# Computing the center of area of a polygon

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## 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}).

## Keywords

Convex Polygon Minimum Area Simple Polygon Lower Envelope Perpendicular Bisector## Preview

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