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Computing

, Volume 32, Issue 4, pp 357–364 | Cite as

An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons

  • G. T. Toussaint
Short Communications

Abstract

LetP={p 1 ,p 2 , ...,p m } andQ={q 1 ,q 2 , ...,q n } be two intersecting convex polygons whose vertices are specified by their cartesian coordinates in order. An optimalO(m+n) algorithm is presented for computing the minimum euclidean distance betweena vertexp i inP and a vertexq j inQ.

Key words

Algorithms complexity computational geometry convex polygons minimum distance Voronoi diagrams 

Ein optimaler Algorithmus zur Berechnung des minimalen Eckenabstandes zwischen zwei sich überschneidenden konvexen Polygonen

Zusammenfassung

SeienP={p 1 ,p 2 , ...,p m } undQ={q 1 ,q 2 , ...,q n } zwei sich überschneidende konvexe Polygone, deren Ecken durch die kartesischen Koordinaten in der richtigen Reihenfolge festgelegt sind. Wir geben einen optimalenO(m+n)-Algorithmus für die Berechnung der minimalen euklidischen Distanz zwischen einer Eckep i inP und einer Eckeq j inQ an.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • G. T. Toussaint
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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