Existence and computation of spherical rational quartic curves for Hermiteinterpolation

We study the existence and computation of spherical rational quartic curves that interpolate Hermite data on a sphere, i.e. two distinct endpoints and tangent vectors at the two points. It is shown that spherical rational qua rtic curves interpolating such data always exist, and that the family of th ese curves has n degrees of freedom for any given Hermite data on S-n, n gr eater than or equal to 2. A method is presented for generating all spherica l rational quartic curves on S-n interpolating given Hermite data.