Algorithmica

, Volume 10, Issue 6, pp 457–472

Numerical stability of a convex hull algorithm for simple polygons

  • J. W. Jaromczyk
  • G. W. Wasilkowski
Article

DOI: 10.1007/BF01891832

Cite this article as:
Jaromczyk, J.W. & Wasilkowski, G.W. Algorithmica (1993) 10: 457. doi:10.1007/BF01891832

Abstract

A numerically stable and optimalO(n)-time implementation of an algorithm for finding the convex hull of a simple polygon is presented. Stability is understood in the sense of a backward error analysis. A concept of the condition number of simple polygons and its impact on the performance of the algorithm is discussed. It is shown that if the condition number does not exceed (1+O(ε))/(3ε), then, in floating-point arithmetic with the unit roundoffε, the algorithm produces the vertices of a convex hull for slightly perturbed input points. The relative perturbation does not exceed 3ε(1+O(ε)).

Key words

Convex hullSimple polygonFloating-point arithmeticRobust implementation

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • J. W. Jaromczyk
    • 1
  • G. W. Wasilkowski
    • 1
  1. 1.Department of Computer ScienceUniversity of KentuckyLexingtonUSA