TOPOLOGICAL INVARIANTS FOR LINES

A set of topological invariants for relations between lines embedded i n the 2-dimensional Euclidean space is given. The set of invariants is proven to be necessary and sufficient to characterize topological equ ivalence classes of binary relations between simple lines. The topolog y of arbitrarily complex geometric scenes is described with a variatio n of the same set of invariants. Polynomial time algorithms are given to assess topological equivalence of two scenes. The relevance of iden tifying such a set of invariants and efficient algorithms is due to ap plication areas of spatial database systems, where a model for describ ing topological relations between planar features is sought.