Equi-affine minimal-degree moving frames for polynomial curves

Hoon Hong; Irina A. Kogan

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arXiv · 2402.06610

Equi-affine minimal-degree moving frames for polynomial curves

Hoon Hong·Irina A. Kogan

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Abstract

We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the parameter shifts. We show that any matrix-completion algorithm can be turned into an equivariant moving frame algorithm via an equivariantization procedure that we develop. We prove that if a matrix-completion algorithm is of minimal degree then so is the resulting equivariant moving frame algorithm. We propose a novel minimal-degree matrix-completion algorithm, complementing the existing body of literature on this topic.

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BibTeX RIS

Hoon Hong, Irina A. Kogan. 2024-02-09. Equi-affine minimal-degree moving frames for polynomial curves. https://arxiv.org/abs/2402.06610

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