research-article

Motion from Shape Change

Authors:

Yousuf Soliman,

Marcel Padilla,

Felix Knöppel,

Ulrich Pinkall,

Peter SchröderAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 42, Issue 4

Article No.: 107, Pages 1 - 11

https://doi.org/10.1145/3592417

Published: 26 July 2023 Publication History

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.

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Cited By

Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658174
Soliman YPadilla MGross OKnöppel FPinkall USchröder P(2024)Going with the FlowACM Transactions on Graphics10.1145/365816443:4(1-12)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658164

Index Terms

Motion from Shape Change
1. Applied computing
  1. Arts and humanities
    1. Architecture (buildings)
      1. Computer-aided design
  2. Physical sciences and engineering
    1. Physics
2. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 42, Issue 4

August 2023

1912 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3609020

Issue’s Table of Contents

Copyright © 2023 ACM.

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Association for Computing Machinery

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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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Cited By

Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658174
Soliman YPadilla MGross OKnöppel FPinkall USchröder P(2024)Going with the FlowACM Transactions on Graphics10.1145/365816443:4(1-12)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658164

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