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CGAL 4.11 - 2D Arrangements
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CGAL 4.11 - 2D Arrangements
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#include <CGAL/Arrangement_with_history_2.h>
CGAL::Arrangement_2< Traits, Dcel >.
An object arr of the class Arrangement_with_history_2 represents the planar subdivision induced by a set of input curves \( \cal C\). The arrangement is represented as a doubly-connected edge-list (Dcel). As is the case for the Arrangement_2<Traits,Dcel>, each Dcel vertex is associated with a point and each edge is associated with an \( x\)-monotone curve whose interior is disjoint from all other edges and vertices. Each such \( x\)-monotone curve is a subcurve of some \( C \in \cal C\) - or may represent an overlap among several curves in \( \cal C\).
The Arrangement_with_history_2 class-template extends the Arrangement_2 class-template by keeping an additional container of input curves representing \( \cal C\), and by maintaining a cross-mapping between these curves and the arrangement edges they induce. This way it is possible to determine the inducing curve(s) of each arrangement edge. This mapping also allows the traversal of input curves, and the traversal of edges induced by each curve.
The Arrangement_with_history_2 template has two parameters:
Traits template-parameter should be instantiated with a model of the ArrangementTraits_2 concept. The traits class defines the Curve_2 type, which represents an input curve. It also defines the types of \( x\)-monotone curves and two-dimensional points, namely ArrangementTraits_2::X_monotone_curve_2 and ArrangementTraits_2::Point_2, respectively, and supports basic geometric predicates on them. Dcel template-parameter should be instantiated with a class that is a model of the ArrangementDcelWithRebind concept. The value of this parameter is by default Arr_default_dcel<Traits>. ArrangementDcel Arr_default_dcel<Traits> ArrangementTraits_2 Arrangement_2<Traits,Dcel> insertion functions removal functions overlaying arrangements Types | |
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typedef Arrangement_with_history_2 < Traits_2, Dcel > | Self |
a private type used as an abbreviation of the Arrangement_with_history_2 type hereafter. | |
| typedef unspecified_type | Traits_2 |
| the traits class in use. | |
| typedef Traits_2::Point_2 | Point_2 |
| the point type, as defined by the traits class. | |
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typedef Traits_2::X_monotone_curve_2 | X_monotone_curve_2 |
| the \( x\)-monotone curve type, as defined by the traits class. | |
| typedef Traits_2::Curve_2 | Curve_2 |
| the curve type, as defined by the traits class. | |
In addition, the nested types | |
| typedef unspecified_type | Curve_handle |
| a handle for an input curve. | |
| typedef unspecified_type | Curve_iterator |
| a bidirectional iterator over the curves that induce the arrangement. More... | |
| typedef unspecified_type | Induced_edge_iterator |
| an iterator over the edges induced by an input curve. More... | |
| typedef unspecified_type | Originating_curve_iterator |
| an iterator for the curves that originate a given arrangement edge. More... | |
Creation | |
| Arrangement_with_history_2 () | |
| constructs an empty arrangement containing one unbounded face, which corresponds to the whole plane. | |
| Arrangement_with_history_2 (const Self &other) | |
| copy constructor. | |
| Arrangement_with_history_2 (Traits_2 *traits) | |
constructs an empty arrangement that uses the given traits instance for performing the geometric predicates. | |
Assignment Methods | |
| Self & | operator= (other) |
| assignment operator. | |
| void | assign (const Self &other) |
| assigns the contents of another arrangement. | |
| void | clear () |
| clears the arrangement. | |
Access Functions for Input Curves | |
See the | |
| Size | number_of_curves () const |
| returns the number of input curves that induce the arrangement. | |
| Curve_iterator | curves_begin () |
| returns the begin-iterator of the curves inducing the arrangement. | |
| Curve_iterator | curves_end () |
| returns the past-the-end iterator of the curves inducing the arrangement. | |
| Size | number_of_induced_edges (Curve_handle ch) const |
returns the number of arrangement edges induced by the curve ch. | |
