The orthogonal convex skull problem

Derick Wood, Chee Yap

Research output: Contribution to journalArticle

Abstract

We give a combinatorial definition of the notion of a simple orthogonal polygon being k-concave, where k is a nonnegative integer. (A polygon is orthogonal if its edges are only horizontal or vertical.) Under this definition an orthogonal polygon which is 0-concave is convex, that is, it is a rectangle, and one that is 1-concave is orthoconvex in the usual sense, and vice versa. Then we consider the problem of computing an orthoconvex orthogonal polygon of maximal area contained in a simple orthogonal polygon. This is the orthogonal version of the potato peeling problem. An O(n2) algorithm is presented, which is a substantial improvement over the O(n7) time algorithm for the general problem.

Original languageEnglish (US)
Pages (from-to)349-365
Number of pages17
JournalDiscrete and Computational Geometry
Volume3
Issue number1
DOIs
StatePublished - Dec 1988

Fingerprint

Orthogonal Polygons
Simple Polygon
Peeling
Potato
Rectangle
Polygon
Horizontal
Non-negative
Vertical
Integer
Computing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

The orthogonal convex skull problem. / Wood, Derick; Yap, Chee.

In: Discrete and Computational Geometry, Vol. 3, No. 1, 12.1988, p. 349-365.

Research output: Contribution to journalArticle

Wood, Derick ; Yap, Chee. / The orthogonal convex skull problem. In: Discrete and Computational Geometry. 1988 ; Vol. 3, No. 1. pp. 349-365.
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