Miyata Lab@JAIST Visual Computing (Procedural Modeling) Immersed - PowerPoint PPT Presentation

Miyata Lab@JAIST • Visual Computing (Procedural Modeling) Immersed Rigid Body Dynamics Realistic coupling motion among turbulence and bodies Haoran Xie Japan Advanced Institute of Science and Technology In Kent State University 12/19/2013 H.Xie@JAIST 1 12/19/2013 H.Xie@JAIST 2 I mmersed B ody D ynamics Miyata Lab@JAIST • Fun Computing (IVRC, SIGGRAPH Emerging Teh, Laval virtual) 12/19/2013 H.Xie@JAIST 3 H.XIE 1

Challenges Free Fall Fluid Simulations (e.g. S2013) Dispersed Flows (e.g. S2010) Rigid-body Simulations (e.g. S2012) Turbulent Flows (e.g. SA2010) � Unsteady dynamics of participated objects � Vortical loads from the surrounding flow Two-way Coupling (e.g. SA2012) @picture from Youtube, www-inmagine.com, www-personal.umich.edu/~nori/ 12/19/2013 H.Xie@JAIST 6 Phenomena What happened? –from physics view [YANG et al., J. Comput. Phys., [ZHONG et al. J. Fluid Mech. 2012] (2013)] H.XIE 2

In Computer Graphics, An Active and Exciting Topic • e.g. in 2013, – Coins falling in water, arXiv, Fluid Dynamics, (2013.12) – Experimental study of a freely falling plate with an inhomogeneous mass distribution, Physical Review E, (2013.11) How to achieve Realistic simulations in Realtime ? – Experimental investigation of freely falling thin disks. Part 2. Transition of three- dimensional motion from zigzag to spiral, J. Fluid Mech., (2013.10) � – Flexible body with drag independent of the flow velocity J. Fluid Mech., (2013.10) High-Reynolds-number Flow � Turbulent Flows – Influence of aspect ratio on tumbling plates, J. Fluid Mech., (2013.9) � Unsteady Forces – Bi-stability of a pendular disk in laminar and turbulent flows, J. Fluid Mech., (2013.7) – Numerical simulation of the dynamics of freely falling discs, Physics of Fluids, (2013.4) – Falling styles of disks, J. Fluid Mech., (2013.3) – Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion, J. Fluid Mech., (2013.2) • Research Groups: Eva Kanso(USC), C. Lee(Peking Uni.), J. Zhang(Cornel), J. Magnaudet(IMFT, France) , etc. 12/19/2013 H.Xie@JAIST 9 Introduction • Rigid body motion in viscous flow – Procedural motion synthesis approach • Data-driven motion synthesis techniques Topic 1: Data-driven Approach • Discrete-time Markov chain model • Noise-based wind interaction 12/19/2013 H.Xie@JAIST 12 H.XIE 3

Free Fall: Related Works Free Fall: Related Works • Physical Research • Graphical Research – From Maxwell,1854 ｰ Lattice Boltzmann Method [WEI et al. 2004] ｰ Chaotic dynamics [FIELD et al. 1997] ｰ Example-based approach [VAZUQUEZ et al. 2008] ｰ Numerical solution [ANDERSEN et al.2005] ｰ Sketch-based method [LI et al. 2010] ｰ Motion classification [RAZAVI 2010] ｰ Commercial CG tools (LightWave 10 etc.) ｰ 3D experiments [ZHONG et al.2011] 12/19/2013 H.Xie@JAIST 13 12/19/2013 H.Xie@JAIST 14 System Overview Parameter Redefinition Motion Modeling Primitive Motion Input Phase Diagram Synthesis parameters Trajectory Trajectory Database Search Tree Motion Synthesis Wind Field Markov Chain Motion Lightweight rigid Motion Graph Model Classification body simulation 12/19/2013 H.Xie@JAIST 15 12/19/2013 H.Xie@JAIST 16 H.XIE 4

Phase Diagram Measured Trajectories Measured trajectories of six Primitive motions (a) (b) (c) (d) (e) (f) Steady Periodic Transitional Periodic Transitional Periodic Decent Fluttering Chaotic Tumbling Helix Spiral 12/19/2013 H.Xie@JAIST 17 12/19/2013 H.Xie@JAIST 18 Force Model of Free Fall in 2D (ODEs*) [TANABE et al. 1994] Force Model 12/19/2013 H.Xie@JAIST 19 12/19/2013 H.Xie@JAIST 20 H.XIE 5

