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

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

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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.

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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Authors and Affiliations

  1. School of Computer Science, McGill University, 805 Sherbrooke Street West, H3A 2K6, Montreal, Quebec, Canada

    G. T. Toussaint

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  1. G. T. Toussaint
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Research supported by N.S.E.R.C. grant no. A9293.

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Toussaint, G.T. An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons. Computing 32, 357–364 (1984). https://doi.org/10.1007/BF02243778

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  • DOI: https://doi.org/10.1007/BF02243778

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