Are topological relations dependent on the shape of spatial objects?

Topology is normally considered as independent of shape of spatial objects. This may not necessarily be true in describing relations between spatial objects in GIS. In this paper, we present proof that the topological relations between spatial objects are dependent on the shape of spatial objects. That is, that the topological relations of non-convex sets cannot be deformed to the topological relations of convex sets. The significant theoretical value of this paper is on its findings that topology of spatial objects is shape dependent.This indicates that when we want to describe topological relations between spatial objects in GIS, both topology and the shape of objects need to be considered. As a result, spatial data modeling, query and analysis based on the existing understanding of topology of spatial objects may need re-assessed.

作 者： SHI Wenzhong LIU Kimfung   作者單位： Advanced Research Centre for Spatial Information Technology, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China  刊 名： 自然科學進展（英文版）  SCI 英文刊名： PROGRESS IN NATURAL SCIENCE  年，卷(期)： 2005 15(11)  分類號： P4  關鍵詞： topological relations   homeomorphic map   convex set   interior   boundary   components  

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