Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I have two rays, one of length $L_1$ and one of length $L_2$. I anchor these rays, each at one end, on the 3-space points $p_1$ and $p_2$. Assuming that the Euclidean distance between $p_1$ and $p_2$ is $\leq (L_1+L_2)$, what solution space defines the points where these rays can be oriented to touch at their free ends? How might I sample uniformly from this solution space?

share|improve this question

1 Answer 1

up vote 0 down vote accepted

Sample points uniformly from the circle of intersection between the two spheres of radii $L_1$ and $L_2$ centered on $p_1$ and $p_2$ respectively:
     Two spheres
     (Image from Mathalino.com.)

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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