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Sorry, if this question is dumb, but:

When you try to fill the circle with other circles - its called Apollonian circles, and there are resources about it, and some example algorithms. But i want to know the name of the generic algorithm of placing circles within the polygon, in same fashion as apollonian ones are placed in the circle.

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    Your wish is my command.2012-01-24

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It appears that it is called an Apollonian packing of the polygon.