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
References
[1]
Alexander M. Bronstein, Michael M. Bronstein, and Ron Kimmel. 2008. Numerical Geometry of Non-rigid Shapes. Springer.
[2]
Fang Da, David Hahn, Christopher Batty, Chris Wojtan, and Eitan Grinspun. 2016. Surface-only Liquids. ACM Trans. Graph. 35, 4 (2016), 78:1--12.
[3]
Daniel Daye. 2019. Rigged and Animated Scan of Timber Rattlesnake. https://sketchfab.com/. CC Attribution-NonCommercial.
[4]
J. Elgeti, R. G. Winkler, and G. Gompper. 2015. Physics of Microswimmers---Single Particle Motion and Collective Behavior: a Review. Rep. Prog. Phys. 78 (2015).
[5]
Leonhard Euler. 1744. Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes. Bousquet, Lausanne & Geneva. English translation at WikiSource.
[6]
Cliff Frohlich. 1979. Do Springboard Divers Violate Angular Momentum Conservation? Amer. J. Phys. 47, 7 (1979), 583--592.
[7]
Cliff Frohlich. 1980. The Physics of Somersaulting and Twisting. Sci. Am. 242, 3 (1980), 154--165.
[8]
Graphics & Extended Reality Lab. 2022. Large Whip Snake. https://sketchfab.com/. CC Attribution.
[9]
J. Gray and G. J. Hancock. 1955. The Propulsion of Sea-Urchin Spermatozoa. J. Exp. Biol. 32, 4 (1955), 802--814.
[10]
Jeffrey S. Guasto, Jonathan B. Estrada, Filippo Menolascina, Lisa J. Burton, Mohak Patel, Christian Franck, A. E. Hosoi, Richard K. Zimmer, and Roman Stocker. 2020. Flagellar Kinematics Reveals the Role of Environment in Shaping Sperm Motility. J. Roy. Soc. Interface 17, 20200525 (2020), 10 pages.
[11]
Ernst Hairer and Gerhard Wanner. 2015. Euler Methods, Explicit, Implicit, Symplectic. In Encyclopedia of Applied and Computational Mathematics, Björn Engquist (Ed.). Springer, 451--455.
[12]
David L. Hu, Jasmine Nirody, Terri Scott, and Michael J. Shelley. 2009. The Mechanics of Slithering Locomotion. Proc. Nat. Acad. Sci. 106, 25 (2009), 10081--10085.
[13]
E. Ju, J. Won, J. Lee, B. Choi, J. Noh, and M. Gyu Choi. 2013. Data-Driven Control of Flapping Flight. ACM Trans. Graph. 32, 5 (2013), 151:1--12.
[14]
T. R. Kane and M. P. Scher. 1969. A Dynamical Explanation of the Falling Cat Phenomenon. Int. J. Solids Structures 5 (1969), 663--670.
[15]
Eva Kanso, Jerrold E. Marsden, Clancy W. Rowley, and J. B. Melli-Huber. 2005. Locomotion of Articulated Bodies in a Perfect Fluid. J. Non-L. Sci. 15 (2005), 255--289.
[16]
Gustav Kirchhoff. 1870. Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit. J. Reine Angew. Math. 1870, 71 (1870), 237--262.
[17]
Gustav Kirchhoff. 1876. Vorlesungen über mathematische Physik. Teubner, 233--250.
[18]
V. V. Kozlov and S. M. Ramodanov. 2001. The Motion of a Variable Body in an Ideal Fluid. J. Appl. Math. Mech. 65, 4 (2001), 579--587.
[19]
Philip V. Kulwicki and Edward J. Schlei. 1962. Weightless Man: Self-Rotation Techniques. Technical Report AMRL-TDR-62-129. Beh. Sci. Lab., Wright-Patterson AFB.
[20]
V. M. Kuznetsov, B. A. Lugovtsov, and Y. N. Sher. 1967. On the Motive Mechanism of Snakes and Fish. Arch. Rat. Mech. 25 (1967), 367--387.
[21]
L. D. Landau and E. M. Lifshitz. 1976. Mechanics (third ed.). Course of Theoretical Physics, Vol. 1. Butterworth Heinemann.
[22]
Eric Lauga and Thomas R. Powers. 2009. The Hydrodynamics of Swimming Microorganisms. Rep. Prog. Phys. 72, 096601 (2009), 36pp.
[23]
Michael Lentine, Jon Tomas Gretarsson, Craig Schroeder, Avi Robinson-Mosher, and Ronald Fedkiw. 2011. Creature Control in a Fluid Environment. IEEE Trans. Vis. Comp. Graph. 17, 5 (2011), 682--693.
