De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911775316770816 |
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| author | Hanik, Martin Nava-Yazdani, Esfandiar von Tycowicz, Christoph |
| author_facet | Hanik, Martin Nava-Yazdani, Esfandiar von Tycowicz, Christoph |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application Hanik, Martin Nava-Yazdani, Esfandiar von Tycowicz, Christoph Differential Geometry Applications 53Zxx, 41Axx, 65Dxx 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. |
| title | De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application |
| topic | Differential Geometry Applications 53Zxx, 41Axx, 65Dxx |
| url | https://arxiv.org/abs/2402.07550 |