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Topological Invariants for Lines
January/February 1998 (vol. 10 no. 1)
pp. 38-54

Abstract—A set of topological invariants for relations between lines embedded in the 2-dimensional Euclidean space is given. The set of invariants is proven to be necessary and sufficient to characterize topological equivalence classes of binary relations between simple lines. The topology of arbitrarily complex geometric scenes is described with a variation of the same set of invariants. Polynomial time algorithms are given to assess topological equivalence of two scenes. The relevance of identifying such a set of invariants and efficient algorithms is due to application areas of spatial database systems, where a model for describing topological relations between planar features is sought.

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Index Terms:
Lines, spatial data modeling, spatial relations, topological invariants, homeomorphism.
Citation:
Eliseo Clementini, Paolino Di Felice, "Topological Invariants for Lines," IEEE Transactions on Knowledge and Data Engineering, vol. 10, no. 1, pp. 38-54, Jan.-Feb. 1998, doi:10.1109/69.667085
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