A counterexample to an algorithm for computing monotone hulls of simple polygons

Godfried T. Toussaint, Hossam El Gindy

Research output: Contribution to journalArticle

Abstract

A two-stage algorithm was recently proposed by Sklansky (1982) for computing the convex hull of a simple polygon P. The first step is intended to compute a simple polygon P* which is monotonic in both the x and y directions and which contains the convex hull vertices of P. The second step applies a very simple convex hull algorithm on P*. In this note we show that the first step does not always work correctly and can even yield non-simple polygons, invalidating the use of the second step. It is also shown that the first step can discard convex hull vertices thus invalidating the use of any convex hull algorithm in the second step.

Original languageEnglish (US)
Pages (from-to)219-222
Number of pages4
JournalPattern Recognition Letters
Volume1
Issue number4
DOIs
StatePublished - May 1983

Keywords

  • Convex hull
  • algorithms
  • complexity
  • computational geometry
  • maximal polygons
  • monotone hull
  • pattern recognition
  • simple polygons
  • weakly externally visible polygons

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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