| Induced_edge_iterator | induced_edges_begin (Curve_handle ch) const |
returns the begin-iterator of the edges induced by the curve ch. | |
| Induced_edge_iterator | induced_edges_end (Curve_handle ch) const |
returns the past-the-end iterator of the edges induced by the curve ch. | |
| Size | number_of_originating_curves (Halfedge_handle e) const |
returns the number of input curves that originate the edge e. | |
| Originating_curve_iterator | originating_curves_begin (Halfedge_handle e) const |
returns the begin-iterator of the curves originating the edge e. | |
| Originating_curve_iterator | originating_curves_end (Halfedge_handle e) const |
returns the past-the-end iterator of the curves originating the edge e. | |
Modifying Arrangement Edges | |
The following functions override their counterparts in the See the | |
| Halfedge_handle | split_edge (Halfedge_handle e, const Point_2 &p) |
splits the edge e into two edges (more precisely, into two halfedge pairs), at a given split point p. More... | |
| Halfedge_handle | merge_edge (Halfedge_handle e1, Halfedge_handle e2) |
merges the edges represented by e1 and e2 into a single edge. More... | |
| Face_handle | remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true) |
removes the edge e from the arrangement. More... | |
Additional Inherited Members | |
 Public Types inherited from CGAL::Arrangement_2< Traits, Dcel > | |
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typedef Arrangement_2 < Traits_2, Dcel > | Self |
a private type used as an abbreviation of the Arrangement_2 type hereafter. | |
| typedef Traits | Traits_2 |
| the traits class in use. | |
| typedef Traits_2::Point_2 | Point_2 |
| the point type, as defined by the traits class. | |
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typedef Traits_2::X_monotone_curve_2 | X_monotone_curve_2 |
| the \( x\)-monotone curve type, as defined by the traits class. | |
| typedef Dcel::Size | Size |
the size type (equivalent to size_t). | |
| typedef unspecified_type | Vertex_handle |
| a handle for an arrangement vertex. | |
| typedef unspecified_type | Halfedge_handle |
| a handle for a halfedge. More... | |
| typedef unspecified_type | Face_handle |
| a handle for an arrangement face. | |
| typedef unspecified_type | Vertex_iterator |
| a bidirectional iterator over the vertices of the arrangement. More... | |
| typedef unspecified_type | Halfedge_iterator |
| a bidirectional iterator over the halfedges of the arrangement. More... | |
| typedef unspecified_type | Edge_iterator |
| a bidirectional iterator over the edges of the arrangement. More... | |
| typedef unspecified_type | Face_iterator |
| a bidirectional iterator over the faces of arrangement. More... | |
| typedef unspecified_type | Unbounded_face_iterator |
| a bidirectional iterator over the unbounded faces of arrangement. More... | |
| typedef unspecified_type | Halfedge_around_vertex_circulator |
| a bidirectional circulator over the halfedges that have a given vertex as their target. More... | |
| typedef unspecified_type | Ccb_halfedge_circulator |
| a bidirectional circulator over the halfedges of a CCB (connected component of the boundary). More... | |
| typedef unspecified_type | Hole_iterator |
| a bidirectional iterator over the holes (i.e., inner CCBs) contained inside a given face. More... | |
| typedef unspecified_type | Isolated_vertex_iterator |
| a bidirectional iterator over the isolated vertices contained inside a given face. More... | |
| Public Member Functions inherited from CGAL::Arrangement_2< Traits, Dcel > | |
| Arrangement_2 () | |
| constructs an empty arrangement containing one unbounded face, which corresponds to the entire plane. | |
| Arrangement_2 (const Self &other) | |
| copy constructor. | |
| Arrangement_2 (const Traits_2 *traits) | |
constructs an empty arrangement that uses the given traits instance for performing the geometric predicates. | |
| Self & | operator= (other) |
| assignment operator. | |
| void | assign (const Self &other) |
| assigns the contents of another arrangement. | |
| void | clear () |
| clears the arrangement. | |
| Traits_2 * | get_traits () |
| returns the traits object used by the arrangement instance. More... | |
| bool | is_empty () const |
| determines whether the arrangement is empty (contains only the unbounded face, with no vertices or edges). | |
