Abstract:
Geographic Information Systems (GIS) have driven the demand for analytical tools to model the topological relationships among spatial objects. In response to this need, we explore an algebraic approach for the structural analysis of spatial topology, encompassing concepts such as Simplices, the Order of Simplices, Faces of Simplices, Simplicial Complexes, Skeletons of Simplicial Complexes, Oriented Simplexes, and Connectedness of Spatial Objects. This investigation involves interpreting the spatial topological relations using Egenhofer matrices, including eight spatial topological relations matrices derived from two Egenhofer 4-intersection models and two Egenhofer 9-intersection models. We utilize matrix addition and multiplication modulo 2 for this purpose. Furthermore, we introduce the 8-intersection and the 2×4 Matrix Representation of Topological Relations involving three objects, A, B, and C, as well as the 16-intersection models and the 2×8 Matrix Representation of Topological Relations for four objects, A, B, C, and D.
ANALYSIS OF TOPOLOGICAL RELATIONSHIPS OF SPATIAL OBJECTS VIA EGENHOFER MATRICES MODELING, GET MORE, ACTUARIAL SCIENCE PROJECT TOPICS AND MATERIALS