[24]
P. Liljebäck, Ky. Y. Pettersen, Ø. Stavdahl, and J. T. Gravdahl. 2012. A Review on Modeling, Implementation, and Control of Snake Robots. Rob. Aut. Syst. 60, 1 (2012), 29--40.
[25]
M. Marey. 1894. Photographs of a Tumbling Cat. Nature 51 (1894), 80--81.
[26]
Jerrold E. Marsden and Matthew West. 2001. Discrete Mechanics and Variational Integrators. Act. Num. 10 (May 2001), 357--514.
[27]
Gavin S. Miller. 1988. The Motion Dynamics of Snakes and Worms. In Proc. ACM/SIGGRAPH Conf. ACM, 169--173.
[28]
Sehee Min, Jungdam Won, Seunghwan Lee, Jungnam Park, and Jehee Lee. 2019. SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators. ACM Trans. Graph. 38, 6 (2019), 208:1--12.
[29]
R. Montgomery. 1993. Dynamics and Control of Mechanical Systems; The Falling Cat and Related Problems. Number 1 in Fields Inst. Commun. Fields Institute, Chapter Gauge Theory of the Falling Cat, 193--218.
[30]
Emmy Noether. 1918. Invariante Variationsprobleme. Nachr. König. Ges. Wiss. Math. Phys. Klasse (1918), 235--257. Engl. translation https://arxiv.org/abs/physics/0503066.
[31]
Jim Ostrowski and Joel Burdick. 1998. The Geometric Mechanics of Undulatory Robotic Locomotion. I. J. Rob. Res. 17, 7 (1998), 683--701.
[32]
Marcel Padilla, Albert Chern, Felix Knöppel, Ulrich Pinkall, and Peter Schröder. 2019. On Bubble Rings and Ink Chandeliers. ACM Trans. Graph. 38, 4 (2019), 129:1--14.
[33]
Louis Poinsot. 1851. Théorie Nouvelle de la Rotation des Corps. Bachelier.
[34]
E. M. Purcell. 1977. Life at Low Reynolds Number. Amer. J. Phys. 45, 3 (1977), 3--11.
[35]
Michel Rieutord. 2015. Fluid Dynamics: An Introduction. Springer.
[36]
Perrin E. Schiebel, Jennnifer M. Reiser, Alex M. Hubbard, Lillian Chen, D. Zeb Rocklin, and Daniel I. Goldman. 2019. Mechanical Diffraction Reveals the Role of Passive Dynamics in a Slithering Snake. Proc. Nat. Acad. Sci. 116, 11 (2019), 4798--4803.
[37]
Alfred Shapere and Frank Wilczek. 1989a. Geometry of Self-Propulsion at Low Reynolds Number. J. Fluid Mech. 198 (1989), 557--585.
[38]
Alfred Shapere and Frank Wilczek. 1989b. Gauge Kinematics of Deformable Bodies. Amer. J. Phys. 57, 6 (1989), 514--518.
[39]
Hon. J. W. Strutt, M. A. (Lord Rayleigh). 1871. Some General Theorems Relating to Vibrations. Proc. Lond. Math. Soc. s1-4, 1 (1871), 357--368.
[40]
Jie Tan, Yuting Gu, Greg Turk, and C. Karen Liu. 2011. Articulated Swimming Creatures. ACM Trans. Graph. 30, 4 (2011), 58:1--12.
[41]
Xiaoyuan Tu and Demetri Terzopoulos. 1994. Artificial Fishes: Physics, Locomotion, Perception, Behavior. In Proc. ACM/SIGGRAPH Conf. 43--50.
[42]
Steven Vogel. 1983. Life in Moving Fluids (2nd ed.). Princeton University Press.
[43]
Hermann von Helmholtz. 1882. Zur Theorie der stationären Ströme in reibenden Flüssigkeiten. In Wissenschaftliche Abhandlungen. Vol. I. J. A. Barth, 223--230.
[44]
Barlomiej Waszak. 2018. Limbless Movement Simulation with a Particle-Based System. Comp. Anim. Virt. Worlds 29, 2 (2018), 1--21.
[45]
Steffen Weißmann and Ulrich Pinkall. 2012. Underwater Rigid Body Dynamics. ACM Trans. Graph. 31, 4 (2012), 104:1--7.
[46]
Wayne L. Wooten and Jessica K. Hodgins. 1996. Animation of Human Diving. Comp. Graph. Forum 15, 1 (1996), 3--13.
[47]
Jia-Chi Wu and Zoran Popović. 2003. Realistic Modeling of Bird Flight Animations. ACM Trans. Graph. 22, 3 (2003), 888--895.
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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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