For simplicity, assume that the distribution has bounded support, i.e:
There is some Mx and My such that f(x,y) is zero for abs(x) > Mx and abs(y) > My.
One could probably do without this condition but it would a little more involved and in practice (unless you have a heavy-tailed distribution) it wont make much difference.
With this assumption, a general way to do it for any f(x,y) is as follows:
Let Mz = max(f(x,y)) over all x and y.
Now use rand to choose 3 numbers uniformly in the Box (-Mx < x < Mx) x (-My < y < My) x (z < Mz):
x = 2*Mx*(rand-0.5);
y = 2*My*(rand-0.5);
z = Mz*rand;
if z > f(x,y), reject x and y
otherwise add (x,y) to your set of generated points.
Best Regards,
Sandeep
