Suppose you are given a 3-D sphere of known radius. Input of n points is provided, which have been selected randomly on the surface of the sphere. Each input field consists of a polar angle theta (Θ) and azimuthal angle phi, Φ (in spherical coordinate system).
Now I need to find a new point (n+1) such that this point has average maximum distance from every other point present of the surface. If I take the sum of all the distances from this new point (n+1) to the previous points. Then the average must be the maximum.
The output must be provided in the spherical coordinate system. Also the distance between two points is over the surface, not straight lines going through the sphere.
How can this problem be solved? Which algorithms are useful for this problem and what are their running time complexities?

  • $\begingroup$ Try to formulate as LP or QP. $\endgroup$ – Eugene Jan 11 '17 at 11:08
  • $\begingroup$ @Eugene Can you please elaborate a bit on that? $\endgroup$ – Ugnes Jan 11 '17 at 13:47

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