title: Dispersing n points uniformly on a sphere
body: <p>I am trying to disperse n points on a sphere such that each point has the "same" area "around" it. Basically, I'm trying to integrate a function over a sphere by evaluating at n points and assuming that each area element is the same (and equal to 4pi r^2/n).</p>
  
  <p>My question is very related to <a href="https://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere">this one</a>, but I can't seem to agree that the code presented in the "accepted" answer works as desired (see attached photo, generated by choosing R = 1000, nx = ny = 40). Clearly, my points are much more concentrated at the poles and very un-concentrated along the equator.</p>
  
  <p>Any suggestions?
  <img src="https://i.stack.imgur.com/ghSZe.png" alt=""></p>
  
  <p>EDIT: For reference, I did find <a href="http://persson.berkeley.edu/distmesh/" rel="nofollow noreferrer">some software</a> that generates a mesh such that each point has equal "area" around it (scroll down to see uniform area distribution on a sphere), but rather than implement their code I went with a less-time consuming approach: I simply iterated over the azimuthal and polar angles ([0,2pi] and [0,pi]) and computed the ''infinitesimal'' area of each patch (da = r^2 sin theta dtheta dphi). This is basically all I need for integration over the sphere, I was just hoping that uniform-area distribution wouldn't be so hard to implement.</p>