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.
Highlights
This paper presents a detailed technical description and properties of the dual half-edge (DHE) topological data structure and its application in the Geographic Information Sciences (GIS), in building interior modelling
The novel DHE data structure shown in this paper was designed to achieve our ultimate goal
Model construction, based on Euler operators, includes automatic updates of the dual representing the logical structure of the model
Summary
This paper presents a detailed technical description and properties of the dual half-edge (DHE) topological data structure and its application in the Geographic Information Sciences (GIS), in building interior modelling It includes associated navigation and construction operators necessary for a convenient usage of DHE. Adjacent cells of a complex are connected by a shared face, which is represented by a dual edge ((FFiigguurree 33aa)). The DHE conforms to the definition of a complex-based non-manifold geometric model [11]—it allows for representation of solids where a dual node represents a volume and all primal edges and nodes connected with this node define the volume boundary; dangling faces, edges and combination of them are possible. The only construction entities kept in the DHE model are half-edges and vertices: faces and volumes are represented in the dual structure. The full set of navigation operators is described by Equations (1)–(9)
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