\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D Triangulation
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CGAL::Constrained_triangulation_plus_2< Tr > Class Template Reference

#include <CGAL/Constrained_triangulation_plus_2.h>

Inherits from

Tr.

Definition

The class Constrained_triangulation_plus_2 implements a constrained triangulation with an additional data structure called the constraint hierarchy 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.

According to its intersection tag, the base class will support intersecting input constraints 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 and refining the input constraints into sub-constraints which are edges (more precisely constrained edges) of the triangulation. In this context, the constraint hierarchy keeps track of the input constraints and of their refinement in the triangulation. This data structure maintains for each input constraints the sequence of intersection vertices added on this constraint. The constraint hierarchy also allows the user to retrieve the set of constrained edges of the triangulation, and for each constrained edge, the set of input constraints that overlap it.

Template Parameters
Trmust be either a CGAL::Constrained_triangulation_2 or a CGAL::Constrained_Delaunay_triangulation_2
See Also
CGAL::Constrained_triangulation_2<Traits,Tds>
CGAL::Constrained_Delaunay_triangulation_2<Traits,Tds>
ConstrainedTriangulationTraits_2
ConstrainedDelaunayTriangulationTraits_2
Examples:
Triangulation_2/constrained_hierarchy_plus.cpp, and Triangulation_2/constrained_plus.cpp.

Types

typedef Tr Triangulation
 The triangulation base class.
 
typedef Itag Intersection_tag
 The intersection tag.
 
typedef unspecified_type Constraint_iterator
 An iterator to visit all the input constraints. More...
 
typedef unspecified_type Subconstraint_iterator
 An iterator to visit all the sub-constraints of the triangulation. More...
 
typedef unspecified_type Vertices_in_constraint_iterator
 An iterator on the vertices of the chain of triangulation edges representing a constraint. More...
 
typedef Context
 This type is intended to describe a constraint enclosing a sub-constraint and the position of the sub-constraint in this constraint. More...
 
typedef Context_iterator
 An iterator on constraints enclosing a given sub-constraint. More...
 

Creation

 Constrained_triangulation_plus_2 (const Geom_traits &gt=Geom_traits())
 Introduces an empty triangulation.
 
 Constrained_triangulation_plus_2 (const Constrained_triangulation_plus_2 &ct)
 Copy constructor.
 
 Constrained_triangulation_plus_2 (std::list< Constraint > &lc, const Geom_traits &t=Geom_traits())
 Introduces a constrained triangulation from the list of constraints lc.
 
template<class InputIterator >
 Constrained_triangulation_plus_2 (InputIterator first, InputIterator last, const Geom_traits &gt=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 Constrained_triangulation_plus_2 overwrites the following insertion and removal member functions for points and constraints.

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 InputIterator >
size_type insert (InputIterator first, InputIterator last)
 Inserts the points in the range [first,last). More...
 
void insert_constraint (Point a, Point b)
 Inserts the constraint segment ab in the triangulation.
 
void push_back (const Constraint &c)
 Inserts the constraint c.
 
void insert_constraint (Vertex_handle va, Vertex_handle vb)
 Inserts a constraint whose endpoints are the vertices pointed by va and vb in the triangulation.
 
void remove_constraint (Vertex_handle va, Vertex_handle vb)
 Removes the constraint joining the vertices pointed by va and vb. More...
 

Queries

Constraint_iterator constraints_begin () const
 Returns a Constraint_iterator pointing on the first constraint.
 
Constraint_iterator constraints_end () const
 Returns a Constraint_iterator pointing past the last constraint.
 
Subconstraint_iterator subconstraints_begin () const
 Returns a Subconstraint_iterator pointing on the first sub-constraint.
 
Subconstraint_iterator subconstraints_end () const
 Returns a Subconstraint_iterator pointing past the last sub-constraint.
 
int number_of_enclosing_constraints (Vertex_handle va, Vertex_handle vb)
 Returns the number of constraints enclosing the sub-constraint (va,vb). More...
 
Context context (Vertex_handle va, Vertex_handle vb)
 Returns the Context relative to one of the constraints enclosing the sub-constraint (va,vb). More...
 
Context_iterator contexts_begin (Vertex_handle va, Vertex_handle vb)
 Returns an iterator pointing on the first Context of the sequence of Contexts corresponding to the constraints enclosing the sub-constraint(va,vb). More...
 
Context_iterator contexts_end (Vertex_handle va, Vertex_handle vb)
 Returns an iterator past the last Context of the sequence of Contexts corresponding to the constraints enclosing the (va,vb). More...
 
