Cited By
View all- Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
Motion from Shape Change
Authors: 
Oliver Gross, Yousuf Soliman, Marcel Padilla, Felix Knöppel, Ulrich Pinkall, Peter SchröderAuthors Info & Claims
Oliver Gross, Yousuf Soliman, Marcel Padilla, Felix Knöppel, Ulrich Pinkall, Peter SchröderAuthors Info & ClaimsArticle No.: 107, Pages 1 - 11
Abstract
We consider motion effected by shape change. Such motions are ubiquitous in nature and the human made environment, ranging from single cells to platform divers and jellyfish. The shapes may be immersed in various media ranging from the very viscous to air and nearly inviscid fluids. In the absence of external forces these settings are characterized by constant momentum. We exploit this in an algorithm which takes a sequence of changing shapes, say, as modeled by an animator, as input and produces corresponding motion in world coordinates. Our method is based on the geometry of shape change and an appropriate variational principle. The corresponding Euler-Lagrange equations are first order ODEs in the unknown rotations and translations and the resulting time stepping algorithm applies to all these settings without modification as we demonstrate with a broad set of examples.
Supplementary Material
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Publication History
Published: 26 July 2023
Published in TOG Volume 42, Issue 4
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- Funded by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109
- Einstein Foundation Berlin
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View all- Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
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