The task should be very common, what are the best and easiest to implement algorithms to compute the volume of union/intersection of given bodies? Or union/intersection area for 2D figures.
I don't mean straightforward integration to get the volume, it shouldn't be very convenient. I was thinking about some kind of naive Monte Carlo (the ratio of hit to thrown points), but it has very poor convergence. Or maybe approximating bodies as unions of simpler ones, for which the intersections are known, though it's (a bit) complex.