DCELbased

DCELbased refers to representations and algorithms that rely on the doubly connected edge list (DCEL) for modeling planar subdivisions and embedded graphs. A DCEL-based model organizes the subdivision into vertices, edges (as pairs of half-edges), half-edges themselves, and faces, with a network of pointers that supports efficient navigation around boundaries and at vertices.

In a DCEL, each half-edge has an origin vertex, a twin half-edge in the opposite direction, a next and a previous half-edge along the boundary of its incident face, and a reference to the face it borders. Each vertex stores coordinates and a reference to an incident half-edge. Each edge is represented by its two half-edges, and each face stores a reference to one of its boundary half-edges, enabling traversal of the entire boundary, including the outer face.

DCEL-based structures enable robust planar graph operations, such as traversing boundary cycles, determining adjacency among faces, and performing topological queries or boolean operations on regions. They support incremental construction and dynamic edits, though maintaining consistency during updates can be complex. The approach excels at representing planar straight-line graphs and is well-suited for algorithms that require reliable navigation of faces, edges, and vertices.

Applications of DCEL-based representations include geographic information systems, computer-aided design, computational geometry, and mesh or arrangement processing. They underpin tasks such as polygon union/intersection, subdivision and carving of planar maps, and the extraction of boundary polygons from complex subdivisions. Variants like the winged-edge and other DCEL-like structures share similar goals, with differences in data organization and pointer conventions.