Journal article Open Access

Characterizations of Star-Shaped, L-Convex, and Convex Polygons

Thomas Shermer; Godfried T. Toussaint

A chord of a simple polygon P is a line segment [xy] that intersects the boundary of P only at both endpoints x and y. A chord of P is called an interior chord provided the interior of [xy] lies in the interior of P. P is weakly visible from [xy] if for every point v in P there exists a point w in [xy] such that [vw] lies in P. In this paper star-shaped, L-convex, and convex polygons are characterized in terms of weak visibility properties from internal chords and starshaped subsets of P. A new Krasnoselskii-type characterization of isothetic star-shaped polygons is also presented.

Files (398.8 kB)
Name Size
398.8 kB Download
All versions This version
Views 11
Downloads 22
Data volume 797.6 kB797.6 kB
Unique views 11
Unique downloads 11


Cite as