Topological spatial relation calculation in constrained Delaunay triangulation: an algebraic method

Jiatian Li; Chunxiao Wang; Li Ma; Hao Chen; Dehong Yang; Xuequn Wu

doi:10.1117/12.813092

7 November 2008 Topological spatial relation calculation in constrained Delaunay triangulation: an algebraic method

Jiatian Li, Chunxiao Wang, Li Ma, Hao Chen, Dehong Yang, Xuequn Wu

Proceedings Volume 7146, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses; 714602 (2008) https://doi.org/10.1117/12.813092
Event: Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Geo-Simulation and Virtual GIS Environments, 2008, Guangzhou, China

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.

Citation Download Citation

Jiatian Li, Chunxiao Wang, Li Ma, Hao Chen, Dehong Yang, and Xuequn Wu "Topological spatial relation calculation in constrained Delaunay triangulation: an algebraic method", Proc. SPIE 7146, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses, 714602 (7 November 2008); https://doi.org/10.1117/12.813092

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