Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems

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