Abstract
The paper presents a geometric algorithm for the generation of smooth interpolating splines on Riemannian manifolds and extends previous work of the authors. Contrary to the variational approach to splines on manifolds, where the curves appear as solutions of highly nonlinear differential equations and geometric integration methods are required, our proposal generates explicit formulas. For low dimensional manifolds, the algorithm is visually very appealing because it resembles a simple geometric construction, somehow similar to the De Casteljau algorithm for the generation of Bezier curves. Our approach is however rather more flexible than the De Casteljau algorithm and also computationally less intensive, both on Euclidean spaces and on other Riemannian manifolds.
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