2024/02/12 by Hanik, Martin, Nava-Yazdani, Esfandiar, von Tycowicz, Christoph
#41Axx #53Zxx #65Dxx #Applications (stat.AP) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.07550
For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.