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Going with the Flow

Published: 19 July 2024 Publication History

Abstract

Given a sequence of poses of a body we study the motion resulting when the body is immersed in a (possibly) moving, incompressible medium. With the poses given, say, by an animator, the governing second-order ordinary differential equations are those of a rigid body with time-dependent inertia acted upon by various forces. Some of these forces, like lift and drag, depend on the motion of the body in the surrounding medium. Additionally, the inertia must encode the effect of the medium through its added mass. We derive the corresponding dynamics equations which generalize the standard rigid body dynamics equations. All forces are based on local computations using only physical parameters such as mass density. Notably, we approximate the effect of the medium on the body through local computations avoiding any global simulation of the medium. Consequently, the system of equations we must integrate in time is only 6 dimensional (rotation and translation). Our proposed algorithm displays linear complexity and captures intricate natural phenomena that depend on body-fluid interactions.

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References

[1]
Akira Azuma and Kunio Yasuda. 1989. Flight Performance of Rotary Seeds. J. Theor. Biol. 138 (1989), 23--53.
[2]
Nawaf Bou-Rabee and Jerrold E Marsden. 2009. Hamilton-Pontryagin Integrators on Lie Groups Part I: Introduction and Structure-Preserving Properties. Found. Comp. Math. 9, 2 (2009), 197--219.
[3]
Christopher E. Brennen. 2004. Internet Book on Fluid Dynamics. Dankat Publishing, Chapter Values of the Added Mass.
[4]
Tyson Brochu, Todd Keeler, and Robert Bridson. 2012. Linear-Time Smoke Animation with Vortex Sheet Meshes. Proc. Symp. Comp. Anim. (2012), 87--95.
[5]
Nicholas Caplan and Trevor N. Gardner. 2007. A Fluid Dynamic Investigation of the Big Blade and Macon Oar Blade Designs in Rowing Propulsion. J. Sports Sci. 25, 6 (2007), 643--650.
[6]
Mark Carlson, Peter J. Mucha, and Greg Turk. 2004. Rigid Fluid: Animating the Interplay between Rigid Bodies and Fluid. ACM Trans. Graph. 23, 3 (2004), 377--384.
[7]
S. J. Corkery, H. Babinsky, and W. R. Graham. 2019. Quantification of Added-Mass Effects using Particle Image Velocimetry Data for a Translating and Rotating Flat Plate. J. Fl. Mech. 870 (2019), 492--518.
[8]
Anthony R. Dobrovolskis. 1996. Inertia of Any Polyhedron. Icarus 124, 2 (1996), 698--704.
[9]
Oliver Gross, Yousuf Soliman, Marcel Padilla, Felix Knöppel, Ulrich Pinkall, and Peter Schröder. 2023. Motion from Shape Change. ACM Trans. Graph. 42, 4 (2023), 107:1--11.
[10]
Luke Heisinger, Paul Newton, and Eva Kanso. 2014. Coins Falling in Water. J. Fl. Mech. 742 (2014), 243--253.
[11]
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.
[12]
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.
[13]
Liliya Kharevych, Weiwei, Yiying Tong, Eva Kanso, Jerrold Marsden, Peter Schröder, and Mathieu Desbrun. 2006. Geometric, Variational Integrators for Computer Animation. In Proc. Symp. Comp. Anim. Eurographics Ass., 43--51.
[14]
Gustav Kirchhoff. 1870. Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit. J. Reine Angew. Math. 1870, 71 (1870), 237--262.
[15]
Gustav Kirchhoff. 1876. Vorlesungen über mathematische Physik. Teubner, 233--250.
[16]
Marin Kobilarov, Keenan Crane, and Mathieu Desbrun. 2009. Lie Group Integrators for Animation and Control of Vehicles. ACM Trans. Graph. 28, 2 (2009), 16:1--14.
[17]
Injae Lee and Haecheon Choi. 2017. Flight of a Falling Maple Seed. Phys. R. Fl. 2, 9 (2017), 090511:1--3.
[18]
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.
[19]
Eric Limacher, Chris Morton, and David Wood. 2018. Generalized Derivation of the Added-Mass and Circulatory Forces for Viscous Flow. Phys. R. Fl. 3, 1 (2018), 014701:1--25.
[20]
Eric Limacher, Chris Morton, and David Wood. 2019. On the Calculation of Force from PIV Data Using the Generalized Added-Mass and Cirulatory Force Decomposition. Exp. in Fl. 60, 4 (2019), 1--22.
[21]
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.
[22]
Andreas Müller. 2021. Review of the exponential and Cayley map on SE (3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems. Proc. Roy. Soc. A 477, 2253 (2021), 20210303.
[23]
Oktar Ozgen, Marcelo Kallmann, Lynnette Es Ramirez, and Carlos Fm Coimbra. 2010.
[24]
Underwater Cloth Simulation with Fractional Derivatives. ACM Trans. Graph. 29, 3 (2010), 23:1--9.
[25]
M. Piñeirua, R. Godoy-Diana, and B. Thiria. 2015. Resistive Thrust Production can be as crucial as Added Mass Mechanisms for Inertial Undulatory Swimmers. Phys. R. E 92, 2 (2015), 021001:1--6.
[26]
Peter Schröder. 2008. What can we Measure? In Discrete Differential Geometry, Alexander I. Bobenko, Peter Schröder, John M. Sullivan, and Günther M. Ziegler (Eds.). Oberwolfach Seminars, Vol. 38. Birkhäuser Verlag.
[27]
Jie Tan, Yuting Gu, Greg Turk, and C. Karen Liu. 2011. Articulated Swimming Creatures. ACM Trans. Graph. 30, 4 (2011), 58:1--12.
[28]
Xiaoyuan Tu and Demetri Terzopoulos. 1994. Artificial Fishes: Physics, Locomotion, Perception, Behavior. In Proc. ACM/SIGGRAPH Conf. 43--50.
[29]
Xinyue Wei, Minghua Liu, Zhan Ling, and Hao Su. 2022. Approximate convex decomposition for 3D meshes with collision-aware concavity and tree search. ACM Trans. Graph. 41, 4, Article 42 (jul 2022), 18 pages.
[30]
Steffen Weißmann and Ulrich Pinkall. 2012. Underwater Rigid Body Dynamics. ACM Trans. Graph. 31, 4 (2012), 104:1--7.
[31]
Jakub Wejchert and David Haumann. 1991. Animation Aerodynamics. In Comp. Graph. (Proc. of ACM/SIGGRAPH Conf.), Vol. 25. 19--22.
[32]
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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  • (2024)CBIL: Collective Behavior Imitation Learning for Fish from Real VideosACM Transactions on Graphics10.1145/368790443:6(1-17)Online publication date: 19-Dec-2024

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Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 43, Issue 4
July 2024
1774 pages
EISSN:1557-7368
DOI:10.1145/3675116
Issue’s Table of Contents
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 July 2024
Published in TOG Volume 43, Issue 4

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Author Tags

  1. rigid body dynamics
  2. shape change
  3. lift
  4. drag
  5. kirchhoff tensor
  6. swimming

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  • (2024)CBIL: Collective Behavior Imitation Learning for Fish from Real VideosACM Transactions on Graphics10.1145/368790443:6(1-17)Online publication date: 19-Dec-2024

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