We construct a computationally inexpensive 3D extension of Andrew's plots by considering curves generated by Frenet-Serret equations and induced by optimally smooth 2D Andrew's plots. We consider linear isometries from a Euclidean data space to infinite dimensional spaces of 2D curves, and parametrize the linear isometries that produce (on average) optimally smooth curves over a given dataset. This set of optimal isometries admits many degrees of freedom, and (using recent results on generalized Gauss sums) we identify a particular a member of this set which admits an asymptotic projective "tour" property. Finally, we consider the unit-length 3D curves (filaments) induced by these 2D Andrew's plots, where the linear isometry property preserves distances as "relative total square curvatures". This work concludes by illustrating filament plots for several datasets. Code is available at https://github.com/n8epi/filaments

翻译：我们通过考虑Frenet-Serret方程式产生的曲线和最佳平滑的 2D Andrew 方块的引力,为Andrew 的地块构建了一个计算成本低廉的3D延伸。 我们考虑的是从Euclidean数据空间到2D曲线的无限维度空间的线性异缩缩缩图,并且对产生(平均)最佳滑动曲线的线性异缩图进行准美化,这组最佳的异构体承认了多种程度的自由,并且(使用关于普遍标数的最近结果)我们确定了这组图集中某一成员,其中含有一种无效果的投影“tour”属性。 最后,我们考虑的是由2D Andrew 方块的地块引出的3D 线性曲线(线性曲线), 其线性属性保持的距离是“ 相对的全方形曲线”。 这项工作通过为多个数据集绘制丝形图而结束。 代码可在 https://github.com/n8epi/filamentamentments查阅到 http://http://http://http://www.