Octupoles for octahedral symmetry

Yuri Nesterenko

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arXiv · 2301.11925

Octupoles for octahedral symmetry

Yuri Nesterenko

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Abstract

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 \quad \textbullet \ implicit equations for the manifold of octupoles possessing octahedral symmetry up to multiplication by $-1$, \quad \textbullet \ corresponding rotationally invariant measure of octupole's deviation from the specified symmetry, \quad \textbullet \ smoothing penalty term compensating the lack of octupoles' symmetries during a field optimization.

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Yuri Nesterenko. 2023-01-23. Octupoles for octahedral symmetry. https://arxiv.org/abs/2301.11925

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