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

摘要

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 2.(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.