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I would like to know how to calculate the volume of a solid object that is represented by Boundary representation (B-Rep)? Any hints? Thanks in advance

Maxence
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user467689
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  • http://mathoverflow.net/questions/979/algorithm-for-finding-the-volume-of-a-convex-polytope – atomocopter Oct 06 '10 at 14:40
  • Typically the software that generated the B-Rep object will calculate the volume for you. So why are you asking the question? – brainjam Oct 06 '10 at 15:07

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You can use Gauss' theorem to turn the volume integral into a surface integral. You probably remember Stoke's theorem and Green's theorem from calculus. It's basically the same idea. It is fairly easy to evaluate if you can turn your B-Rep into a set of planar polygons. You can find some details here and here.

This isn't going to turn out well if your surface is non-manifold, but the problem isn't well defined in that case anyways.

MPG
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