Separating two simple polygons by a sequence of translations

R. Pollack*, M. Sharir, S. Sifrony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

Let P and Q be two disjoint simple polygons having m and n sides, respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mnα(mn) log m log n) where α(k) is the extremely slowly growing inverse Ackermann's function. Since in the worst case Ω(mn) translations may be necessary to separate Q from P, our algorithm is close to optimal.

Original languageEnglish
Pages (from-to)123-136
Number of pages14
JournalDiscrete and Computational Geometry
Volume3
Issue number1
DOIs
StatePublished - Dec 1988

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