Bézier Splines Interpolation on Stiefel and Grassmann Manifolds
Year: 2024
Author: Ines Adouani, Chafik Samir
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1554–1578
Abstract
We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm. To that end, we reduce interpolation problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. The interpolated curve enjoy a number of nice properties: The solution exists and is optimal in many common situations. For applications, the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2303-m2022-0201
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1554–1578
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Optimization Bézier spline Curve fitting Grassmann manifolds Stiefel manifolds Canonical metrics.
Author Details
Ines Adouani Email
Chafik Samir Email