### 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(n^{2}) algorithm is presented, which is a substantial improvement over the O(n^{7}) time algorithm for the general problem.

Original language | English (US) |
---|---|

Pages (from-to) | 349-365 |

Number of pages | 17 |

Journal | Discrete and Computational Geometry |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1988 |

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### ASJC Scopus subject areas

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

### Cite this

*Discrete and Computational Geometry*,

*3*(1), 349-365. https://doi.org/10.1007/BF02187918

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

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 3, no. 1, pp. 349-365. https://doi.org/10.1007/BF02187918

}

TY - JOUR

T1 - The orthogonal convex skull problem

AU - Wood, Derick

AU - Yap, Chee

PY - 1988/12

Y1 - 1988/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=30244448943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30244448943&partnerID=8YFLogxK

U2 - 10.1007/BF02187918

DO - 10.1007/BF02187918

M3 - Article

AN - SCOPUS:30244448943

VL - 3

SP - 349

EP - 365

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -