# Computing the link center of a simple polygon

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

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

### Abstract

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distancefrom x to any other point in P is minimized, where the link distance between two points x, y inside P isdefined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We proveseveral geometric properties of the link center and present an algorithm that calculates this set in time0(n2), where n is the number of sides of P. We also give an 0 (n log n) algorithm for finding apoint x in an approximate link center, namely the maximal link distance from x to any point in P is at most one more than the value attained from the link center.

Original language English (US) Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987 Association for Computing Machinery, Inc 1-10 10 0897912314, 9780897912310 https://doi.org/10.1145/41958.41959 Published - Oct 1 1987 3rd Annual Symposium on Computational Geometry, SCG 1987 - Waterloo, CanadaDuration: Jun 8 1987 → Jun 10 1987

### Other

Other 3rd Annual Symposium on Computational Geometry, SCG 1987 Canada Waterloo 6/8/87 → 6/10/87

Simple Polygon
Computing
Set of points
Straight
Calculate
Path

### ASJC Scopus subject areas

• Geometry and Topology
• Computational Mathematics

### Cite this

Lenhart, W., Pollack, R., Sack, J., Seidel, R., Shari, M., Suri, S., ... Yap, C. (1987). Computing the link center of a simple polygon. In Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987 (pp. 1-10). Association for Computing Machinery, Inc. https://doi.org/10.1145/41958.41959

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

Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987. Association for Computing Machinery, Inc, 1987. p. 1-10.

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

Lenhart, W, Pollack, R, Sack, J, Seidel, R, Shari, M, Suri, S, Toussaint, G, Whitesides, S & Yap, C 1987, Computing the link center of a simple polygon. in Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987. Association for Computing Machinery, Inc, pp. 1-10, 3rd Annual Symposium on Computational Geometry, SCG 1987, Waterloo, Canada, 6/8/87. https://doi.org/10.1145/41958.41959
Lenhart W, Pollack R, Sack J, Seidel R, Shari M, Suri S et al. Computing the link center of a simple polygon. In Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987. Association for Computing Machinery, Inc. 1987. p. 1-10 https://doi.org/10.1145/41958.41959
Lenhart, W. ; Pollack, R. ; Sack, J. ; Seidel, R. ; Shari, M. ; Suri, S. ; Toussaint, Godfried ; Whitesides, S. ; Yap, Chee. / Computing the link center of a simple polygon. Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987. Association for Computing Machinery, Inc, 1987. pp. 1-10
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