## Computing the center of area of a convex polygon

PETER BRASS and
LAURA HEINRICH-LITAN

**Abstract**
The center of area of a planar convex set C is the point p
for which the minimum area cut off from C by any halfplane
containing p is maximized. Properties of this point
were studied already long ago in classical geometry,
but it is quite nontrivial to really determine this point
for a given convex set. We give an O(n^2 (\log n)^3 \alpha(n))-algorithm
to compute the center of area of a convex n-gon,
which improves a previous O(n^6 (\log n)^2)-algorithm
of Diaz and O'Rourke.

Technical Report B 02-10, Freie Universität Berlin, Fachbereich Mathematik
und Informatik, 2002.