Designing and Implementing a General Purpose Halfedge Data Structure

Abstract

Halfedge data structures (HDS) are fundamental in representing combinatorial geometric structures, useful for representing any planar structures such as plane graphs and planar maps, polyhedral surfaces and boundary representations (BREPs), two-dimensional views of a three dimensional scene, etc. Many variants have been proposed in the literature, starting with the winged-edge data structure of Baumgart[2], the DCEL of [15,9], the quad-edge data structure [11], the halfedge data structure [18,12, and refs. therein]. They have been proposed in various frameworks (references too many to give here):

• Plane structures: including planar maps for GIS, 2D Boolean modeling, 2D graphics, scienti.c computations, computer vision. The requirements on HDS are that that some edges may be in.nite (e.g., Voronoi diagrams), or border edges (e.g., for bounded polygonal domains), it may include holes in the facets (planar maps), and that if so, one of the connected boundary cycle is distinguished as the outer boundary (the others are inner holes).

• Boundary representation of three-dimensional solids: including Brep representation, solid modeling, polyhedral surfaces, 3D graphics. The requirements here vary slightly: holes may still be allowed, but there is no need to distinguish an outer boundary, in.nite edges are not always useful but border edges might need to be allowed.