Smooth Interpolation of Key Frames in a Riemannian Shell Space
This work provides a novel geometric framework for animating shell surfaces, benefiting computer graphics and animation by enabling smooth interpolation of key frames with physically meaningful distortion metrics.
The paper develops interpolating splines and subdivision schemes on the Riemannian manifold of shell surfaces, enabling smooth key frame animation of shells with a metric that measures bending and membrane distortion. Numerical results demonstrate the potential for key frame animation using two subdivision shell models.
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.