Does anyone know of any open source software for drawing/calculating the area of intersection of different shapes?

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I would like to be able to draw any number of different shapes and determine the area of their intersections. I'm looking for free, open source software. I thought about trying to code something up myself, but it would save a lot of time and trouble if there is something out there that can do it already. Any suggestions?

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I have access to MATLAB (I didn't think about mentioning that in the question... oops), and had already searched for a solution utilizing it, but apparently overlooked the one that existed. I searched again and found the function Polygons_intersection on the Matlab Central File Exchange. It is perfect for my needs.

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You can do it with Inkscape or directly in PostScript: use one of the shapes as a clipping path and then paint the other shape.