Vertices_in_constraint_iterator vertices_in_constraint_begin (Vertex_handle va, Vertex_handle vb)
 Returns an iterator on the first vertex on the constraint (va,vb). More...
 
Vertices_in_constraint_iterator vertices_in_constraint_end (Vertex_handle va, Vertex_handle vb)
 Returns an iterator past the last vertex on the constraint (va,vb). More...
 

Member Typedef Documentation

An iterator to visit all the input constraints.

The order of visit is arbitrary. The value type of this iterator is a pair std::pair<Vertex_handle, Vertex_handle> corresponding to the endpoints of the constraint.

An iterator to visit all the sub-constraints of the triangulation.

The order of visit is arbitrary. The value type of this iterator is a pair std::pair<Vertex_handle, Vertex_handle> corresponding to the vertices of the sub-constraint.

An iterator on the vertices of the chain of triangulation edges representing a constraint.

The value type of this iterator is Vertex_handle.

Constructor & Destructor Documentation

template<typename Tr >
template<class InputIterator >
CGAL::Constrained_triangulation_plus_2< Tr >::Constrained_triangulation_plus_2 ( InputIterator  first,
InputIterator  last,
const Geom_traits &  gt = Geom_traits() 
)

Introduces a constrained triangulation from the constraints in the range [first,last).

Template Parameters
InputIteratormust be an input iterator with the value type Constraint.

Member Function Documentation

template<typename Tr >
Context CGAL::Constrained_triangulation_plus_2< Tr >::context ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns the Context relative to one of the constraints enclosing the sub-constraint (va,vb).

Precondition
va and vb refer to the vertices of a constrained edge of the triangulation.
template<typename Tr >
Context_iterator CGAL::Constrained_triangulation_plus_2< Tr >::contexts_begin ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns an iterator pointing on the first Context of the sequence of Contexts corresponding to the constraints enclosing the sub-constraint(va,vb).

Precondition
va and vb refer to the vertices of a constrained edge of the triangulation.
template<typename Tr >
Context_iterator CGAL::Constrained_triangulation_plus_2< Tr >::contexts_end ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns an iterator past the last Context of the sequence of Contexts corresponding to the constraints enclosing the (va,vb).

Precondition
va and vb refer to the vertices of a constrained edge of the triangulation.
template<typename Tr >
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).

See Also
Triangulation_2::locate()
template<typename Tr >
template<class InputIterator >
size_type CGAL::Constrained_triangulation_plus_2< Tr >::insert ( InputIterator  first,
InputIterator  last 
)

Inserts the points in the range [first,last).

Returns the number of inserted points.

Template Parameters
InputIteratormust be an input iterator with the value type Point.
template<typename Tr >
int CGAL::Constrained_triangulation_plus_2< Tr >::number_of_enclosing_constraints ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns the number of constraints enclosing the sub-constraint (va,vb).

Precondition
va and vb refer to the vertices of a constrained edge of the triangulation.

Assignment.

All the vertices and faces are duplicated. The constraint hierarchy is also duplicated.

template<typename Tr >
void CGAL::Constrained_triangulation_plus_2< Tr >::remove_constraint ( Vertex_handle  va,
Vertex_handle  vb 
)

Removes the constraint joining the vertices pointed by va and vb.

Precondition
va and vb have to refer to the endpoint vertices of an input constraint.
template<typename Tr >
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.

template<typename Tr >
Vertices_in_constraint_iterator CGAL::Constrained_triangulation_plus_2< Tr >::vertices_in_constraint_begin ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns an iterator on the first vertex on the constraint (va,vb).

Precondition
va and vb refer to the vertices of an input constraint.
template<typename Tr >
Vertices_in_constraint_iterator CGAL::Constrained_triangulation_plus_2< Tr >::vertices_in_constraint_end ( Vertex_handle  va,
Vertex_handle  vb 
)

Returns an iterator past the last vertex on the constraint (va,vb).

Precondition
va and vb refer to the vertices of an input constraints.

Member Data Documentation

template<typename Tr >
typedef CGAL::Constrained_triangulation_plus_2< Tr >::Context

This type is intended to describe a constraint enclosing a sub-constraint and the position of the sub-constraint in this constraint.

It provides three member functions vertices_begin(), vertices_end() and current() returning iterators of the type Vertices_in_constraint_iterator on the sequence of vertices of the enclosing constraint. These iterators point respectively on the first vertex of the enclosing constraint, past the last vertex and on the first vertex of the sub-constraint.

template<typename Tr >
typedef CGAL::Constrained_triangulation_plus_2< Tr >::Context_iterator

An iterator on constraints enclosing a given sub-constraint.

The value type of this iterator is Context.