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Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems

Author

Listed:
  • 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
    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.

Suggested Citation

  • Knut Hüper & Fátima Silva Leite, 2023. "Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3545-:d:1218649
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