16 Mar
2008
16 Mar
'08
10:06 p.m.
So, we can find g(r) independently by integrating with respect to theta.
we get g(r)= 1/sigma^2 * e^-(r^2/sigma^2)
Ah, here's a missing factor of 2 in the exponent. That should be
g(r)= 1/sigma^2 * e^-(r^2/ ( 2*sigma^2) )
And the correct formulae are
x=r*cos(theta) = sigma * sqrt(-2 * ln (1-U1) ) * cos (2*pi*U2) y=r*sin(theta) = sigma * sqrt(-2 * ln (1-U1) ) * sin (2*pi*U2)
I thought I missed something...