From: mailbox@dmitry-kazakov.de   
      
   On 2023-01-11 03:41, Ben Bacarisse wrote:   
   > "Dmitry A. Kazakov"  writes:   
   >   
   >> On 2023-01-09 21:37, Ben Bacarisse wrote:   
   >>> "Dmitry A. Kazakov"  writes:   
   >>>   
   >>>> On 2023-01-09 04:25, Ben Bacarisse wrote:   
   >>>>> "Dmitry A. Kazakov"  writes:   
   >>>>>   
   >>>> Firstly, this is comp.programming group.   
   >>> Do you consider discussion algorithms off topic here?  Seriously?   
   >>   
   >> No, I consider off topic discussing mathematical problems /=   
   >> algorithms. You did not discuss any algorithms so far.   
   >   
   > Algorithms don't come out of thin air.  The objective must be discussed   
   > first.  You can't seriously think that everyone here should remain   
   > silent until, out of nowhere, someone says "consider this algorithm to   
   > find the average of a set of points".   
      
   > I explained in the text you cut.  Maybe your reference to the thousands   
   > of minimisation algorithms was just an off the cuff remark, but it reads   
   > as if you were suggesting using one as them as the solution to this   
   > programming task.   
      
   Sure. I highly doubt that production code, if ever existed, would use   
   some novel algorithm.   
      
   >> Anyway, there are lengthy papers on spherical averages introducing   
   >> iterative solutions, some with source code for the algorithms. That is   
   >> the right way to compute it, if you really wanted...   
   >   
   > I'd like to read one.  Do you have a citation, please?   
      
   Perhaps this could be a starting point:   
      
   "Spherical Averages and Applications to Spherical Splines and   
   Interpolation" Samuel R. Buss, Jay P. Fillmore   
      
   It is not area of my interest and research is not a programming task   
   either. And you still completely miss the key point about stating the   
   problem. The problems come from the problem spaces. Spherical geometry   
   is used in remote sensing, navigation, computer graphics (spherical   
   polygons and triangles) etc. You must look for works in these   
   application areas first. If the problem were *real* you would already   
   have that step behind.   
      
   >> [Again, it is not programming. In case of spherical geometry a   
   >> programmer will find an expert mathematician and who will have the   
   >> problem properly stated.   
   >   
   > The problem has been properly stated.  We seek an algorithm that finds a   
   > point that minimises the sum of squares of the great-circle distances   
   > between that point and the input points.  You could have asked if any of   
   > this was unclear.  To me it is both clear and intuitive.   
   >   
   >> The next stop is by an expert applied mathematician who will outline a   
   >> workable numeric solution. Then the programmer can start.]   
   >   
   > Ah, you hand off the task of devising algorithms to mathematicians?   
      
   Yep, *numeric* algorithms is an area of applied mathematics.   
      
   > That would make programming very dull.  Anyway, you would not tackle   
   > this sort of problem until an expert applied mathematician has done   
   > everything except code up a workable numerical solution.  Is that also   
   > the case for the average angle problem?   
      
   If you are not familiar with spherical geometry, numerical approximation   
   and optimization, yes.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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