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Endpoint geodesic formulas on Graßmannians applied to interpolation problems
Please always quote using this URN: urn:nbn:de:bvb:20-opus-327016
- Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order interpolation problems on manifolds. This will be illustrated with the geometric de Casteljau construction offering an excellent alternative to the variational approach which gives rise to Riemannian polynomials and splines.
Author: | Knut Hüper, Fátima Silva Leite |
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URN: | urn:nbn:de:bvb:20-opus-327016 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik |
Language: | English |
Parent Title (English): | Mathematics |
ISSN: | 2227-7390 |
Year of Completion: | 2023 |
Volume: | 11 |
Issue: | 16 |
Article Number: | 3545 |
Source: | Mathematics (2023) 11:16, 3545. https://doi.org/10.3390/math11163545 |
DOI: | https://doi.org/10.3390/math11163545 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Graßmannians; Lie group actions; MSC: 14M15; MSC: 53C22; MSC: 53C35; de Casteljau Algorithm; endpoint geodesics; reflections; rotations |
Release Date: | 2024/03/06 |
Date of first Publication: | 2023/08/16 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |