convolution of an SO3Kernel function with a function or a kernel on SO(3)
We convolute an SO3Kernel \(f\) with another SO3Kernel or an SO3Fun \(g\) by the convolution
\[ (f {*}_L g)(R) = \frac1{8\pi^2} \int_{SO(3)} f(q) \cdot g(q^{-1}\,R) \, dq \]
which in this case is similar to the so caled right sided convolution, see SO3FunHarmonic/conv.
The convolution of an SO3Kernel with an S2Kernel or an S2Fun \(h\) is defined by
\[ (f * h)(\xi) = \frac1{8\pi^2} \int_{SO(3)} f(q) \cdot h(q^{-1}\,\xi) \, dq \].
Syntax
Input
psi1, psi2 | SO3Kernel |
phi1 | S2Kernel |
SO3F1 | SO3Fun |
sF1 | S2Fun |
Output
psi | SO3Kernel |
SO3F2 | SO3Fun |
sF2 | S2Fun |
phi2 | S2Kernel |
See also
SO3FunHarmonic.conv SO3FunRBF.conv S2FunHarmonic.conv S2Kernel.conv