Integrating Space, Time, Version, and Scale using Alexandrov Topologies
Norbert Paul, Patrick Erik Bradley · International Journal of 3-D Information Modeling · 2015
This article introduces a novel approach to higher dimensional spatial database design. Instead of extending the canonical Solid–Face–Edge–Vertex schema of topological data, these classes are replaced altogether by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes are replaced by one separate binary relation BoundedBy on SpatialEntity which defines a so-called Alexandrov topology on SpatialEntity and thus exposes mathematical principles of spatial data design. This has important consequences: First, a mathematical definition of topological “dimension” for spatial data can be given. Second, every topology for data of arbitrary dimension has such a simple representation. Also, version histories have a canonical Alexandrov topology, and generalizations can be consistently modeled by continuous foreign keys between LoDs. The result is a relational database schema for spatial data of dimension 6 and more which seamlessly integrates 4D space-time, levels of details and version history. Topological constructions enable queries across these different aspects.