   Sphere tesselation with arbitrary number of vertices.
  I have this idea that is surely unoriginal, but I can''t seem to find (Google) any good resources (i.e. papers, slides, code, experiences, etc.) on it.  Basically, points are randomly sampled onto a surface and step-wise repel eachother with a logarithmic weight based on the dot product.  After enough iterations, the points should be evenly distributed within a reasonable margin.  It''s kind of like sprinkling a sphere with a number of monopolar magnets and letting them find a comfortable equilibrium.  Anyways, I''m worried about unforseen problems or mistakes that I would like to avoid if they have already been made.  Has anyone come across any good resources on this algorithm?Does anyone know the "official" name for this algorithm?- Jon    Interests: my money-pit car, computer hardware/programming, anything 3D''93 RX-7  
  Not sure what the algorithm is called... it''s closely related to fibbonacci number theory, IIRC. Anyways, this algorithm would work, but it seems like it would take quite a few iterations to get it to look right.    How appropriate. You fight like a cow.  ;  This sounds just like gradient descent which is used for all sorts of things, for example training neural networks or searching anytime that the state space is too large to search every possible state. Just try looking up gradient descent or maybe ask in the AI or math and physics forums.Hope this helps.-erc  ;  sounds like it might produce some cool results.if you want to implement this, i would just write a simple simulation of the vertices witch repell eachother over this sphere, and let it run for a while. it cant be that hard. for example: the repelling force is the inner product of the two vectors, and the axis along witch both vertices are accelerated is the crossproduct of the two.  ;  If you use a physical simulation to do this, do NOT forget friction.  ;  I have done it, a long time a go. I used 1/distance^2 formulas for the repeling force, some friction and re-scaling after each iteration to make sure that all the points remain in the sphere. Your idea of using some metric based on the dot product is probably better, but I haven''t tried it. The nice thing about what I did is that you can play with it in many different ways. For instance, remove the re-scaling condition, make the 1/distance^2 force attractive (as in gravity), add a 1/distance^3 repeling force (to avoid collisions) and you get a nice distribution inside a sphere; add some rotation to that, and you get a planet that is ellipsoidal because of the rotation, like Earth. Actually, that was the problem I was originally trying to solve, and got yours as a modification.You should try to use force as proportional to speed instead of acceleration. That is essencially equivalent to having a lot of friction, and the system is likely to be simpler and more stable.To get a polygonal model from the set of vertices, compute the convex hull of the points. I haven''t done that, but it''s a classical problem in Computational Geometry.