Animation of Trees CS 658

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

Who Cares Visual effects for 3D animation Games Forestry ecologists

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

Why this problem is hard

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

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

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

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

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

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?

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

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

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

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)

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.

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

Modal Analysis Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no. 6674 INRIA 2008

Modal Analysis Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no. 6674 INRIA 2008

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

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

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

Motion Capture

Motion Capture

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

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

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

Ball and Stick Model Image from Diener et al., “Wind projection basis for real-time animation of trees” Raport de recherche no. 6674 INRIA 2008

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