Computing the center of area of a polygon

Abstract

The center of area of a polygon P is the unique point p* that maximizes the minimum area overlap between P and any halfplane that includes p*. We present several “numerical” algorithms for finding the coordinates of p* for a polygon of n vertices. These algorithms are numerical in the sense that we have been careful to express the algorithm complexities as a function of G, the number of bits used to represent the coordinates of the polygon vertices, and K, the number of desired bits of precision in the output coordinates of p*. For a convex polygon the algorithm runs in O(nGK); non-convex polygons offer considerably more challenge. For orthogonal non-convex polygons, we have an algorithm that runs in O(n ² GK), but for general non-convex polygons, our algorithm's time complexity is O(n ⁴ log nG K+n ³ G ² K+nGK ²).