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Splines in the Space of Shells

Heeren, Behrend and Rumpf, Martin and Schröder, Peter and Wardetzky, Max and Wirth, Benedikt (2016) Splines in the Space of Shells. Computer Graphics Forum, 35 (5). ISSN 1467-8659. http://resolver.caltech.edu/CaltechAUTHORS:20160715-133020806

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1111/cgf.12968DOIArticle
http://diglib.eg.org/handle/10.1111/cgf12968PublisherArticle
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.
Funders:
Funding AgencyGrant Number
Alfried Krupp von Bohlen und Halbach-StiftungUNSPECIFIED
FWF Der WissenschaftsfondsS117 (NFN)
Hausdorff CenterUNSPECIFIED
Bundesministerium für Bildung und Forschung (BMBF)UNSPECIFIED
Classification Code:I.3.3 [Computer Graphics]: Picture/Image Generation—Line and curve generation
Record Number:CaltechAUTHORS:20160715-133020806
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160715-133020806
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69063
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:15 Jul 2016 20:45
Last Modified:15 Jul 2016 20:45

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