norm edit page

Calculate the L2-norm also known as texture index of a SO3FunHarmonic, by using Parsevalls equality for the integral

\[ t = \sqrt{\frac1{8\pi^2}\int_{SO(3)} |f( R ) |^2 dR},\]

with \(vol(SO(3)) = \int_{SO(3)} 1 dR = 8\pi^2\). The Wigner-D functions (one Wigner-coefficient is 1 and all others are 0) are L2-normalized.

We can compute the Sobolev norm of an SO3FunHarmonic by

\[ t = \sqrt{ \sum_{n=0}^N (2n+1)^{2s} \, \sum_{k,l=-n}^n \abs{\hat{f}_n^{k,l}}^2 },\]

where \(s\) is the Sobolev index. (The default case \(s=0\) corresponds to the L2-norm.)


t = norm(SO3F)
t = norm(SO3F,'Sobolev')


SO3F SO3FunHarmonic


t double


resolution choose mesh width by calculation of mean