CGAL 5.3 - 2D Boolean Operations on Nef Polygons
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#include <CGAL/Nef_polyhedron_2.h>
CGAL::Nef_polyhedron_2< T >::Topological_explorer.
a decorator to examine the underlying plane map.
An instance E
of the data type Explorer
is a decorator to explore the structure of the plane map underlying the Nef polyhedron. It inherits all topological adjacency exploration operations from Topological_explorer
. Explorer
additionally allows one to explore the geometric embedding.
The position of each vertex is given by a so-called extended point, which is either a standard affine point or the tip of a ray touching an infinimaximal square frame centered at the origin. A vertex v
is called a standard vertex if its embedding is a standard point and non-standard if its embedding is a non-standard point. By the straightline embedding of their source and target vertices, edges correspond to either affine segments, rays or lines or are part of the bounding frame.
Creation
Explorer
is copy constructable and assignable. An object can be obtained via the Nef_polyhedron_2::explorer()
method of Nef_polyhedron_2
.
Types | |
Iterators, handles, and circulators are inherited from | |
typedef unspecified_type | Point |
the point type of finite vertices. | |
typedef unspecified_type | Ray |
the ray type of vertices on the frame. | |
Operations | |
bool | is_standard (Vertex_const_handle v) |
returns true iff v 's position is a standard point. | |
Point | point (Vertex_const_handle v) |
returns the standard point that is the embedding of v . More... | |
Ray | ray (Vertex_const_handle v) |
returns the ray defining the non-standard point on the frame. More... | |
bool | is_frame_edge (Halfedge_const_handle e) |
returns true iff e is part of the infinimaximal frame. | |
Additional Inherited Members | |
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typedef unspecified_type | Plane_map |
The underlying plane map type. | |
typedef unspecified_type | Point |
The point type of vertices. | |
typedef unspecified_type | Mark |
All objects (vertices, edges, faces) are attributed by a Mark object. | |
typedef unspecified_type | Size_type |
The size type. | |
typedef unspecified_type | Halfedge_around_vertex_const_circulator |
circulating the outgoing halfedges in \( A(v)\). | |
typedef unspecified_type | Halfedge_around_face_const_circulator |
circulating the halfedges in the face cycle of a face f . | |
typedef unspecified_type | Hole_const_iterator |
iterating all holes of a face f . More... | |
typedef unspecified_type | Isolated_vertex_const_iterator |
iterating all isolated vertices of a face f . More... | |
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Vertex_const_handle | source (Halfedge_const_handle e) |
returns the source of e . | |
Vertex_const_handle | target (Halfedge_const_handle e) |
returns the target of e . | |
Halfedge_const_handle | twin (Halfedge_const_handle e) |
returns the twin of e . | |
bool | is_isolated (Vertex_const_handle v) |
returns true iff \( A(v) = \emptyset\). | |
Halfedge_const_handle | first_out_edge (Vertex_const_handle v) |
returns one halfedge with source v . More... | |
Halfedge_const_handle | last_out_edge (Vertex_const_handle v) |
returns the halfedge with source v that is the last in the circular iteration before encountering first_out_edge(v) again. More... | |
Halfedge_const_handle | cyclic_adj_succ (Halfedge_const_handle e) |
returns the edge after e in the cyclic ordered adjacency list of source(e) . | |
Halfedge_const_handle | cyclic_adj_pred (Halfedge_const_handle e) |
returns the edge before e in the cyclic ordered adjacency list of source(e) . | |
Halfedge_const_handle | next (Halfedge_const_handle e) |
returns the next edge in the face cycle containing e . | |
Halfedge_const_handle | previous (Halfedge_const_handle e) |
returns the previous edge in the face cycle containing e . | |
Face_const_handle | face (Halfedge_const_handle e) |
returns the face incident to e . | |
Face_const_handle | face (Vertex_const_handle v) |
returns the face incident to v . More... | |
Halfedge_const_handle | halfedge (Face_const_handle f) |
returns a halfedge in the bounding face cycle of f (Halfedge_const_handle() if there is no bounding face cycle). | |
Vertex_const_iterator | vertices_begin () |
iterator over vertices of the map. | |
Vertex_const_iterator | vertices_end () |
past-the-end iterator for vertices. | |
Halfedge_const_iterator | halfedges_begin () |
iterator over halfedges of the map. | |
Halfedge_const_iterator | halfedges_end () |
past-the-end iterator for halfedges. | |
Face_const_iterator | faces_begin () |
iterator over faces of the map. | |
Face_const_iterator | faces_end () |
past-the-end iterator for faces | |
Halfedge_around_vertex_const_circulator | out_edges (Vertex_const_handle v) |
returns a circulator for the cyclic adjacency list of v . | |
Halfedge_around_face_const_circulator | face_cycle (Face_const_handle f) |
returns a circulator for the outer face cycle of f . | |
Hole_const_iterator | holes_begin (Face_const_handle f) |
returns an iterator for all holes in the interior of f . More... | |
Hole_const_iterator | holes_end (Face_const_handle f) |
returns the past-the-end iterator of f . | |
Isolated_vertex_const_iterator | isolated_vertices_begin (Face_const_handle f) |
returns an iterator for all isolated vertices in the interior of f . | |
Isolated_vertex_const_iterator | isolated_vertices_end (Face_const_handle f) |
returns the past the end iterator of f . | |
const Point & | point (Vertex_const_handle v) |
returns the embedding of v . | |
const Mark & | mark (Vertex_const_handle v) |
returns the mark of v . | |
const Mark & | mark (Halfedge_const_handle e) |
returns the mark of e . | |
const Mark & | mark (Face_const_handle f) |
returns the mark of f . | |
Size_type | number_of_vertices () |
returns the number of vertices. | |
Size_type | number_of_halfedges () |
returns the number of halfedges. | |
Size_type | number_of_edges () |
returns the number of halfedge pairs. | |
Size_type | number_of_faces () |
returns the number of faces. | |
Size_type | number_of_face_cycles () |
returns the number of face cycles. | |
Size_type | number_of_connected_components () |
calculates the number of connected components of P . | |
void | print_statistics (std::ostream &os=std::cout) |
print the statistics of P : the number of vertices, edges, and faces. | |
void | check_integrity_and_topological_planarity (bool faces=true) |
checks the link structure and the genus of P . | |
Point CGAL::Nef_polyhedron_2< T >::Explorer::point | ( | Vertex_const_handle | v | ) |
returns the standard point that is the embedding of v
.
E.is_standard(v)
. Ray CGAL::Nef_polyhedron_2< T >::Explorer::ray | ( | Vertex_const_handle | v | ) |
returns the ray defining the non-standard point on the frame.
!E.is_standard(v)
.