De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application

• DOI: 10.48550/arxiv.2402.07550
• Publication Date: 2024-02-12
• Authors: Martin Hanik; Esfandiar Nava-Ya...; Christoph von Tyc...
• Keywords: Geometric analysis

For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design found wide range of applications fields such scientific computing, discrete geometry to name but few. With increasing interest nonlinear data science, its constructive approach shown provide principled way generalize parametric smooth curves manifolds. These have remarkable new the analysis parameter-dependent, geometric data. This article provides survey recent theoretical developments this exciting area well morphometrics longitudinal medicine, archaeology, meteorology.