Michal Iwanicki

I have seen lots of thrashing about with Directional Gaussians but no exploration of the underlying Quadrature they are trying to represent.

Spherical Gaussians have global support on the sphere, which made them not really that interesting for our use case

Haven't looked much into wavelets, but main concern for them is that you might needs quite a few coeffs for decent quality of reconstruction

Coeff count depends on speed of convergence. Haar is too local, SH is too smooth, need wavelets that converge fast by breaking these rules.

What does the middle ground between the local/discontinuous to smooth/global dimension look like?

We know Biorthogonal Bases and Parseval Tight Frames allow us to break rules of basis design and still get good results. What else can bend?

Good questions :) Though i think of BiOB and all the PTF math as just consequence of projection minimizing L2 error rather than bending ;)

But should we really focus on looking for basis with more locality than SH and more smoothness than Haar? I'm not convinced