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Published 2016 | Supplemental Material
Journal Article Open

Splines in the Space of Shells

Heeren, Behrend
Rumpf, Martin
Schröder, Peter ORCID icon
Wardetzky, Max
Wirth, Benedikt
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Abstract

Cubic splines in Euclidean space minimize the mean squared acceleration among all curves interpolating a given set of data points. We extend this observation to the Riemannian manifold of discrete shells in which the associated metric measures both bending and membrane distortion. Our generalization replaces the acceleration with the covariant derivative of the velocity. We introduce an effective time-discretization for this novel paradigm for navigating shell space. Further transferring this concept to the space of triangular surface descriptors-edge lengths, dihedral angles, and triangle areas-results in a simplified interpolation method with high computational efficiency.

Additional Information

© 2016 The Author(s). Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. Eurographics Symposium on Geometry Processing 2016 Maks Ovsjanikov and Daniele Panozzo (Guest Editors). Benedikt Wirth's research was supported by the Alfried Krupp Prize for Young University Teachers awarded by the Alfried Krupp von Bohlen und Halbach-Stiftung. Behrend Heeren and Martin Rumpf acknowledge support by the FWF in Austria under the grant S117 (NFN) and by the Hausdorff Center. Max Wardetzky acknowledges support from the BMBF research project MusiKa. Keyframes and rest poses were kindly provided by Michael Black, Bob Sumner, Niloy Mitra, Olga Sorkine-Hornung and William Smith. The authors thank Dennis Tiege for rendering.

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