Polar figure computation by a kernel method from a set of individual grain orientations on $SO(3)$

The polar figures of materials are computed by a kernel method using a given sample of orientations on the group $SO(3)$. The computational errors are analyzed depending on recovery parameters, such as the sample size, regularization parameter, and the number of series terms taken into account in the computation. Numerical results and visual representations of polar figures are given for a model specimen with a texture described by a central normal distribution on $SO(3)$.