2009/09/01 by Sanjiang Li, Li, Sanjiang
Computer Science · Social Sciences · #68T30 #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #Constraint Satisfaction and Optimization #Data Management and Algorithms #FOS: Computer and information sciences #Geographic Information Systems Studies #cs.AI #cs.CG #msc:68T30
paper · pdf · doi:10.48550/arxiv.0909.0109
A short version appeared in KR-10. Several results have been rephrased and omitted proofs are given here. (Sanjiang Li. A Layered Graph Representation for Complex Regions, in Proceedings of the 12th International Conference on the Principles of Knowledge Representation and Reasoning (KR-10), pages 581-583, Toronto, Canada, May 9-13, 2010)
openalex publication_date 2009/09/01 · arxiv created 2013/10/18 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches emphasised the topological relations between spatial objects, this work studies the internal topological structure of bounded plane regions, which could consist of multiple pieces and/or have holes and islands to any finite level. The insufficiency of simple regions (regions homeomorphic to closed disks) to cope with the variety and complexity of spatial entities and phenomena has been widely acknowledged. Another significant drawback of simple regions is that they are not closed under set operations union, intersection, and difference. This paper considers bounded semi-algebraic regions, which are closed under set operations and can closely approximate most plane regions arising in practice.