Get a point inside a polygon

I have a 2D polygon of arbitrary geometry. I need to find any point that is inside of that polygon. The center won't work because the polygon might be convex. Is there a way to quickly find a point inside an arbitrary geometry?

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I assume that "polygon" is a set bounded by simple closed broken line (?). Do you need a kind of algorithm? Say what if you take a point $p$ on a side of polygon; take a line $\ell$ in general position; count number of intersections of $\ell$ with other sides before $p$ and go bit left from $p$ if the number is even and bit to the right if it is odd... – Anton Petrunin Feb 25 2011 at 18:08
Sure - you just look at the polygon, and pick a point inside it. But maybe when you say you "have a 2D polygon," you don't mean you have a piece of paper with the polygon on it. So, what do you mean? Unless we know in what way you "have" this polygon, we can't give a sensible procedure for saying anything about it, much less finding a point inside it. – Gerry Myerson Feb 26 2011 at 5:08