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Quadratic Interpolation on Spheres

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Abstract

Riemannian quadratics are C 1 curves on Riemannian manifolds, obtained by performing the quadratic recursive deCastlejeau algorithm in a Riemannian setting. They are of interest for interpolation problems in Riemannian manifolds, such as trajectory-planning for rigid body motion. Some interpolation properties of Riemannian quadratics are analysed when the ambient manifold is a sphere or projective space, with the usual Riemannian metrics.

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Noakes, L. Quadratic Interpolation on Spheres. Advances in Computational Mathematics 17, 385–395 (2002). https://doi.org/10.1023/A:1016277023669

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  • DOI: https://doi.org/10.1023/A:1016277023669