Formal Description and Modeling Topological Relations in 3D Based on Dimension-Extended and Euler-Poincare Characteristics

funds for young scholar (&nbsp: 200609) Abstract: Formal description and representation of topological relations between 3D spatial features is one of the key issues in developing 3D GIS. The criteria on the description and determination of topological relations are topological invariants, which may be dimension, separations, Euler-Poincare characteristics etc. This paper is concentrated on some basic issues of modeling topological relations using these invariants. With the introduction of the concept of pure k- complex (0≤k≤3), formal description of spatial features in the GIS is given. An approach is proposed to describe the topological relations between 3D spatial features with topological components of k-complex (0≤k≤3), i.e. boundary and interior. The topological relationship set: {disjoint, touches, within, crosses, overlaps, contains, equal} for the pair of spatial features were defined with dimension-extended. The topological relations for the pair of k-complex were examined with dimension-extended 4-intersection prior to calculate of Euler-Poincare characteristics. The model based on dimension-extended and Euler-Poincare characteristics can distinguish the topological relations of 3D spatial features more details than the classic 4/9-intersection model