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：平方根速度变换在曲线函数与形状数据的弹性分析中至关重要。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，我们将此方法应用于若干类曲面与增广曲线的内在比较，这些对象源于实际应用，例如管状曲面、直纹曲面、球面带、蛋白质分子及飓风路径。