Octupoles for octahedral symmetry

01/23/2023

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by   Yuri Nesterenko, et al.

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Spherical harmonics of degree 4 are widely used in volumetric frame fields design due to their ability to reproduce octahedral symmetry. In this paper we show how to use harmonics of degree 3 (octupoles) for the same purpose, thereby reducing number of parameters and computational complexity. The key ingredients of the presented approach are • implicit equations for the manifold of octupoles possessing octahedral symmetry up to multiplication by -1, • corresponding rotationally invariant measure of octupole's deviation from the specified symmetry, • smoothing penalty term compensating the lack of octupoles' symmetries during a field optimization.