Formal Framework of 3D Spatial Features and Topological Property Based on Manifold Topology

The lack of compressive theory and formal description methods about 3D spatial features and their topological properties have been a major impediment to practical 3D spatial data model implementation. This paper focused on the research of a topological model based on space partition for 3D GIS. In terms of point-set topology and combination topology, the formal definition of 3D spatial features are described as orientable n-pseudomanifolds(0≤n≤3),and it can be represented by complexes which is the union of same or lower simplexes. From the number of important topological properties of n-pseudomanifolds and continuous map about homeomorphism and homotopy, the topological properties such as space partition, orientability, connectivity and Euler characteristic are determined. According to the formal description of simplexes and complexes, the formal framework of 3D spatial features is presented.