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The concept of resolution in the domain of rotations
Stefano Trapani1, Xavier Siebert, Jorge Navaza
1Institut de Biologie Structurale J. P. Ebel, UMR 5075, CNRS, 41 rue Jules Horowitz, 38027 Grenoble, France. stefano.trapani@ibs.fr
Abstract:
The metric of the SO(3) group of rotations can be used to define the angular resolution of a function of rotations. The resolution is related to the degree of the highest representation present in the expansion of the function in terms of Wigner functions. The peculiar non-Euclidean metric of the rotation domain, however, implies that the terms which effectively contribute to the expansion vary through two-dimensional sections of the rotation domain and are within limiting resolution circles in two-dimensional reciprocal sections. This reconciles an economic sampling of the expansion with the acceleration provided by fast Fourier transform (FFT) techniques.
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