A list of pages concerning the frequent question
“How can I arrange N points evenly on a sphere?”
- Overviews
- Applications
- Exact optimization
- Overviews
- Packing: maximize the least separation (exponent -∞) (Tammes or Fejes Tóth Problem)
- Electrostatic repulsion (exponent -1) (Thomson Problem) (Fekete points)
- Maximize product of distances (exponent 0)
- 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
- t-designs
- 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
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this page created 2002 Mar 31,
last addition 2009 Nov 23