Doubly Connected Edge List - Data Structure

Data Structure

DCEL is more than just a doubly linked list of edges. In the general case, a DCEL contains a record for each edge, vertex and face of the subdivision. Each record may contain additional information, for example, a face may contain the name of the area. Each edge usually bounds two faces and it is therefore convenient to regard each edge as half-edge. Each half-edge bounds a single face and thus has a pointer to that face. A half-edge has a pointer to the next half-edge and previous half-edge of the same face. To reach the other face, we can go to the twin of the half-edge and then traverse the other face. Each half-edge also has a pointer to its origin vertex (the destination vertex can be obtained by querying the origin of its twin).

Each vertex v contains the coordinates of the vertex and also stores a pointer to an arbitrary edge that has v as its origin. Each face stores a pointer to some half-edge of its outer boundary (if the face is unbounded then pointer is null). It also has a list of half-edges, one for each hole that may be incident within the face. If the vertices or faces do not hold any interesting information, there is no need to store them, thus saving space and reducing the data structure complexity.