MODELING THE TOPOLOGICAL RELATIONSHIP OF SPATIAL OBJECTS USING EGENHOFER MATRICES

Abstract

The analytical needs in geographic information systems (GIS) have led to the interpretation of formal methods of modeling the topological relationship of spatial objects using Egenhofer-matrices. As a result, we investigate the algebraic approach for the structural analysis of a spatial topology- Simplices, The Order of Simplices, Faces of Simplices, Simplicial Complex, Skeletons of Simplicial Complex. Oriented Simplex, Connectedness of Spatial Objects. The matrix interpretation of the eight spatial topological relations matrices of two Egenhofer 4-intersection models and that of the two Egenhofer 9-intersection models using matrix addition and multiplication modulo 2. We also developed the 8-intersection and The 2x4 Matrix Representation of Topological Relations of Three Objects A, B and C. 16- intersection models and The 2x8 Matrix Representation Of Topological Relations Of Four Objects A, B, C And D. using the Egenhofer’s 4 and 9- Intersections Models.