Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems

Knut Hüper () and Fátima Silva Leite
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Knut Hüper: Institute of Mathematics, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany
Fátima Silva Leite: Institute of Systems and Robotics-Coimbra, 3030-290 Coimbra, Portugal

Mathematics, 2023, vol. 11, issue 16, 1-23

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.

Keywords: Graßmannians; Lie group actions; rotations; reflections; endpoint geodesics; de Casteljau Algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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