Sample random points over intersection of surfaces

What would be the most efficient way, in python, to sample random two-dimensional numbers from a complicated intersection of surfaces ?

For instance, consider the intersection of many disks or the complementary of the union of many disks.

I know I could simply draw points from a box containing the two-dimensional zone of interest and then check if the desired conditions are satisfied, but I'm wondering if there is a much efficient solution to draw random points directly from the delimited surface !

Thanks