Elastic Analysis of Augmented Curves and Constrained Surfaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914731437064192 |
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| author | Nava-Yazdani, Esfandiar |
| author_facet | Nava-Yazdani, Esfandiar |
| contents | The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover, utilizing natural geometric constructions, we employ the approach for intrinsic comparison within several classes of surfaces and augmented curves, which arise in the real world applications such as tubes, ruled surfaces, spherical strips, protein molecules and hurricane tracks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_04944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elastic Analysis of Augmented Curves and Constrained Surfaces Nava-Yazdani, Esfandiar Differential Geometry Numerical Analysis 53Axx, 53-11, 63Dxx G.1.2; G.1.3; J.2; I.6.3; I.6.4 The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover, utilizing natural geometric constructions, we employ the approach for intrinsic comparison within several classes of surfaces and augmented curves, which arise in the real world applications such as tubes, ruled surfaces, spherical strips, protein molecules and hurricane tracks. |
| title | Elastic Analysis of Augmented Curves and Constrained Surfaces |
| topic | Differential Geometry Numerical Analysis 53Axx, 53-11, 63Dxx G.1.2; G.1.3; J.2; I.6.3; I.6.4 |
| url | https://arxiv.org/abs/2402.04944 |