| Size | number_of_vertices () const |
| returns the number of vertices in the arrangement. | |
| Size | number_of_isolated_vertices () const |
| returns the total number of isolated vertices in the arrangement. | |
| Vertex_iterator | vertices_begin () |
| returns the begin-iterator of the vertices in the arrangement. | |
| Vertex_iterator | vertices_end () |
| returns the past-the-end iterator of the vertices in the arrangement. | |
| unspecified_type | vertex_handles () |
| returns a range over handles of the arrangement vertices . | |
| Size | number_of_vertices_at_infinity () const |
| returns the number of arrangement vertices that lie at infinity and are not associated with valid points. More... | |
| Size | number_of_halfedges () const |
| returns the number of halfedges in the arrangement. | |
| Halfedge_iterator | halfedges_begin () |
| returns the begin-iterator of the halfedges in the arrangement. | |
| Halfedge_iterator | halfedges_end () |
| returns the past-the-end iterator of the halfedges in the arrangement. | |
| unspecified_type | halfedge_handles () |
| returns a range over handles of the arrangement halfedges . | |
| Size | number_of_edges () const |
returns the number of edges in the arrangement (equivalent to arr.number_of_halfedges() / 2). | |
| Edge_iterator | edges_begin () |
| returns the begin-iterator of the edges in the arrangement. | |
| Edge_iterator | edges_end () |
| returns the past-the-end iterator of the edges in the arrangement. | |
| unspecified_type | edge_handles () |
| returns a range over handles of the arrangement edges . | |
| Face_handle | unbounded_face () |
| returns a handle for an unbounded face of the arrangement. More... | |
| Size | number_of_faces () const |
| returns the number of faces in the arrangement. | |
| Face_iterator | faces_begin () |
| returns the begin-iterator of the faces in the arrangement. | |
| Face_iterator | faces_end () |
| returns the past-the-end iterator of the faces in the arrangement. | |
| unspecified_type | face_handles () |
| returns a range over handles of the arrangement faces . | |
| Size | number_of_unbounded_faces () const |
| returns the number of unbounded faces in the arrangement. More... | |
| Unbounded_face_iterator | unbounded_faces_begin () |
| returns the begin-iterator of the unbounded faces in the arrangement. | |
| Unbounded_face_iterator | unbounded_faces_end () |
| returns the past-the-end iterator of the unbounded faces in the arrangement. | |
| Face_handle | fictitious_face () |
| returns a handle to the fictitious face of the arrangement. More... | |
| Vertex_handle | non_const_handle (Vertex_const_handle v) |
| casts the given constant vertex handle to an equivalent mutable handle. | |
| Halfedge_handle | non_const_handle (Halfedge_const_handle e) |
| casts the given constant halfedge handle to an equivalent mutable handle. | |
| Face_handle | non_const_handle (Face_const_handle f) |
| casts the given constant face handle to an equivalent mutable handle. | |
| Vertex_handle | insert_in_face_interior (const Point_2 &p, Face_handle f) |
inserts the point p into the arrangement as an isolated vertex in the interior of the face f and returns a handle for the newly created vertex. More... | |
| Halfedge_handle | insert_in_face_interior (const X_monotone_curve_2 &c, Face_handle f) |
inserts the curve c that is entirely contained in the interior of a given face f. More... | |
| Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
inserts the curve c into the arrangement, such that its left endpoint corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
inserts the curve c into the arrangement, such that its right endpoint corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Vertex_handle v1, Vertex_handle v2) |
inserts the curve c into the arrangement, such that both c's endpoints correspond to existing arrangement vertices, given by v1 and v2. More... | |
| Halfedge_handle | insert_in_face_interior (const X_monotone_curve_2 &c, Halfedge_handle fict_pred1, Halfedge_handle fict_pred2=Halfedge_handle()) |
inserts an unbounded curve c into the arrangement, such that c is entirely contained within a single unbounded face of the arrangement. More... | |
| Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
inserts the curve c into the arrangement, such that its left endpoint corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
