Calculate the L2-norm also known as texture index of a SO3FunHarmonic, by using Parseval's 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.)
Syntax
t = norm(SO3F)
t = norm(SO3F,s)Input
| SO3F | SO3FunHarmonic |
| s | double (Sobolev index) |
Output
| t | double |
Options
| resolution | choose mesh width by calculation of mean |