0
$\begingroup$

given a unit circle and N points, how should I scatter these points inside the circle to obtain a maximum pairwise distance? i.e., the average distance (euclidean) between each pair of points will be maximal.

I guess that the answer is some uniform circular distribution, however, I can't generate one..

For 1D it's just np.arange(min_x, max_x, dx) But for 2D? What should be the dRadius and dTheta? Because with every increase in R I can place more points..

|cite|improve this question
$\endgroup$
  • 2
    $\begingroup$ Using the complex circle, it's just points of the form $$e^{\frac{ki\theta}n},\;k\in\mathbb Z$$ $\endgroup$ – Don Thousand Oct 20 at 16:00
  • $\begingroup$ Instead of the average pairwise distance, you may want to maximize the minimum pairwise distance. This gives you something more similar to what one would intuitively consider a uniform scattering of points in a disk; in particular, the problem is equivalent to circle packing in a circle. $\endgroup$ – Rahul Oct 20 at 16:18
  • $\begingroup$ K and N are uniformly distributed? $\endgroup$ – Jenia Golbstein Oct 20 at 16:34

Your Answer

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

Browse other questions tagged or ask your own question.