I have a circle of radius r and access to a random number generator. What is a method to generate random (x,y) values distributed along the circle's perimeter?

  • 4
    $\begingroup$ Generate a random angle $\theta$ between $0$ and $2\pi$. Take $(x,y)=(r\cos\theta, r\sin\theta)$. $\endgroup$
    – mjqxxxx
    Dec 7 '12 at 15:18

The simplest method would be to generate a random angle $\theta \in [0,2\pi]$. Then convert from polar to Cartesian with $(x,y) = (r \cos \theta , r \sin \theta)$.

Note that if your random number generator returns a number $k \in [0,1]$ then $\theta = 2\pi k$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.