Topologically Consistent Space, Time, Version, and Scale Using Alexandrov Topologies

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Author(s): Patrick E. Bradley (Karlsruhe Institute of Technology, Germany)and Norbert Paul (IEP Industrie Elektronik Paul GmbH, Germany)
Copyright: 2018
Pages: 31
Source title: Contemporary Strategies and Approaches in 3-D Information Modeling
Source Author(s)/Editor(s): Bimal Kumar (Glasgow Caledonian University, UK)
DOI: 10.4018/978-1-5225-5625-1.ch003

Keywords: Civil Engineering / Engineering Science Reference / Government & Law / Urban & Regional Development

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Abstract

A novel approach to higher dimensional spatial database design is introduced by replacing the canonical solid–face–edge–vertex schema of topological data by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes by one separate binary relation BoundedBy on SpatialEntity defining an Alexandrov topology. This exposes mathematical principles of spatial data design. The first consequence is a mathematical definition of topological “dimension” for spatial data. Another is that every topology for spatial data is an Alexandrov topology. 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, seamlessly integrating space-time, LoDs, and version history. Topological constructions enable queries across these different aspects. Giving points coordinates amounts can give rise to topological inconsistencies which can be measured with topological invariants.

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Topologically Consistent Space, Time, Version, and Scale Using Alexandrov Topologies

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