Algorithms for computing the center of area of a convex polygon

Abstract

The center of area of a convex polygonP is the unique pointp * that maximizes the minimum area overlap betweenP and any halfplane that includesp *. We show thatp * is unique and present two algorithms for its computation. The first is a combinatorial algorithm that runs in timeO (n 6 log2 n). The second is a “numerical” algorithm that runs in timeO(GK(n+K)) whereK represents the number of desired bits of precision in the output coordinates andG the number of bits used to represent the coordinates of the input polygon vertices. We conclude with a discussion of implementation issues and related results.