NEARLY CONVEX SETS AND THE SHAPE OF LEGISLATIVE DISTRICTS
James R. Bozeman, Lauren Pyrik, Julie Theoret · 2008
In this paper we examine how close a polygonal planar set is to being convex. This is accomplished by considering the ratio of the area of the largest convex set contained in the original polygon to the area of the convex hull of the set. Algorithms for determining the convex hull and for determining the largest convex set interior to the polygon are exhibited. After defining when such sets are nearly convex we then use this result to decide when legislative districts are nicely shaped.