The square root velocity transformation is crucial for efficiently employing the elastic approach in functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover, utilizing natural geometric constructions, we employ the approach for intrinsic comparison within several classes of surfaces and augmented curves, which arise in the real world applications such as tubes, ruled surfaces spherical strips, protein molecules and hurricane tracks.

翻译：平方根速度变换对于在曲线函数与形状数据分析中高效采用弹性方法至关重要。本研究探讨了该变换下曲线的基本几何性质。此外，利用自然几何构造，我们将该方法应用于若干类曲面与增强曲线的内蕴比较，这些曲面与曲线源于实际应用场景，如管道、直纹曲面、球面带、蛋白质分子和飓风轨迹。