A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds

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• 作者：Krzysztof A. Krakowski^a ; ^d ; ^{k.krakowski@uksw.edu.pl" class="auth_mail" title="E-mail the corresponding author} ; Luí ; s Machado^c ; ^d ; ^{lmiguel@utad.pt" class="auth_mail" title="E-mail the corresponding author} ; Fá ; tima Silva Leite^b ; ^d ; ^{fleite@mat.uc.pt" class="auth_mail" title="E-mail the corresponding author} ; Jorge Batista^e ; ^d ; ^{batista@isr.uc.pt" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34C40 ; 51M35 ; 53C22 ; 58E10 ; 65D18
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：84-99
• 全文大小：1335 K

文摘

The main objective of this paper is to propose a new method to generate smooth interpolating curves on Stiefel manifolds. This method is obtained from a modification of the geometric Casteljau algorithm on manifolds and is based on successive quasi-geodesic interpolation. The quasi-geodesics introduced here for Stiefel manifolds have constant speed, constant covariant acceleration and constant geodesic curvature, and in some particular circumstances they are true geodesics.