Comments on: Random point in circle

By: billy

billy — Fri, 15 May 2009 12:04:36 +0000

The best is asking a Mathematician
http://mathworld.wolfram.com/DiskPointPicking.html

Second, if you want to use that in a Montecarlo simulation (Ask an Engeneer) and he/she’ll probaby respond: use Mersenne Twister (periodicity of any sequence is about 2^19937 iterations, nice, VERY nice). Also (and obvious) won’t appear the unpleasant Marsaglia Effect.

And last, the method that the author has posted is the BASIS of the russian roulette that’s perfect when multidimensional analisis is required, i.e. BRDF of four, five or even six dimensions.

By: mini

mini — Sat, 09 May 2009 10:54:31 +0000

It depends on what your random functions are, just use Mersenne twister pseudo-random number generator and you wont have any problems. The non-uniform things can be dealt with.

By: Max

Max — Thu, 02 Apr 2009 17:15:24 +0000

mini, SomeGuy’s solution has non-uniform distribution (it’ll
produce more points near the center), as Robert already noted.

May I also remind you, that sin and cos can be computed
simultaneously up to a very good precision while using
only six multiplications.

As for your solution, I didn’t look much into it, but
I’m quite sure that it has non-uniform distribution.

By: mini

mini — Thu, 02 Apr 2009 11:48:06 +0000

if we want to find the fastest solution and doing sin, cos, sqrt etc. needs to be as minimal as it can be.

Max’s solution isnt the best one here, as it uses all three of those costly functions – and it’s bad. If you dont want to use the loop, then go for the algorithm that SomeGuy told us here:

angle = random(0, 360);
dist = random(0, circle_radius);
x = cos(angle) * dist;
y = sin(angle) * dist;

Or even try my better(not the best) solution, where only one costly function is used:

(where R – given radius):

r = random(0, R);
x = r*random(-1, 1);
y = r-2*sqrt(r*r – x*x);

any better implementations?