De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application
- 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.
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| Author: | Martin Hanik, Esfandiar Navayazdani, Christoph von Tycowicz |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Computer Aided Geometric Design |
| Volume: | 110 |
| First Page: | 102288 |
| Year of first publication: | 2024 |
| Page Number: | 24 |
| ArXiv Id: | http://arxiv.org/abs/2402.07550 |
| DOI: | https://doi.org/10.1016/j.cagd.2024.102288 |
