A C++ algorithm to compute the coefficients of a function development in a spherical harmonics convergent series

Hey, it looks really cool, it's clear that you've dedicated real time and effort to it, even the code is commented. I love seeing this kind of stuff done in C++, so I'm already loving it, but I'll try to give you some useful feedback:

• Most people (starting with me) are not familiar with what this SAF functions are, what do they describe, explain or what they're useful for. So, unless you target your code to very specific coders, your README would benefit from a more top-down (on abstraction) structure:
  • Summary or link to an explanation of what Spherical Armonics Function are (I still have no clue) try to reduce to the minimum the amount of math language here. If there is something graphical you can show (even if it is a wikimedia image) put it here to make it easier to understand.
  • The how-to-use: at least one use case example of the algorithm/program/library, better if with reproducible input and output (don't put it at the end!).
  • Installation.
  • More in-depth explanation.

It is the usual information flow in good READMEs (go from practical to theorical). The contents you have now are at least very similar, so this means just rearrange some information.

• As you have the good habit of documenting your code, and also are not afraid of using third party tools (like valgrind or doctest) I would recommend you trying Doxygen to generate a documentation from the code. Also you can put there the heavy algorithm explanation; there is nothing wrong with putting it in the README but generally makes more sense in a separate document.

If you look to other scientific-type repositories, most are as I more or less described here. This one for example has that practical-to-theorical, show-to-explain structure and a separate document for in-depth stuff.

I hope you find it useful, all these are just suggestions. Good work and keep it up!

Edit: After reading a bit about this functions I see it's a very specific topic, so take my advice with a grain of salt, because it's better suited for a more general-public code.