The shape of spherical quartics

We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves. With the help of the generalized stereographic projection (Dietz et al., 1993), we construct a two-parameter family of spherical quartics solving this problem. We study the shape of these solutions and derive criteria which guarantee solutions without cusps or self-intersections.

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