The Dual Half-Edge—A Topological Primal/Dual Data Structure and Construction Operators for Modelling and Manipulating Cell Complexes

Abstract

There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that expresses both the geometric representations of individual rooms and their topological relationships. Volumes and faces are expressed as vertices and edges respectively in the dual space, permitting a model just based on the storage of primal and dual vertices and edges. Attributes may be attached to all of these entities permitting, for example, shortest path queries between specified rooms, or to the exterior. Storage costs are shown to be comparable to other non-manifold models, and construction with local Euler-type operators is demonstrated with two large university buildings. This is intended to enhance current developments in 3D Geographic Information Systems for interior and exterior city modelling.

Keywords

• three-dimensional modelling
• solid modelling
• data structures
• Euler operators