Pre-computed Trajectory Database Trajectories of Primitive motions • Segmentation • (2D) Fluttering, Tumbling and Chaotic – Positions: Harmonic functions Feature Vector – Trajectory Search Tree – Orientations Turning Points • Linear interpolation with the segments of ODEs • Clustering • (3D) Helix and Spiral Motion – Top view of motion prototypes – Unified harmonic function Descent Tumbling Spiral Helix Fluttering 12/19/2013 H.Xie@JAIST 21 12/19/2013 H.Xie@JAIST 22 Chaotic Motion classification Synthesized Trajectories of Motion Prototypes (a) (b) (c) (d) (e) (f) Steady Periodic Transitional Periodic Transitional Periodic Decent Fluttering Chaotic Tumbling Helix Spiral 12/19/2013 H.Xie@JAIST 23 12/19/2013 H.Xie@JAIST 24 H.XIE 6

Markov chain Model Hypothesis Group4 Group1 Group7 Group2 Group5 Group6 Group3 12/19/2013 H.Xie@JAIST 25 12/19/2013 H.Xie@JAIST 26 Wind-field Motion Graph with Markov chain 12/19/2013 H.Xie@JAIST 27 12/19/2013 H.Xie@JAIST 28 H.XIE 7

Wind characteristics Wind characteristics Logarithmic wind law: Kolmogoro's law : p is the wind direction 12/19/2013 H.Xie@JAIST 29 12/19/2013 H.Xie@JAIST 30 2D Wind field 3D Wind field 12/19/2013 H.Xie@JAIST 31 12/19/2013 H.Xie@JAIST 32 H.XIE 8

Simulation Results Simulation Results Japanese one yen coin Leaf Steady Decent Periodic Tumbling Transitional Helix Periodic Fluttering motion Ground truth Simulation result Ground truth Simulation result 12/19/2013 H.Xie@JAIST 33 12/19/2013 H.Xie@JAIST 34 Simulation Results Simulation Results-Wind A piece of paper Paths in wind Periodic Tumbling Periodic Spiral motion 5.0m/s 1.0m/s 3.0m/s Ground truth Simulation result 12/19/2013 H.Xie@JAIST 35 12/19/2013 H.Xie@JAIST 36 H.XIE 9

Simulation Results Simulation Results Falling in wind Falling in wind Original 3.0m/s Original 3.0m/s 5.0m/s 5.0m/s 12/19/2013 H.Xie@JAIST 37 12/19/2013 H.Xie@JAIST 38 Results: ����� Conclusion • A framework for generating free fall animation by data- driven motion synthesis and pre-computed trajectory database in wind field • A bout the physical details of free fall motions, looking through physical nature • A bout the motion synthesis of free fall motions ● Realistic freely falling animation in real-time 12/19/2013 H.Xie@JAIST 39 12/19/2013 H.Xie@JAIST 40 H.XIE 10

Related work • Two-way Coupling – Fluid(Euler) + Rigid Bodies (Lagrangian) � � � �������������������� ������������������� ������������������� ������������������� ������������������� �������������������� ������������������� ������������������� � � � – Fully Lagrangian meshless method ���������������� ���������������� ���������������� ���������������� Topic 2: Stochastic Modeling ������������������������ ����������������������� ����������������������� ����������������������� � � � • Turbulent Flows – Wavelet Noise [SIGGRAPH08] – Synthetic turbulence [SA2009] • Anisotropic particles [SA2010] � No work about freely moving bodies in • Stochastic particles [EG2011] turbulent flows Related work Related work • Motions inside Flow • Underwater Dynamics – Underwater rigid-body dynamics [SIGGRPAH12] – Swimming motions [SCA04, TVCG11, SIGGRAPH11] • Kirchhoff tensor due to added-mass effects – Flying motions [SCA03,SIGGRAPH03,09] – Underwater cloth dynamics [SIGGRPAH10] – Bubble dynamics [EG09,SIGGRAPH13] Vortex shedding • Fractional derivatives due to Basset forces period Measured data of falling parallelograms [Varshney et al. Physical Review E(2013)] � Cannot explain motion’s unsteady nature � For inviscid flows Steady coefficients in CG (e.g. SIGGRAPH03) � A sensitive motion � For low-Reynolds-number flows H.XIE 11

Previous work Framework Flow Effects • Motion Planning Potential flow Vortex flow – Rapidly-Exploring Random Trees [TVC2005] – Motion Graphs [TVC2013] Rigid-body Simulator Dynamic Dynamic Kirchhoff Kirchhoff Vortical Vortical Equations Equations Tensors Tensors Loads Loads Dynamical Systems Langevin Turbulent Simulator Mean Mean Energy Energy � For simple geometries Flow Flow Model Model � Miss surrounding flow info Immersed Rigid-body Dynamics Precomput Runtime ation Rigid-body Simulator Rigid-body Simulator • Kinematic Equations • Dynamic Equations – Newton-Euler Equations World frame – Kirchhoff Equations [Lamb,1945] Voritical Loads – Generalized Kirchhoff Equations Skew Matrix Buoyancy-corrected Gravity Kirchhoff Tensors H.XIE 12