Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems-Reference-Cited by-同舟云学术

Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems

Published:2023-08-16 Issue:16 Volume:11 Page:3545
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Hüper Knut¹,Silva Leite Fátima²³

Affiliation:

1. Institute of Mathematics, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany

2. Institute of Systems and Robotics-Coimbra, 3030-290 Coimbra, Portugal

3. Department of Mathematics, University of Coimbra, 3001-143 Coimbra, Portugal

Abstract

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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/16/3545/pdf

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