document: Quadratic interpolation on spheres Riemannian quadratics are C/sup 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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