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CGAL 5.3 - 2D Triangulations
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CGAL 5.3 - 2D Triangulations
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#include <CGAL/Constrained_triangulation_plus_2.h>
Tr.
The class Constrained_triangulation_plus_2<Tr> provides a constrained triangulation with an additional data structure that keeps track of the input constraints and of their refinement in the triangulation.
The class Constrained_triangulation_plus_2<Tr> inherits from its template parameter Tr, which has to be instantiated by a constrained or constrained Delaunay triangulation. The intersection tag of the base class determines whether intersecting input constraints are supported or not. When intersections of input constraints are supported, the base class constructs a triangulation of the arrangement of the constraints, introducing new vertices at each proper intersection point.
The data structure maintains for each input constraint the sequence of vertices on this constraint. These vertices are either vertices of the input constraint or intersection points.
The triangulation also enables the retrieval of the set of subconstraints of the triangulation (not ordered along constraints). It further enables the retrieval of the set of input constraints that induce a subconstraint. As it is straightforward to obtain a subconstraint from a constrained edge e, one can obtain the input constraints which induce e.
| Tr | must be either a CGAL::Constrained_triangulation_2 or a CGAL::Constrained_Delaunay_triangulation_2 |
Classes | |
| class | Context |
| A context enables the access to the vertices of a constraint that pass through a subconstraint. More... | |
Related Functions | |
(Note that these are not member functions.) | |
| template<typename Tr > | |
| std::ostream & | operator<< (std::ostream &os, const Constrained_triangulation_plus_2< Tr > &ctp) |
Writes the triangulation as for Tr, then writes one constraint per line, starting with the number of vertices and the indices of the vertices of the constraint. | |
| template<typename Tr > | |
| std::istream & | operator>> (std::istream &is, Constrained_triangulation_plus_2< Tr > &ctp) |
Reads a triangulation from stream is and assigns it to the triangulation. | |
Types | |
| typedef Tr | Triangulation |
| The triangulation base class. | |
| typedef Tr::Intersection_tag | Intersection_tag |
The intersection tag as defined in Tr. | |
| typedef unspecified_type | Constraint_id |
| The identifier of a polyline constraint. More... | |
| typedef unspecified_type | Constraint_iterator |
| An iterator to visit all the input constraints. More... | |
| typedef Iterator_range< Constraint_iterator > | Constraints |
| A range type for iterating over all constraints. | |
| typedef std::pair< Vertex_handle, Vertex_handle > | Subconstraint |
A subconstraint is a pair of vertices that correspond to an Edge. | |
| typedef unspecified_type | Subconstraint_iterator |
| An iterator to visit all the subconstraints of the triangulation. More... | |
| typedef Iterator_range< Subconstraint_iterator > | Subconstraints |
| A range type for iterating over all subconstraints. | |
| typedef unspecified_type | Vertices_in_constraint_iterator |
| An iterator on the vertices of the chain of subconstraints representing a constraint. More... | |
| typedef unspecified_type | Context_iterator |
| An iterator on constraints enclosing a given subconstraint. More... | |
| typedef Iterator_range< Context_iterator > | Contexts |
| range type for iterating over contexts. | |
Creation | |
| Constrained_triangulation_plus_2 (const Geom_traits >=Geom_traits()) | |
| Introduces an empty triangulation. | |
| Constrained_triangulation_plus_2 (const Constrained_triangulation_plus_2 &ct) | |
| Copy constructor. | |
| template<class ConstraintIterator > | |
| Constrained_triangulation_plus_2 (ConstraintIterator first, ConstraintIterator last, const Geom_traits >=Geom_traits()) | |
Introduces a constrained triangulation from the constraints in the range [first,last). More... | |
Assignment | |
| Constrained_triangulation_plus_2 | operator= (const Constrained_triangulation_plus_2 &tr) |
| Assignment. More... | |
| void | swap (Constrained_triangulation_plus_2 tr) |
The triangulations tr and this triangulation are swapped. More... | |
Insertion and Removal | |
The class | |
| Vertex_handle | insert (const Point &p, Face_handle start=Face_handle()) |
inserts point p as a vertex of the triangulation. | |
| Vertex_handle | insert (const Point &p, Locate_type lt, Face_handle loc, int li) |
inserts point p in the triangulation at the location given by (lt,loc,i). More... | |
| Vertex_handle | push_back (const Point &p) |
Equivalent to insert(p). | |
| template<class PointIterator > | |
| size_type | insert (PointIterator first, PointIterator last) |
inserts the points in the range [first,last). More... | |
| Constraint_id | insert_constraint (Point a, Point b) |
inserts the constraint segment ab in the triangulation. More... | |
