Bézier Splines Interpolation on Stiefel and Grassmann Manifolds (Journal of Computational Mathematics, 2024)
We propose a new method for smoothly interpolating a given set of data points onGrassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm. Tothat end, we reduce interpolation problem to the classical Euclidean setting, allowing usto directly leverage the extensive toolbox of spline interpolation. The interpolated curveenjoy a number of nice properties: The solution exists and is optimal in many commonsituations. For applications, the structures with respect to chosen Riemannian metrics aredetailed resulting in additional computational advantages.