Symmetry will not do you any good. Remember that we are interested in the ratio of the surface areas; dividing the image in four parts is similar to multiplying both the numerator and the denominator by four. It won’t increase the speed of convergence.

Excluding some parts of the image might help, but only if you know the exact fraction of both bodies you are excluding and come up with an efficient way to select random points uniformly distributed over the area you are including. I’m guessing just selecting random points in a square is faster. (certainly easier to implement…)

Thanks for your input! If you come up with a more efficient strategy be sure to let me know; I’ll implement it if I can.

]]>After that, you need some sort of way to avoid putting dots in a place that you already know is inside the circle. Or some other way to get closer and closer to the interesting area.

]]>