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Exploring the Geometry of the Space of Shells

Heeren, B. and Rumpf, M. and Schröder, P. and Wardetzky, M. and Wirth, B. (2014) Exploring the Geometry of the Space of Shells. Computer Graphics Forum, 33 (5). pp. 247-256. ISSN 0167-7055. doi:10.1111/cgf.12450.

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We prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time- and space-discrete geodesic calculus. In particular we show how to shoot geodesics with prescribed initial data, and we give a construction for parallel transport in shell space. This enables, for example, natural extrapolation of paths in shell space and transfer of large nonlinear deformations from one shell to another with applications in animation, geometric, and physical modeling. Finally, we examine some aspects of curvature on shell space.

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Schröder, P.0000-0002-0323-7674
Additional Information:© 2014 The Author(s). © 2014 The Eurographics Association and John Wiley & Sons Ltd. Article first published online: 23 AUG 2014. We would like to thank Mario Botsch for providing the input meshes for Fig. 2 as well as Tim Winkler, Jens Drieseberg and Kai Hormann for sharing their data and results to enable the comparison in Fig. 4. Facial expression data is taken from [ZSCS04]; we thank William Smith for helping us with processing the data. Additional data was kindly provided by Niloy Mitra and Olga Sorkine. Behrend Heeren was supported by the BMBF via; Martin Rumpf was supported by DFG project Ru 567/14-1. Max Wardetzky was partially supported by the BMBF project MuSiKa.
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DFGRu 567/14-1
Issue or Number:5
Record Number:CaltechAUTHORS:20140929-111525392
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Official Citation:Heeren, B., Rumpf, M., Schröder, P., Wardetzky, M., & Wirth, B. (2014). Exploring the Geometry of the Space of Shells. Computer Graphics Forum, 33(5), 247-256. doi: 10.1111/cgf.12450
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50094
Deposited On:30 Sep 2014 20:11
Last Modified:10 Nov 2021 18:52

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