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

Abstract

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 GIS HistoryThis 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), particularly in building interior modelling. It includes associated navigation and construction operators necessary for a convenient usage of DHE. Previous papers describing DHE [1][2][3] reported on the importance of the primal/dual approach, some applications, model representation and preliminary development, but with only a brief discussion of technical details and properties. DHE is compared with some other similar data structures.Early 2D GIS data structures were designed for polygon (choropleth) maps, where the objective was to combine the sets of individual digitized polygon boundaries to form a network. Various approaches were attempted, but finally an arc-based structure predominated, where an "arc" consisted of an intermediate set of digitized points between the "nodes" at boundary junctions. This was closely related to the winged-edge structure [4], with pointers to the four adjacent arcs and the two bounding polygons. The winged-edge structure was developed by Baumgart [4] and provided a way to connect

A Spatial Reasoning Framework Based on Non-Manifold Topology

“…The connection between adjacent cells or faces can then be represented as an edge connecting their centroids. A variant of dual graph is the Dual Half-Edge (DHE) (Boguslawski et al 2016), which can describe the connection between the interior rooms of a building. It has seen applications in pathfinding and escape route computation.…”

“…It is an established research area in numerous disciplines, including Architecture, Robotics, and Computer Games. The state-of-the-art pathfinding structures including the DHE (Boguslawski et al 2016) and the navigation mesh (van Toll et al 2018), which is akin to a mesh or, topologically, a shell consisting of convex polygons overlaid on the planar surfaces in a 3D environment. Pathfinding algorithms are typically based on graph search algorithms, such as the Dijkstra's algorithm (Dijkstra 1959).…”

“…There have been some modified frameworks to deal with 3D structures, for example the 3D isovist algorithm (Suleiman, Joliveau, and Favier 2013) and mixed-dimensional RCC (Izadi, Stock, and Guesgen 2017). However, to the best of the authors' knowledge, the state-of-the-art pathfinding systems either use the topologically 1D dual graph (Boguslawski and Gold 2016), or the topologically 2D navigation mesh (van Toll et al 2018). A more in-depth review and investigation will be needed in these areas.…”

“…), space syntax(Hillier et al 1976), dual graph(Boguslawski and Gold 2016), pathfinding(van Toll et al 2018), room lighting reasoning(Smith 2006), and sound propagation(Raghuvanshi and Snyder 2018).Region Connection Calculus. Region ConnectionCalculus (RCC) provides a formal topological connection between two entities called regions.…”

Tessellations in GIS: Part II–making changes

“…Imai (1996) constructed an incremental by slicing the 3D DT -data points inside the shell have higher values than the specified contour surface. Boguslawski and Gold (2016) developed a half-edgebased data structure, the Dual Half-Edge (DHE), for the incremental construction of building models where full navigation within and between rooms may be achieved by examining both of the linked primal and dual graphs. This again is a tessellation, in the full 3D sense.…”