中${\boldsymbol{C^3}}$紧可定向曲面的合集的完全${\boldsymbol{SE(3)}}$不变量 $\mathbb{R}^{\boldsymbol{3}}$

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-08-30 DOI:10.1137/21M1445776

Yair Hayut, D. Lehavi

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引用次数: 0

摘要

我们引入$\mathbb{R}^3$中紧$C^1$可定向曲面(带边界)到刚性变换的不变量。我们的不变量是曲面的函数矩的四阶多项式。我们给出了一种有效且数值稳定的反演算法，用于从不变量中检索曲面，该算法适用于$C^3$-曲面的comeagre子集。

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Complete ${\boldsymbol{SE(3)}}$ Invariants for a Comeagre Set of ${\boldsymbol{C^3}}$ Compact Orientable Surfaces in $\mathbb{R}^{\boldsymbol{3}}$

We introduce invariants for compact $C^1$-orientable surfaces (with boundary) in $\mathbb{R}^3$ up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective and numerically stable inversion algorithm for retrieving the surface from the invariants, which works on a comeagre subset of $C^3$-surfaces.

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