From: mailbox@dmitry-kazakov.de   
      
   On 2023-01-08 16:45, Tim Rentsch wrote:   
   > "Dmitry A. Kazakov"  writes:   
      
   >> Averaging arcs is equivalent to averaging angles.   
   >   
   > Angles are a one-dimensional measure.   
      
   Averaging arcs is still equivalent to averaging angles, which is trivial   
   result of elementary trigonometry.   
      
   > Finding an arc length   
   > "average" of points on a sphere needs a two-dimensional result.   
      
   Points do not have arcs.   
      
   >>> Now that I think about it, finding the point that minimizes the   
   >>> great circle distances squared would be at least computationally   
   >>> unpleasant.   
   >>   
   >> See above, it is just angles to average.   
   >   
   > Apparently you have not yet understood the problem.   
      
   Again, averages of arcs and angles are equivalent up to a multiplier.   
      
   > Why don't   
   > you try writing a program that inputs a set of points normalized   
   > to be on the unit sphere, and then calculates the arc length   
   > average point (on the unit sphere) of those input points?   
      
   Why don't you write a formula specifying your need?   
      
   Programs are written according to the specifications. Numeric programs   
   require a properly stated problem, rather than a bunch of words   
   arbitrarily thrown in a meaningless sentence as above.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)