CGAL::Topological_explorer

Definition

An instance D of the data type Topological_explorer is a decorator for interfacing the topological structure of a plane map P (read-only).

A plane map P consists of a triple $$(V, E, F) of vertices, edges, and faces. We collectively call them objects. An edge e is a pair of vertices (v,w) with incidence operations v = source(e), w = target(e). The list of all edges with source v is called the adjacency list A(v).

Edges are paired into twins. For each edge e = (v,w) there's an edge twin(e) = (w,v) and twin(twin(e)) == e¹.

An edge e = (v,w) knows two adjacent edges en = next(e) and ep = previous(e) where source(en) = w, previous(en) = e and target(ep) = v and next(ep) = e. By this symmetric previous-next relationship all edges are partitioned into face cycles. Two edges $$e and $$e' are in the same face cycle if $$e = next^*(e'). All edges e in the same face cycle have the same incident face $$f = face(e). The cyclic order on the adjacency list of a vertex v = source(e) is given by cyclic_adj_succ(e) = twin(previous(e)) and cyclic_adj_pred(e) = next(twin(e)).

A vertex v is embedded via coordinates point(v). By the embedding of its source and target an edge corresponds to a segment. P has the property that the embedding is always order-preserving. This means a ray fixed in point(v) of a vertex v and swept around counterclockwise meets the embeddings of target(e) ($$e A(v)) in the cyclic order defined by the list order of A.

The embedded face cycles partition the plane into maximal connected subsets of points. Each such set corresponds to a face. A face is bounded by its incident face cycles. For all the edges in the non-trivial face cycles it holds that the face is left of the edges. There can also be trivial face cycles in form of isolated vertices in the interior of a face. Each such vertex v knows its surrounding face f = face(v).

Plane maps are attributed, for each object $$u V E F we attribute an information mark(u) of type Mark. Mark fits the concepts assignable, default-constructible, and equal-comparable.

Types

Local types are handles, iterators and circulators of the following kind: Vertex_const_handle, Vertex_const_iterator, Halfedge_const_handle, Halfedge_const_iterator, Face_const_handle, Face_const_iterator. Additionally the following circulators are defined.

Operations

Vertex_const_handle	D.source ( Halfedge_const_handle e)
		returns the source of e.
Vertex_const_handle	D.target ( Halfedge_const_handle e)
		returns the target of e.
Halfedge_const_handle	D.twin ( Halfedge_const_handle e)	returns the twin of e.
bool	D.is_isolated ( Vertex_const_handle v)
		returns true iff $$A(v) = .
Halfedge_const_handle	D.first_out_edge ( Vertex_const_handle v)
		returns one halfedge with source v. It's the starting point for the circular iteration over the halfedges with source v. Precondition:  !is_isolated(v).
Halfedge_const_handle	D.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. Precondition:  !is_isolated(v).
Halfedge_const_handle	D.cyclic_adj_succ ( Halfedge_const_handle e)
		returns the edge after e in the cyclic ordered adjacency list of source(e).
Halfedge_const_handle	D.cyclic_adj_pred ( Halfedge_const_handle e)
		returns the edge before e in the cyclic ordered adjacency list of source(e).
Halfedge_const_handle	D.next ( Halfedge_const_handle e)	returns the next edge in the face cycle containing e.
Halfedge_const_handle	D.previous ( Halfedge_const_handle e)
		returns the previous edge in the face cycle containing e.
Face_const_handle	D.face ( Halfedge_const_handle e)	returns the face incident to e.
Face_const_handle	D.face ( Vertex_const_handle v)	returns the face incident to v. Precondition:  is_isolated(v).
Halfedge_const_handle	D.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).

Iteration

Associated Information

Statistics and Integrity

Footnotes