added at the end of this path.

If Mesh is a `Polyhedron_3`, takes time proportional to the number of darts/halfedges.

## ◆ can_be_pushed_by_label()

template<typename Mesh >

bool CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::can_be_pushed_by_label | ( | const std::string & | l | ) | const

returns `true` iff the dart/halfedge with label `l` can be added at the end of this path.

Precondition
  Mesh must be a model of `PolygonalSchema` concept.

## ◆ extend_negative_turn()

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::extend_negative_turn | ( | std::size_t | nb | ) |

adds the dart/halfedge obtained by turning `nb` times around the target vertex of the last dart/halfedge in this path, in the negative circular order.

To extend with a negative 1 turn thus amounts to extend with the composite pointer: `opposite(prev(opposite()))`.

Precondition
  !`is_empty()`

Examples
  Surface_mesh_topology/open_path_homotopy.cpp.

## ◆ extend_positive_turn()

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::extend_positive_turn | ( | std::size_t | nb | ) |

adds the dart/halfedge obtained by turning `nb` times around the target vertex of the last dart/halfedge in this path, in the positive circular order.

To extend with a positive 1 turn thus amounts to extend with the `next()` pointer. (A zero turn corresponds to the `opposite()` pointer.)

Precondition
  !`is_empty()`

Examples
  Surface_mesh_topology/open_path_homotopy.cpp, Surface_mesh_topology/path_homotopy_double_torus.cpp, Surface_mesh_topology/path_simplicity_double_torus.cpp, and Surface_mesh_topology/path_simplicity_double_torus_2.cpp.

## ◆ operator+=()

template<typename Mesh >

Self & CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::operator+= | ( | const Self & | other | ) |

concatenates `other` to this path.

Precondition
  the last vertex of this path should coincide with the first vertex of `other`.

## ◆ operator[]()

template<typename Mesh >

halfedge_descriptor CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::operator[] | ( | std::size_t | i | ) | const

returns the ith dart of the path.

Precondition
  i<`length()`.

## ◆ push_back()

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::push_back | ( | halfedge_descriptor | hd,
|  | bool | flip = `false`
| ) |  |

adds `hd` at the end of this path.

If `flip` is true, the opposite of `hd` is considered.

Precondition
  `can_be_pushed(hd)`

## ◆ push_back_by_index() [1/2]

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::push_back_by_index | ( | std::initializer_list< std::size_t > | l | ) |

adds successively all dart/halfedges in `l` (a sequence of indices), at the end of the path.

If Mesh is a `Polyhedron_3`, takes time proportional to the number of halfedges. For each index `i`, `can_be_pushed_by_index(i)` should be true.

## ◆ push_back_by_index() [2/2]

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::push_back_by_index | ( | std::size_t | i | ) |

adds the dart/halfedge with index `i` at the end of this path.

If Mesh is a `Polyhedron_3`, takes time proportional to the number of halfedges.

Precondition
  `can_be_pushed_by_index(i)`

Examples
  Surface_mesh_topology/open_path_homotopy.cpp, Surface_mesh_topology/path_homotopy_double_torus.cpp, Surface_mesh_topology/path_simplicity_double_torus.cpp, and Surface_mesh_topology/path_simplicity_double_torus_2.cpp.

## ◆ push_back_by_label()

template<typename Mesh >

void CGAL::Surface_mesh_topology::Path_on_surface< Mesh >::push_back_by_label | ( | const std::string & | s | ) |

adds successively all darts/halfedges in `s` (a sequence of labels separated by spaces) at the end of this path.

For each label, l, `can_be_pushed_by_label(l)` should be true.

Precondition
  Mesh must be a model of `PolygonalSchema` concept.

Examples
  Surface_mesh_topology/path_homotopy_with_symbols.cpp, and Surface_mesh_topology/path_homotopy_with_symbols_2.cpp.