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A two-step algorithm of smooth spline generation on Riemannian manifolds

This paper presents a simple geometric algorithm to generate splines of arbitrary degree of smoothness in Euclidean spaces. Unlike other existing methods, this simple geometric algorithm does not require a recursive procedure and, consequently, introduces a significant reduction in calculation time. The algorithm is then extended to other complete Riemannian manifolds, namely to matrix Lie groups and spheres. ...

A new geometric algorithm to generate smooth interpolating curves on Riemannian...

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. Th...

A multi-input/multi-output system representation of generalized splines in R^n

L-splines - A manifestation of optimal control

We show how to generate a class of Euclidean splines, called L-splines, as solutions of a high-order variational problem. We also show connections between L-splines and optimal control theory, leading to the conclusion that L-splines are manifestations of an optimal behavior ; ISR, project ERBFMRXCT970137