# On separating two simple polygons by a single translation

Research output: Contribution to journalArticle

### Abstract

Let P and Q be two disjoint simple polygons having n sides each. We present an algorithm which determines whether Q can be moved by a single translation to a position sufficiently far from P, and which produces all such motions if they exist. The algorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sided polygon. Since Tarjan and Van Wyk have recently shown that t(n)=O(n log log n) this improves the previous best result for this problem which was O(n log n) even after triangulation.

Original language English (US) 265-278 14 Discrete & Computational Geometry 4 1 https://doi.org/10.1007/BF02187729 Published - Dec 1 1989

Simple Polygon
Triangulate
Triangulation
Polygon
Disjoint
Motion

### ASJC Scopus subject areas

• Theoretical Computer Science
• Geometry and Topology
• Discrete Mathematics and Combinatorics
• Computational Theory and Mathematics

### Cite this

In: Discrete & Computational Geometry, Vol. 4, No. 1, 01.12.1989, p. 265-278.

Research output: Contribution to journalArticle

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