caa a22 4500 445331992 CHVBK 20180317142740.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10707-009-0094-3 doi (NATIONALLICENCE)springer-10.1007/s10707-009-0094-3 Connectivity in the regular polytope representation [Elektronische Daten] [Rodney Thompson, Peter van Oosterom] In order to be able to draw inferences about real world phenomena from a representation expressed in a digital computer, it is essential that the representation should have a rigorously correct algebraic structure. It is also desirable that the underlying algebra be familiar, and provide a close modelling of those phenomena. The fundamental problem addressed in this paper is that, since computers do not support real-number arithmetic, the algebraic behaviour of the representation may not be correct, and cannot directly model a mathematical abstraction of space based on real numbers. This paper describes a basis for the robust geometrical construction of spatial objects in computer applications using a complex called the "Regular Polytope”. In contrast to most other spatial data types, this definition supports a rigorous logic within a finite digital arithmetic. The definition of connectivity proves to be non-trivial, and alternatives are investigated. It is shown that these alternatives satisfy the relations of a region connection calculus (RCC) as used for qualitative spatial reasoning, and thus introduce the rigor of that reasoning to geographical information systems. They also form what can reasonably be termed a "Finite Boolean Connection Algebra”. The rigorous and closed nature of the algebra ensures that these primitive functions and predicates can be combined to any desired level of complexity, and thus provide a useful toolkit for data retrieval and analysis. The paper argues for a model with two and three-dimensional objects that have been coded in Java and which implement a full set of topological and connectivity functions which is shown to be complete and rigorous. The Author(s), 2009 Connectivity nationallicence Topology nationallicence Spatial database nationallicence Spatial algebra nationallicence Region connection calculus nationallicence Boolean connection algebra nationallicence RCC : Region Connection Calculus nationallicence BCA : Boolean Connection Algebra nationallicence Thompson Rodney Department of Environment and Resource Management, Queensland, Australia aut van Oosterom Peter Delft University of Technology, Delft, The Netherlands aut GeoInformatica Springer US; http://www.springer-ny.com 15/2(2011-04-01), 223-246 1384-6175 15:2<223 2011 15 10707 https://doi.org/10.1007/s10707-009-0094-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10707-009-0094-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Thompson Rodney Department of Environment and Resource Management, Queensland, Australia aut NATIONALLICENCE 700 1- van Oosterom Peter Delft University of Technology, Delft, The Netherlands aut NATIONALLICENCE 773 0- GeoInformatica Springer US; http://www.springer-ny.com 15/2(2011-04-01), 223-246 1384-6175 15:2<223 2011 15 10707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer