author = {Huber, Pascal and Perl, Ricardo and Rumpf, Martin},
  title = {Smooth interpolation of key frames in a {R}iemannian shell space},
  journal = {Comput. Aided Geom. Design},
  year = {2017},
  volume = {52 - 53},
  pages = {313 - 328},
  abstract = {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.},
  doi = {},
  pdf = { 1},
  issn = {0167-8396},
  keywords = {cardinal splines, interpolatory subdivision, Riemannian calculus,
	shape space, variational discretization},
  url = {}