An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Rational interpolation on a hypersphere
Computer Aided Geometric Design
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In order to interpolate 2n驴+驴1 points on the unit hypersphere $ \mathcal{S}^{d-1}$ with a vector-valued rational function, we use the Generalised Inverse Rational Interpolants (GIRI) of Graves---Morris. The construction process of these Thiele type rational interpolants is based on the Samelson's inverse for vectors. We show that in general any GIRI of 2n驴+驴1 points of $ \mathcal{S}^{d-1}$ lies on $ \mathcal{S}^{d-1}$ . We also show that the stereographic projection induces a one-to-one correspondence between the set of vector-valued rational functions lying on $ \mathcal{S}^{d-1}$ and the set of Generalised Inverse Rational Fractions in the equator plane.