The Bump kernel is a radial symmetric kernel function depending on a parameter \(r\in (0,pi)\). The function value is 0, if the angle is greater then the halfwidth \(r\). Otherwise it is has a contstant value, such that the mean of the kernel function on \(\mathcal{SO}(3)\) is 1. Hence we use the open set \(U_r = \{ R \in \mathcal{SO}(3) \,|~ \omega®<r \}\) and define the bump kernel \(\psi_r : \matcal{SO}(3) \to \mathbb R\) by
\[ \psi_r® = \frac1{|U_r|} \mathbf{1}_{R \in U_r} \].
Syntax
psi = SO3BumpKernel(40*degree)Options
| halfwidth | angle at which the kernel function has reduced to half its peak value |
| bandwidth | harmonic degree |