WADS 1989: Algorithms and Data Structures pp 171-182

# Computing the center of area of a polygon

• Matthew Díaz
• Joseph O'Rourke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)

## 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(n2GK), but for general non-convex polygons, our algorithm's time complexity is O(n4 log nG K+n3G2K+nGK2).

## Keywords

Convex Polygon Minimum Area Simple Polygon Lower Envelope Perpendicular Bisector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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