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
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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.