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  • $\begingroup$ "There is no need in filtering out random points in a rectangle that don't fall in the prescribed region. The sampling within a region can be done directly with RandomPoint." Isn't it kind of doing the same as filtering out random points internally? Or how does RandomPoint work? $\endgroup$ Commented Nov 23, 2016 at 7:58
  • $\begingroup$ perhaps, it first parametrizes the implicit region in a [0,1]x[0,1] topologically equivalent object and then does non-uniform sampling. This should be faster, but you need to take into account for the differential area change between the original region and the parametrization. $\endgroup$ Commented Nov 23, 2016 at 11:31
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    $\begingroup$ @Trilarion, one does not necessarily have to do rejection sampling; see this for instance. $\endgroup$ Commented Jan 6, 2017 at 18:26
  • $\begingroup$ @J.M. Thanks for the link. The answers there are great. $\endgroup$ Commented Jan 7, 2017 at 10:28