Constructing strongly convex hulls using exact or rounded arithmetic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

Abstract

One useful generalization of the convex hull of a set S of points is the ε-strongly convex δ-hull. It is defined to be a convex polygon P with vertices taken from S such that no point in S lies farther than δ outside P and such that even if the vertices of P are perturbed by as much as ε, P remains convex. It was an open question as to whether an ε-strongly convex O(ε)-hull existed for all positive ε. We give here an O(n log n) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an ε-strongly convex O(ε + μ)-hull in O(n log n) time using rounded arithmetic with rounding unit μ. This is the first rounded arithmetic convex hull algorithm which guarantees a convex output and which has error independent of n.

Original languageEnglish (US)
Title of host publicationProc Sixth Annu Symp Comput Geom
PublisherPubl by ACM
Pages235-243
Number of pages9
ISBN (Print)0897913620
StatePublished - Jan 1 1990
Externally publishedYes
EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
Duration: Jun 6 1990Jun 8 1990

Publication series

NameProc Sixth Annu Symp Comput Geom

Other

OtherProceedings of the Sixth Annual Symposium on Computational Geometry
CityBerkeley, CA, USA
Period6/6/906/8/90

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Li, Z., & Milenkovic, V. (1990). Constructing strongly convex hulls using exact or rounded arithmetic. In Proc Sixth Annu Symp Comput Geom (pp. 235-243). (Proc Sixth Annu Symp Comput Geom). Publ by ACM.