1. Animation of Trees
CS 658

2. The Problem Visually convincing animations of trees moving in wind.
Most focus on small deciduous trees.
Image from Akagi and Kitajima, “Computer animation of swaying trees based on physical simulation” in Computers and Graphics 2006

3. Who Cares
Visual effects for 3D animation
Games
Forestry ecologists

4. Those 2 papers
Why is Habel’s titled “physically guided” and Akagi’s titled “physical simulation”?

5. Why this problem is hard

6. Fluid Dynamics Two way coupled Complex dynamics
Small scale interactions result in significant large scale behavior.

7. Eulerian CFD in 2 minutes
Grid resolution
Pressure
Two-way coupling

8. Eulerian CFD for Trees Trees influence on wind
Virtual resistive bodies
S_b = size of branch
S_c = size of cell
Image from Akagi and Kitajima, “Computer animation of swaying trees based on physical simulation” in Computers and Graphics 2006

9. Eulerian CFD for Trees Adaptive grids Boundary conditions map
Averaging going in
Splitting coming out
Image from Akagi and Kitajima, “Computer animation of swaying trees based on physical simulation” in Computers and Graphics 2006

10. Eulerian CFD for trees
Tables from Akagi and Kitajima, “Computer animation of swaying trees based on physical simulation” in Computers and Graphics 2006

11. Why is this not adequate?
Slow.
Low resolution.
7 leaves per cell.
Good enough?
Streamlining
As will all non-phenomenological methods, you have to draw the line somewhere. Can you get enough realism to make it worth it?

12. Spectral Approximations
It’s hard to get the turbulence right in simulation at small spatial and temporal scales.
Phenomenological approaches to turbulence.

13. A specific example
Image from Habel et al. in “Physically guided animation of trees” in Eurographics 2009

14. Simiu & Scanlan Model Power and freq for wind Structural eng.
First use (I’ve seen) in graphics
from Chuang et al., “Animating pictures with stochastic motion textures” in ACM TOG 2005

15. Chuang’s Spectral Approximation
Approximate displacement of tip by a damped harmonic oscillator with a driving force
Take the Fourier transform of that
Model the driving force spectrum using Simiu & Scanlan’s equation
Turn power spectrum into a velocity spectrum using a Gaussian noise field
Get the spectrum of the tip displacement
Inverse Fourier transform to get tip motion
(After Sun’s 03 ICCV paper which estimates wind from motion)

16. Habel’s Spectral Approximation
Same idea but with significant variations
Different branch dynamics model
3D trees
Smoothing term
Different motion for different hierarchy levels
… and good video clips.

17. Why is this not adequate?
Trees don’t influence the wind.

18. Modal Analysis
Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no INRIA 2008

19. Modal Analysis
Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no INRIA 2008

20. Why is this inadequate? Finding the right linear combination of modes
Determining the modes for an arbitrary tree
They are working on this.

21. Motion Capture Use something to capture tree motion.
Active magnetic markers
Passive optical markers
Video camera
Inclinometers
Process the motion
Replay the motion
Retarget the motion

22. Diener’s MoCap
Image from Diener et al., “Hierarchical retargeting of 2D motion fields to the animation of 3D plant models” SCA 2006

23. Motion Capture

24. Motion Capture

25. Why is this inadequate? Data capture is difficult Data is noisy
When will it be windy, dark and not raining?
Data is noisy
Data is incomplete

26. A Subproblem Animating bending tree branches
If you are going to animate a branch in the wind, the branch better bend.

27. Ball and Stick Model
Image from Akagi and Kitajima, “Computer animation of swaying trees based on physical simulation” in Computers and Graphics 2006

28. Ball and Stick Model
Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no INRIA 2008

29. Bernoulli Beam Model Alpha = taper ratio u(x) = deflection along x
E = elasticity
F = force
Image from Habel et al. in “Physically guided animation of trees” in Eurographics 2009