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What is the name of the point(s) in a polygon, calculated by "shrinking" the polygon until there's no surface left?

Example (the light areas):


Also, of possible, it would be cool to have an algorithm to calculate this in a reasonable time, given the coordinates of the edges.

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What do you mean by shrinking the polygon? – Fabian Apr 6 '11 at 19:09
I haven't heard of a name for it, but a more conventional characterization of it (if I understand your figure correctly) would be as the point(s) inside the polygon with maximal distance from its border. – joriki Apr 6 '11 at 19:10
@Fabian look at @joriki's comment, that is what I meant. – Attila O. Apr 6 '11 at 19:11
This is known as the "Medial Axis Transform (MAT)" in computer science. You can try searching for this to get more information on the algorithm. – Matt Groff Apr 6 '11 at 19:59
up vote 3 down vote accepted

It's the medial axis. See also the straight skeleton.

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What I'm looking for is the inner end(s) of the longest line(s) of the straight topological skeleton. Or, you might say, the point(s) of the medial axis that are the farthest from the boundary. Do you know what is the name of those points or that point? For monotype polygons, that points is also the centroid. – Attila O. Apr 6 '11 at 20:05
@Attila, see also… – lhf Apr 6 '11 at 22:58

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