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Proceedings Paper

Topological spatial relation calculation in constrained Delaunay triangulation: an algebraic method
Author(s): Jiatian Li; Chunxiao Wang; Li Ma; Hao Chen; Dehong Yang; Xuequn Wu
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Paper Abstract

Topological spatial relation between spatial objects is a very important topic for spatial analysis, query and reasoning in Geographic Information Science (GIS). In this paper, an algebraic method using constrained Delaunay triangulation (CDT) for topological spatial relation is presented. In the part of foundational theory, (i) prove CDT is simplicial complex in R2. (ii) import chain structure in CDT and prove including & approximating theorem and reduced including & approximating theorem, and are used for estimating left, middle and right side properties of triangle. (iii) define the region in CDT and establish region algebra (RA), which use the set of region as computational space and use the intersection operator as a binary operation. (iv) describe basic forms of node and chain which are contained in a set of triangles. In the part of spatial relation calculation, (i) describe spatial object as three entries, i.e. exterior, boundary and interior, with left, middle and right of triangle and their combination. (ii) establish the topological spatial relation calculation model-region nine intersection model (R9IM), which is used the intersection operation and the form operation as basic operations. (iii) calculate thirty-three spatial relations of simple objects with R9IM in the practice application of topological examination.

Paper Details

Date Published: 7 November 2008
PDF: 14 pages
Proc. SPIE 7146, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses, 714602 (7 November 2008); doi: 10.1117/12.813092
Show Author Affiliations
Jiatian Li, Kunming Univ. of Science and Technology (China)
National Geomatics Ctr. of China (China)
Chunxiao Wang, Yuxi Normal Univ. (China)
National Geomatics Ctr. of China (China)
Li Ma, Wuhan Univ. (China)
National Geomatics Ctr. of China (China)
Hao Chen, Wuhan Univ. (China)
National Geomatics Ctr. of China (China)
Dehong Yang, Kunming Univ. of Science and Technology (China)
Xuequn Wu, Kunming Univ. of Science and Technology (China)


Published in SPIE Proceedings Vol. 7146:
Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses
Lin Liu; Xia Li; Kai Liu; Xinchang Zhang, Editor(s)

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