| void | push_back (const std::pair< Point, Point > &c) |
inserts the constraint c. | |
| Constraint_id | insert_constraint (Vertex_handle va, Vertex_handle vb) |
inserts a constraint whose endpoints are the vertices pointed by va and vb in the triangulation. More... | |
| template<class PointIterator > | |
| Constraint_id | insert_constraint (PointIterator first, PointIterator last, bool close=false) |
inserts a polyline defined by the points in the range [first,last) and returns the constraint id. More... | |
| template<class ConstraintIterator > | |
| std::size_t | insert_constraints (ConstraintIterator first, ConstraintIterator last) |
inserts the constraints in the range [first,last). More... | |
| template<class PointIterator , class IndicesIterator > | |
| std::size_t | insert_constraints (PointIterator points_first, PointIterator points_last, IndicesIterator indices_first, IndicesIterator indices_last) |
| Same as above except that each constraint is given as a pair of indices of the points in the range [points_first, points_last). More... | |
| void | split_subconstraint_graph_into_constraints (const std::function< bool(Vertex_handle)> &is_terminal) |
| splits into constraints the graph of subconstraints. More... | |
| void | remove_constraint (Constraint_id cid) |
removes the constraint cid, without removing the points from the triangulation. | |
Access | |
| Constraint_iterator | constraints_begin () const |
returns a Constraint_iterator that points at the first constraint of the triangulation. | |
| Constraint_iterator | constraints_end () const |
| returns the past-the-end iterator of the constraints of the triangulation. | |
| Subconstraints | constraints () const |
| returns a range of constraints. | |
| Subconstraint_iterator | subconstraints_begin () const |
returns a Subconstraint_iterator pointing at the first subconstraint of the triangulation. | |
| Subconstraint_iterator | subconstraints_end () const |
| returns the past-the-end iterator of the subconstraints of the triangulation. | |
| Subconstraints | subconstraints () const |
| returns a range of subconstraints. | |
| int | number_of_enclosing_constraints (Vertex_handle va, Vertex_handle vb) const |
returns the number of constraints enclosing the subconstraint (va,vb). More... | |
| Context | context (Vertex_handle va, Vertex_handle vb) const |
returns the Context relative to one of the constraints enclosing the subconstraint (va,vb). More... | |
| Context_iterator | contexts_begin (Vertex_handle va, Vertex_handle vb) const |
returns an iterator pointing at the first Context of the sequence of contexts corresponding to the constraints enclosing the subconstraint (va,vb). More... | |
| Context_iterator | contexts_end (Vertex_handle va, Vertex_handle vb) const |
returns an iterator past the end Context of the sequence of contexts corresponding to the constraints enclosing the subconstraint (va,vb). More... | |
| Contexts | contexts (Vertex_handle va, Vertex_handle vb) const |
| returns a range of contexts. | |
| Vertices_in_constraint_iterator | vertices_in_constraint_begin (Constraint_id cid) const |
returns an iterator on the first vertex on the constraint cid. | |
| Vertices_in_constraint_iterator | vertices_in_constraint_end (Constraint_id cid) const |
returns an iterator past the last vertex on the constraint cid. | |
| Vertices_in_constraint | vertices_in_constraint (Constraint_id cid) const |
returns a range of the vertices on the constraint cid. | |
Polyline Simplification | |
Advanced
The polyline simplification algorithm described in Chapter Chapter_2D_Polyline_simplification operates on polyline constraints. The algorithm removes in each simplification step a vertex of a constraint and at the same time from the triangulation. The class It enables the simplification algorithm to compute the error introduced by each simplification step: it is the distance of the current sequence (vertices) to the original sequence (points). Those stored points which do not correspond to a vertex can be removed afterward either for a single constraint or for all constraints. The simplification algorithm uses the following types and functions. | |
| typedef unspecified_type | Points_in_constraint_iterator |
| This is an advanced type. More... | |
| Points_in_constraint_iterator | points_in_constraint_begin (Constraint_id cid) const |
| This is an advanced function. More... | |
| Points_in_constraint_iterator | points_in_constraint_end (Constraint_id cid) const |
| This is an advanced function. More... | |
| void | simplify (Vertices_in_constraint_iterator vicq) |
| This is an advanced function. More... | |
| size_type | remove_points_without_corresponding_vertex (Constraint_id cid) |
| This is an advanced function. More... | |
| void | remove_points_without_corresponding_vertex () |
| This is an advanced function. More... | |
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Constraint_id |
The identifier of a polyline constraint.
The class is model of Assignable, CopyConstructible, DefaultConstructible, LessThanComparable and EqualityComparable.
