CGAL 5.6.3 - 2D Conforming Triangulations and Meshes

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CGAL::Delaunay_mesher_2< CDT, Criteria > Class Template Reference
2D Conforming Triangulations and Meshes Reference

`#include <CGAL/Delaunay_mesher_2.h>`

## Definition

template<typename CDT, typename Criteria>
class CGAL::Delaunay_mesher_2< CDT, Criteria >

This class implements a 2D mesh generator.

Template Parameters

  CDT | must be a 2D constrained Delaunay triangulation, and type `CDT::Face` should be a model of the concept `DelaunayMeshFaceBase_2`. The geometric traits class of the instance of `CDT` has to be a model of the concept `DelaunayMeshTraits_2`.
  Criteria | must be a model of the concept `MeshingCriteria_2`. This traits class defines the shape and size criteria for the triangles of the mesh. `Criteria::Face_handle` has to be the same as `CDT::Face_handle`.

Using This Class

The constructor of the class `Delaunay_mesher_2` takes a reference to a `CDT` as an argument. A call to the refinement method `refine_mesh()` will refine the constrained Delaunay triangulation into a mesh satisfying the size and shape criteria specified in the traits class. Note that if, during the life time of the `Delaunay_mesher_2` object, the triangulation is externally modified, any further call to its member methods may crash. Consider constructing a new `Delaunay_mesher_2` object if the triangulation has been modified.

Meshing Domain

The domain to be mesh is defined by the constrained edges and a set of seed points. The constrained edges divides the plane into several connected components. The mesh domain is either the union of the bounded connected components including at least one seed, or the union of the bounded connected components that do no contain any seed. Note that the unbounded component of the plane is never meshed.

See also
  `CGAL::lloyd_optimize_mesh_2`

Examples
  Mesh_2/mesh_class.cpp, and Mesh_2/mesh_optimization.cpp.

## Types
typedef CDT::Geom_traits | Geom_traits
| the geometric traits class.
typedef unspecified_type | Seeds_iterator
| const iterator over defined seeds.

## Creation
| Delaunay_mesher_2 (CDT &t, Criteria criteria=Criteria())
| creates a new mesher, working on `t`, with meshing criteria `criteria`.

## Seeds functions
The following functions are used to define seeds.
void | clear_seeds ()
| sets seeds to the empty set.
template<class InputIterator >
void | set_seeds (InputIterator begin, InputIterator end, const bool mark=false)
| sets seeds to the sequence `[begin, end)`.
Seeds_const_iterator | seeds_begin () const
| Start of the seeds sequence.
Seeds_const_iterator | seeds_end () const
| Past the end of the seeds sequence.

## Meshing methods
The function `set_criteria()` scans all faces to recalculate the list of bad faces, that are faces not conforming to the meshing criteria. This function actually has an optional argument that permits to prevent this recalculation. The filling of the list of bad faces can then be done by a call to `set_bad_faces`.
void | refine_mesh ()
| refines the constrained Delaunay triangulation into a mesh satisfying the criteria defined by the traits.
const Criteria & | get_criteria ()
| returns a const reference to the criteria traits object.
void | set_criteria (Criteria criteria)
| assigns `criteria` to the criteria traits object.
void | set_criteria (Criteria criteria, bool recalculate_bad_faces)
| assigns `criteria` to the criteria traits object.
template<class InputIterator >
void | set_bad_faces (InputIterator begin, InputIterator end)
| This method permits to set the list of bad triangles directly, from the sequence `[begin, end)`, so that the algorithm will not scan the whole set of triangles to find bad ones.

## Step by Step Operations
The `Delaunay_mesher_2` class allows, for debugging or demos, to play the meshing algorithm step by step, using the following methods.
void | init ()
| This method must be called just before the first call to the following step by step refinement method, that is when all vertices and constrained edges have been inserted into the constrained Delaunay triangulation.
bool | is_refinement_done ()
| Tests if the step by step refinement algorithm is done.
bool | step_by_step_refine_mesh ()
| Applies one step of the algorithm, by inserting one point, if the algorithm is not done.

## Member Typedef Documentation

## ◆ Seeds_iterator

template<typename CDT , typename Criteria >

typedef unspecified_type CGAL::Delaunay_mesher_2< CDT, Criteria >::Seeds_iterator

const iterator over defined seeds.

Its value type is `Geom_traits::Point_2`.

## Member Function Documentation

## ◆ clear_seeds()

template<typename CDT , typename Criteria >

void CGAL::Delaunay_mesher_2< CDT, Criteria >::clear_seeds | ( |  | ) |

sets seeds to the empty set.

All finite connected components of the constrained triangulation will be refined.

## ◆ init()

template<typename CDT , typename Criteria >

void CGAL::Delaunay_mesher_2< CDT, Criteria >::init | ( |  | ) |

This method must be called just before the first call to the following step by step refinement method, that is when all vertices and constrained edges have been inserted into the constrained Delaunay triangulation.

It must be called again before any subsequent calls to the step by step refinement method if new vertices or constrained edges have been inserted since the last call.

## ◆ is_refinement_done()

template<typename CDT , typename Criteria >

bool CGAL::Delaunay_mesher_2< CDT, Criteria >::is_refinement_done | ( |  | ) |

Tests if the step by step refinement algorithm is done.

If it returns `true`, the following calls to `step_by_step_refine_mesh` will not insert any points, until some new constrained segments or points are inserted in the triangulation and `init` is called again.

## ◆ set_bad_faces()

template<typename CDT , typename Criteria >
template<class InputIterator >

void CGAL::Delaunay_mesher_2< CDT, Criteria >::set_bad_faces | ( | InputIterator | begin,
|  | InputIterator | end
| ) |  |

This method permits to set the list of bad triangles directly, from the sequence `[begin, end)`, so that the algorithm will not scan the whole set of triangles to find bad ones.

To use if there is a non-naive way to find bad triangles.

Template Parameters

  InputIterator | must be an input iterator with value type `Face_handle`.

## ◆ set_criteria()

template<typename CDT , typename Criteria >

void CGAL::Delaunay_mesher_2< CDT, Criteria >::set_criteria | ( | Criteria | criteria,
|  | bool | recalculate_bad_faces
| ) |  |

assigns `criteria` to the criteria traits object.

If `recalculate_bad_faces` is `false`, the list of bad faces is let empty and the function `set_bad_faces()` should be called before `refine_mesh`.

## ◆ set_seeds()

template<typename CDT , typename Criteria >
template<class InputIterator >

void CGAL::Delaunay_mesher_2< CDT, Criteria >::set_seeds | ( | InputIterator | begin,
|  | InputIterator | end,
|  | const bool | mark = `false`
| ) |  |

sets seeds to the sequence `[begin, end)`.

If `mark==true`, the mesh domain is the union of the bounded connected components including at least one seed. If `mark==false`, the domain is the union of the bounded components including no seed. Note that the unbounded component of the plane is never meshed.

Template Parameters

  InputIterator | must be an input iterator with value type `Geom_traits::Point_2`.

## ◆ step_by_step_refine_mesh()

template<typename CDT , typename Criteria >

bool CGAL::Delaunay_mesher_2< CDT, Criteria >::step_by_step_refine_mesh | ( |  | ) |

Applies one step of the algorithm, by inserting one point, if the algorithm is not done.

Returns `false` iff no point has been inserted because the algorithm is done.