A calculating model and application of topological spatial relations based on delaunay triangulation region algebra

Topological spatial relation is a very important topic for spatial analysis and reasoning in Geographic Information System (GIS). This project proposed a new algebraic approach using constrained Delaunay triangulation (CDT) for topological spatial relation. We imported chain structure in CDT and proved including & approximating theorem and reduced including & approximating theorem, which are used for estimating left, middle and right side properties of triangle. The region in CDT is defined and the region algebra (RA) is established for describing basic forms of node and chain which are contained in a set of triangles. We described spatial object as three entries, i.e. exterior, boundary and interior, with left, middle and right of triangle and their combination and 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. There are 24 spatial relations of simple objects can be calculated by R9IM. © 2008 Binary Information Press.