# Computing the link center of a simple polygon

W. Lenhart, R. Pollack, J. Sack, R. Seidel, M. Sharir, S. Suri, Godfried Toussaint, S. Whitesides, Chee Yap

Research output: Contribution to journalArticle

### Abstract

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized. Here the link distance between two points x, y inside P is defined to be the smallest number of straight edges in a polygonal path inside P connecting x to y. We prove several geometric properties of the link center and present an algorithm that calculates this set in time O(n2), where n is the number of sides of P. We also give an O(n log n) algorithm for finding an approximate link center, that is, a point x such that the maximal link distance from x to any point in P is at most one more than the value attained from the true link center.

Original language English (US) 281-293 13 Discrete and Computational Geometry 3 1 https://doi.org/10.1007/BF02187913 Published - Dec 1988

Simple Polygon
Computing
Set of points
Straight
Calculate
Path

### ASJC Scopus subject areas

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

### Cite this

Lenhart, W., Pollack, R., Sack, J., Seidel, R., Sharir, M., Suri, S., ... Yap, C. (1988). Computing the link center of a simple polygon. Discrete and Computational Geometry, 3(1), 281-293. https://doi.org/10.1007/BF02187913

Computing the link center of a simple polygon. / Lenhart, W.; Pollack, R.; Sack, J.; Seidel, R.; Sharir, M.; Suri, S.; Toussaint, Godfried; Whitesides, S.; Yap, Chee.

In: Discrete and Computational Geometry, Vol. 3, No. 1, 12.1988, p. 281-293.

Research output: Contribution to journalArticle

Lenhart, W, Pollack, R, Sack, J, Seidel, R, Sharir, M, Suri, S, Toussaint, G, Whitesides, S & Yap, C 1988, 'Computing the link center of a simple polygon', Discrete and Computational Geometry, vol. 3, no. 1, pp. 281-293. https://doi.org/10.1007/BF02187913
Lenhart W, Pollack R, Sack J, Seidel R, Sharir M, Suri S et al. Computing the link center of a simple polygon. Discrete and Computational Geometry. 1988 Dec;3(1):281-293. https://doi.org/10.1007/BF02187913
Lenhart, W. ; Pollack, R. ; Sack, J. ; Seidel, R. ; Sharir, M. ; Suri, S. ; Toussaint, Godfried ; Whitesides, S. ; Yap, Chee. / Computing the link center of a simple polygon. In: Discrete and Computational Geometry. 1988 ; Vol. 3, No. 1. pp. 281-293.
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