A default constructed Constraint_id is a singular value that can not be the ID of a constraint.
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Constraint_iterator |
An iterator to visit all the input constraints.
The order of visit is undefined. The value type of this iterator is Constraint_id.
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Context_iterator |
An iterator on constraints enclosing a given subconstraint.
The value type of this iterator is Context.
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Points_in_constraint_iterator |
This is an advanced type.
An iterator on the points of the original constraint before simplification steps are applied. The value type of this iterator is Point. A Vertices_in_constraint_iterator can be converted into a Points_in_constraint_iterator, but not the other way around.
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Subconstraint_iterator |
An iterator to visit all the subconstraints of the triangulation.
The order of visit is undefined. The value type of this iterator is std::pair<Subconstraint,std::list<Context>*> corresponding to the vertices of the subconstraint.
| typedef unspecified_type CGAL::Constrained_triangulation_plus_2< Tr >::Vertices_in_constraint_iterator |
An iterator on the vertices of the chain of subconstraints representing a constraint.
The value type of this iterator is Vertex_handle.
| CGAL::Constrained_triangulation_plus_2< Tr >::Constrained_triangulation_plus_2 | ( | ConstraintIterator | first, |
| ConstraintIterator | last, | ||
| const Geom_traits & | gt = Geom_traits() |
||
| ) |
Introduces a constrained triangulation from the constraints in the range [first,last).
| ConstraintIterator | must be an InputIterator with the value type std::pair<Point,Point> or Segment. |
| Context CGAL::Constrained_triangulation_plus_2< Tr >::context | ( | Vertex_handle | va, |
| Vertex_handle | vb | ||
| ) | const |
returns the Context relative to one of the constraints enclosing the subconstraint (va,vb).
va and vb refer to the vertices of a constrained edge of the triangulation. | Context_iterator CGAL::Constrained_triangulation_plus_2< Tr >::contexts_begin | ( | Vertex_handle | va, |
| Vertex_handle | vb | ||
| ) | const |
returns an iterator pointing at the first Context of the sequence of contexts corresponding to the constraints enclosing the subconstraint (va,vb).
va and vb refer to the vertices of a constrained edge of the triangulation. | Context_iterator CGAL::Constrained_triangulation_plus_2< Tr >::contexts_end | ( | Vertex_handle | va, |
| Vertex_handle | vb | ||
| ) | const |
returns an iterator past the end Context of the sequence of contexts corresponding to the constraints enclosing the subconstraint (va,vb).
va and vb refer to the vertices of a constrained edge of the triangulation. | Vertex_handle CGAL::Constrained_triangulation_plus_2< Tr >::insert | ( | const Point & | p, |
| Locate_type | lt, | ||
| Face_handle | loc, | ||
| int | li | ||
| ) |
inserts point p in the triangulation at the location given by (lt,loc,i).
Triangulation_2::locate() | size_type CGAL::Constrained_triangulation_plus_2< Tr >::insert | ( | PointIterator | first, |
| PointIterator | last | ||
| ) |
inserts the points in the range [first,last).
Returns the number of inserted points.
| PointIterator | must be an InputIterator with the value type Point. |
| Constraint_id CGAL::Constrained_triangulation_plus_2< Tr >::insert_constraint | ( | Point | a, |
| Point | b | ||
| ) |
inserts the constraint segment ab in the triangulation.
If the two points are equal the point is inserted but no constraint, and the default constructed Constraint_id is returned.
| Constraint_id CGAL::Constrained_triangulation_plus_2< Tr >::insert_constraint | ( | Vertex_handle | va, |
| Vertex_handle | vb | ||
| ) |
inserts a constraint whose endpoints are the vertices pointed by va and vb in the triangulation.
If the two vertex handles are equal no constraint is inserted, and the default constructed Constraint_id is returned.
| Constraint_id CGAL::Constrained_triangulation_plus_2< Tr >::insert_constraint | ( | PointIterator | first, |
| PointIterator | last, | ||
| bool | close = false |
||
| ) |
inserts a polyline defined by the points in the range [first,last) and returns the constraint id.
The polyline is considered as a closed curve if the first and last point are equal or if close == true. This enables for example passing the vertex range of a Polygon_2. When traversing the vertices of a closed polyline constraint with a Vertices_in_constraint_iterator the first and last vertex are the same. In case the range is empty Constraint_id() is returned. In case all points are equal the point is inserted but no constraint, and Constraint_id() is returned.
| PointIterator | must be an InputIterator with the value type Point. |
| std::size_t CGAL::Constrained_triangulation_plus_2< Tr >::insert_constraints | ( | ConstraintIterator | first, |
| ConstraintIterator | last | ||
| ) |
inserts the constraints in the range [first,last).
