Topological invariants for lines

Author

Clementini, Eliseo ; Felice, Paolino Di

Author_Institution

Dept. of Electr. Eng., l´´Aquila Univ., Italy

Volume

10

Issue

1

fYear

1998

Firstpage

38

Lastpage

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. 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

Keywords

computational geometry; equivalence classes; topology; visual databases; Euclidean space; geometric scenes; lines; spatial database systems; topological equivalence classes; topological invariants; topological relations; Application software; Data models; Data visualization; Geographic Information Systems; Information systems; Layout; Space technology; Spatial databases; Topology; Visual databases;

fLanguage

English

Journal_Title

Knowledge and Data Engineering, IEEE Transactions on

Publisher

ieee

ISSN

1041-4347

Type

jour

DOI

10.1109/69.667085

Filename

667085