inserts an unbounded curve c into the arrangement, such that its left endpoint is bounded and corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
inserts the curve c into the arrangement, such that its right endpoint corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
inserts an unbounded curve c into the arrangement, such that its right endpoint is bounded and corresponds to a given arrangement vertex. More... | |
| Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Vertex_handle v2) |
inserts the curve c into the arrangement, such that both c's endpoints correspond to existing arrangement vertices, given by pred1->target() and v2. More... | |
| Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Halfedge_handle pred2) |
inserts the curve c into the arrangement, such that both c's endpoints correspond to existing arrangement vertices, given by pred1->target() and pred2->target(). More... | |
| Vertex_handle | modify_vertex (Vertex_handle v, const Point_2 &p) |
sets p to be the point associated with the vertex v. More... | |
| Face_handle | remove_isolated_vertex (Vertex_handle v) |
removes the isolated vertex v from the arrangement. More... | |
| Halfedge_handle | modify_edge (Halfedge_handle e, const X_monotone_curve_2 &c) |
sets c to be the \( x\)-monotone curve associated with the edge e. More... | |
| Halfedge_handle | split_edge (Halfedge_handle e, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2) |
splits the edge e into two edges (more precisely, into two halfedge pairs), associated with the given subcurves c1 and c2, and creates a vertex that corresponds to the split point. More... | |
| Halfedge_handle | merge_edge (Halfedge_handle e1, Halfedge_handle e2, const X_monotone_curve_2 &c) |
merges the edges represented by e1 and e2 into a single edge, associated with the given merged curve c. More... | |
| Face_handle | remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true) |
removes the edge e from the arrangement. More... | |
| bool | is_valid () const |
returns true if arr represents a valid instance of Arrangement_2. More... | |
| typedef unspecified_type CGAL::Arrangement_with_history_2< Traits, Dcel >::Curve_iterator |
a bidirectional iterator over the curves that induce the arrangement.
Its value-type is Curve_2.
| typedef unspecified_type CGAL::Arrangement_with_history_2< Traits, Dcel >::Induced_edge_iterator |
an iterator over the edges induced by an input curve.
Its value type is Halfedge_handle.
| typedef unspecified_type CGAL::Arrangement_with_history_2< Traits, Dcel >::Originating_curve_iterator |
an iterator for the curves that originate a given arrangement edge.
Its value type is Curve_handle.
| Halfedge_handle CGAL::Arrangement_with_history_2< Traits, Dcel >::merge_edge | ( | Halfedge_handle | e1, |
| Halfedge_handle | e2 | ||
| ) |
merges the edges represented by e1 and e2 into a single edge.
The function returns a handle for one of the merged halfedges.
e1 and e2 share a common end-vertex, of degree \( 2\), and the \( x\)-monotone curves associated with e1 and e2 are mergeable into a single \( x\)-monotone curves. | Face_handle CGAL::Arrangement_with_history_2< Traits, Dcel >::remove_edge | ( | Halfedge_handle | e, |
| bool | remove_source = true, |
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| bool | remove_target = true |
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| ) |
removes the edge e from the arrangement.
Since the e may be the only edge incident to its source vertex (or its target vertex), this vertex can be removed as well. The flags remove_source and remove_target indicate whether the endpoints of e should be removed, or whether they should be left as isolated vertices in the arrangement. If the operation causes two faces to merge, the merged face is returned. Otherwise, the face to which the edge was incident is returned.
| Halfedge_handle CGAL::Arrangement_with_history_2< Traits, Dcel >::split_edge | ( | Halfedge_handle | e, |
| const Point_2 & | p | ||
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splits the edge e into two edges (more precisely, into two halfedge pairs), at a given split point p.
The function returns a handle for the halfedge whose source is the same as e->source() and whose target vertex is the split point.
p lies in the interior of the curve associated with e. 
1.8.4