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Eliseo Clementini, Paolino Di Felice, "Topological Invariants for Lines," IEEE Transactions on Knowledge and Data Engineering, vol. 10, no. 1, pp. 3854, January/February, 1998.  
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@article{ 10.1109/69.667085, author = {Eliseo Clementini and Paolino Di Felice}, title = {Topological Invariants for Lines}, journal ={IEEE Transactions on Knowledge and Data Engineering}, volume = {10}, number = {1}, issn = {10414347}, year = {1998}, pages = {3854}, doi = {http://doi.ieeecomputersociety.org/10.1109/69.667085}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Knowledge and Data Engineering TI  Topological Invariants for Lines IS  1 SN  10414347 SP38 EP54 EPD  3854 A1  Eliseo Clementini, A1  Paolino Di Felice, PY  1998 KW  Lines KW  spatial data modeling KW  spatial relations KW  topological invariants KW  homeomorphism. VL  10 JA  IEEE Transactions on Knowledge and Data Engineering ER   
Abstract—A set of topological invariants for relations between lines embedded in the 2dimensional 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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