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Title: A new geometric algorithm to generate smooth interpolating curves on Riemannian manifolds
Authors: Rodrigues, Rui C. 
Leite, Fátima Silva 
Jakubiak, Janusz 
Keywords: Riemannian manifold; Lie group; Spline functions; Geometric algorithm; Casteljau algorithm
Issue Date: 2004
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 04-37 (2004)
Abstract: This paper presents a new geometric algorithm to construct a C k- smooth spline curve that interpolates a given set of data (points and velocities) on a complete Riemannian manifold. Although based on a modification of the de Casteljau procedure, our algorithm is implemented in three steps only independently of the required degree of smoothness, and therefore introduces a significant reduction in complexity. The key role is played by the choice of an appropriate smoothing function which is defined as soon as the degree of smoothness is fixed.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Nacionais

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