Note that this function is not guaranteed to insert the constraints following the order of ConstraintIterator, as spatial_sort() is used to improve efficiency. More precisely, all endpoints are inserted prior to the segments and according to the order provided by the spatial sort. Once endpoints have been inserted, the segments are inserted in the order of the input iterator, using the vertex handles of its endpoints.
| ConstraintIterator | must be an InputIterator with the value type std::pair<Point,Point> or Segment. |
| std::size_t CGAL::Constrained_triangulation_plus_2< Tr >::insert_constraints | ( | PointIterator | points_first, |
| PointIterator | points_last, | ||
| IndicesIterator | indices_first, | ||
| IndicesIterator | indices_last | ||
| ) |
Same as above except that each constraint is given as a pair of indices of the points in the range [points_first, points_last).
The indices must go from 0 to std::distance(points_first, points_last)
| PointIterator | is an InputIterator with the value type Point. |
| IndicesIterator | is an InputIterator with std::pair<Int, Int> where Int is an integral type implicitly convertible to std::size_t |
| int CGAL::Constrained_triangulation_plus_2< Tr >::number_of_enclosing_constraints | ( | Vertex_handle | va, |
| Vertex_handle | vb | ||
| ) | const |
returns the number of constraints enclosing the subconstraint (va,vb).
va and vb refer to the vertices of a constrained edge of the triangulation. | Constrained_triangulation_plus_2 CGAL::Constrained_triangulation_plus_2< Tr >::operator= | ( | const Constrained_triangulation_plus_2< Tr > & | tr | ) |
Assignment.
All the vertices and faces are duplicated. The bidirectional mapping between constraints and subconstraints is also duplicated.
| Points_in_constraint_iterator CGAL::Constrained_triangulation_plus_2< Tr >::points_in_constraint_begin | ( | Constraint_id | cid | ) | const |
This is an advanced function.
Returns an iterator to the first point on the constraint before any simplification step.
| Points_in_constraint_iterator CGAL::Constrained_triangulation_plus_2< Tr >::points_in_constraint_end | ( | Constraint_id | cid | ) | const |
This is an advanced function.
Returns an iterator past the last point on the constraint before any simplification step.
| size_type CGAL::Constrained_triangulation_plus_2< Tr >::remove_points_without_corresponding_vertex | ( | Constraint_id | cid | ) |
This is an advanced function.
Removes the original points that correspond to vertices in the constraint cid which have been removed by the simplify() function.
| void CGAL::Constrained_triangulation_plus_2< Tr >::remove_points_without_corresponding_vertex | ( | ) |
This is an advanced function.
Removes all original points that correspond to vertices in the constraints which have been removed by the simplify() function.
| void CGAL::Constrained_triangulation_plus_2< Tr >::simplify | ( | Vertices_in_constraint_iterator | vicq | ) |
This is an advanced function.
Removes the vertex at vicq from the constraint and the triangulation. The point of that vertex remains stored in the sequence of original points of the constraint until remove_points_without_corresponding_vertex(Constraint_id) or remove_points_without_corresponding_vertex() is called.
The polyline simplification algorithm described in Chapter Chapter_2D_Polyline_simplification operates on polyline constraints and applies simplify() to vertices in constraints based on a cost and stop function.
vicq must neither be the first nor the last vertex on a constraint. vip and vir be defined as vip = std::prev(vicq) and vir = std::next(vicr). *vicp->point() and *vicr->point() must not intersect any constraint. | void CGAL::Constrained_triangulation_plus_2< Tr >::split_subconstraint_graph_into_constraints | ( | const std::function< bool(Vertex_handle)> & | is_terminal | ) |
splits into constraints the graph of subconstraints.
Consider the graph g={V,E} where V is the set of vertices of the triangulation and E is the set of all subconstraints of all constraints of the triangulation.
This function splits into polylines the graph g at vertices of degree greater than 2 and at vertices for which is_terminal(v)==true.
Each computed polyline is stored as a constraint of the triangulation.
| is_terminal | An optional function returning true if the vertex v of degree 2 is a polyline endpoint and false otherwise. If omitted, a function always returning false will be used, that is no degree 2 vertex will be considered as a polyline endpoint. |
split_graph_into_polylines() | void CGAL::Constrained_triangulation_plus_2< Tr >::swap | ( | Constrained_triangulation_plus_2< Tr > | tr | ) |
The triangulations tr and this triangulation are swapped.
This operation should be preferred to the assignment or to the copy constructor if tr is deleted after that.
1.8.13