I'm about to write my thesis and now write a chapter about the basics of Spline Curve Interpolation. I read a bunch of articles on parameterization, especially on Arc-Length parameterization and there is one thing I always wondered about:
is there any terms to describe or prove the quality of a parameterization method? E.g. is there a way to prove that an arc-length parameterization (although it can only be approximated) is an optimal solution in some terms like smoothness or something else. I found this point was never really described in the articles.
Thanks for your help