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A New Geometric Algorithm to Generate Smooth Interpolating Curves on Riemannian Manifolds

Published online by Cambridge University Press:  01 February 2010

Rui C. Rodrigues ,
F. Silva Leite  and
Janusz Jakubiak
Rui C. Rodrigues
Affiliation:
Departamento de Física e Matemática, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal, ruicr@isec.pt, http://www.isec.pt/~ruicr/
F. Silva Leite
Affiliation:
Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal, fleite@mat.uc.pt, http://www.mat.uc.pt/~fleite/
Janusz Jakubiak
Affiliation:
Institute of Engineering Cybernetics, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50–370 Wroclaw, Poland, Janusz.Jakubiak@pwr.wroc.pi

Abstract

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This paper presents a new geometric algorithm to construct a Ck-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, this new algorithm is implemented in only three steps, 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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 251 - 266
Copyright
Copyright © London Mathematical Society 2005

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