A list of pages concerning the frequent question
“How can I arrange N points evenly on a sphere?”
- Exact optimization. Several of these can be considered special cases of the problem "minimize or maximize the sum of pairwise distances raised to an exponent"; for these the exponent is shown.
- Tammes or Fejes Tóth Problem: packing: maximize the least separation (exponent -∞)
- Thomson problem / Fekete points: electrostatic repulsion (exponent -1)
- Whyte's problem: maximize product of distances ("exponent" 0 - sum of logarithms)
- Maximize sum of distances (exponent +1)
- Covering: minimize the greatest Voronoi radius
- Equal area
- Maximize volume of convex hull
- Maximize inradius of convex hull
- Marek Teichmann.
Teichmannn specifies that the inscribed sphere
be concentric with the original sphere;
that makes the problem equivalent to covering.
But is the condition redundant?
Is the maximum inscribed sphere ever not concentric?
- Minimize volume of tangent polyhedron
- Illumination by light sources at infinity
- Hugo Pfoertner seems to have this field to himself.
He tackles three forms of the problem:
- minimize the maximum luminance (analogous to packing)
- maximize the minimum luminance (analogous to covering)
- minimize the difference between minimum and maximum
- Algorithmic approximations
| Anton Sherwood
this page created 2002 Mar 31;
last changes 2016 Jul 24