  Splines and subdivision curves are flexible tools in the design and
manipulation of curves in Euclidean space. In this paper we study
generalizations of interpolating splines and subdivision schemes to the
Riemannian manifold of shell surfaces in which the associated metric measures
both bending and membrane distortion. The shells under consideration are
assumed to be represented by Loop subdivision surfaces. This enables the
animation of shells via the smooth interpolation of a given set of key frame
control meshes. Using a variational time discretization of geodesics efficient
numerical implementations can be derived. These are based on a discrete
geodesic interpolation, discrete geometric logarithm, discrete exponential map,
and discrete parallel transport. With these building blocks at hand discrete
Riemannian cardinal splines and three different types of discrete,
interpolatory subdivision schemes are defined. Numerical results for two
different subdivision shell models underline the potential of this approach in
key frame animation.
