2024/06/13 by Hanik, Martin, Nava-Yazdani, Esfandiar, Von Tycowicz, Christoph
#000 Informatik #Bézier spline #Bézierfold #Informatik #Informationswissenschaft #Riemannian manifold #Riemannian regression #Sasaki metric #Systeme::004 Datenverarbeitung #Wissen #allgemeine Werke::000 Informatik #manifold mixed-effects models
paper · doi:10.14279/depositonce-20778
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.