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Animation CS 551 / 651. Dynamics Modeling and Culling Chenney, Ichnowski, and Forsyth. The world is full of moving things. Cars, people, clouds, leaves on a tree Lasseter believes everything must be moving to look “right” Dynamics The equations that define how they move Simulation

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animation cs 551 651

AnimationCS 551 / 651

Dynamics Modeling and Culling

Chenney, Ichnowski, and Forsyth

the world is full of moving things
The world is full of moving things
  • Cars, people, clouds, leaves on a tree
  • Lasseter believes everything must be moving to look “right”
  • Dynamics
    • The equations that define how they move
  • Simulation
    • The process of computing the dynamics
simulation makes the world go round
Simulation makes the world go ‘round
  • Simulation is expensive
    • Small timesteps for dynamics computations
    • Lots of moving limbs
    • Flexible objects like hair/cloth
    • Collision checks (n2)
reduce costs of simulation
Reduce costs of simulation
  • Perception permits simplification
    • What simulation fidelity is needed?
      • Out-of-view
        • No need to render correct movements
        • What happens when object returns to view?
      • Distant or in periphery
        • Some part of simulation must be accurate
        • Other parts can be approximated
building simpilfications
Building simpilfications
  • How is simplification constructed?
    • Cull DOFs
    • Reduce temporal resolution
    • Permit more collisions
  • Current technology: simplify by hand
preserving accuracy
Preserving accuracy
  • Graceful degradation
    • Suspension of disbelief
      • If simplified thing looks unrealistic, belief in “virtual” world may be jeopardized
    • Accuracy of outcome
      • If simplified thing behaves differently, outcome of game or training application may be wrong
related work
Related work
  • Geometric level of detail (LOD)
    • Cost of rendering geometry must be justified
      • Perceptually based perception metrics
      • Geometric simplification algorithms
      • Visibility culling
    • Do these translateto simulation?

Funkhouser and Sequin, 1993

in a perfect world
In a perfect world
  • For each frame
    • Compute effect on realism vs. all simplifications
    • Set “reality” dial on each object to suit its importance
simplifying periodic systems
Simplifying periodic systems
  • What does periodicity buy us?
    • Object’s description is a function of where it is relative to one “cycle”
      • Find “t”, where it is in the cycle
      • Build f(t), a function mapping t  system state
  • Predicting where the blue-line bus is vs. predicting where Osama is
roller coaster
Roller coaster
  • Where is the car and what is its orientation?
roller coaster1
Roller coaster
  • Build mapping, f(t)
    • Observe position/orientation ofcar during one cycle
      • How long is a cycle?
    • Train neural network to correctly predict mapping
      • f(t) = x, y, z, roll, pitch, yaw
      • Neural net is just a function approximator, so it can do this!
roller coaster2
Roller coaster
  • Using the simplified model
    • Replace true dynamics withneural network
      • Just keep track of t and increment
  • A lot like motion capture
roller coaster3
Roller coaster
  • Are there shortcomings with using motion capture?
    • Not responsive to changesin environment
    • Not alterable
  • Does it matter?
    • Use this simplification when responsiveness and flexibility are not required
simplifying non periodic systems
Simplifying non-periodic systems
  • What does non-periodicity buy us?
    • People aren’t good at predicting future states
      • There is room for error/noise/approximation
    • People get worse at predicting as time elapses
      • Short lapses are predicted using extrapolation
      • Longer lapses are predicted using generalization
      • Really long lapses lack preconceptions
  • Examples of these?
tilt a whirl
Tilt-a-whirl
  • Where are all the cars?
    • A chaotic system where physics matters
tilt a whirl1
Tilt-a-whirl
  • Short time lapses
    • Use previous state as a basis forprediction of future states
      • Extrapolation of accelerations and velocities
tilt a whirl2
Tilt-a-whirl
  • Medium time lapses
    • Use previous state as a basis forprediction of future states
    • Extrapolation only works forsmall dt
    • Use neural network to model change in state afterdt seconds have passed
      • f (statet) = statet+dt
tilt a whirl3
Tilt-a-whirl
  • Medium time lapses
    • Training a neural network
      • Sample system at time t
      • Sample system at time t + dt
      • Network has one input for each DOF
      • Network has one output for each DOF
      • Train network to predict state after t + dt
tilt a whirl4
Tilt-a-whirl
  • Medium time lapses
    • A particular neural network onlypredicts state after dt seconds
    • What if object pops back into view after ½ dt seconds?
      • Build a second neural network for ½ dt
      • Build a third neural network for ¼ dt
tilt a whirl5
Tilt-a-whirl
  • Medium time lapses
    • Any point in time is approximatedby series of neural networks
    • Ex: Approximate 3.75 seconds
      • Let NNs exist for dt = .25, .5, and 1.0
      • state1 = NN1.0 (state0)
      • state2 = NN1.0 (state1)
      • state3 = NN1.0 (state2)
      • state3.5 = NN0.5 (state3)
      • state3.75 = NN0.25 (state3.5)
medium time lapses
Medium time lapses

Position after dt

Velocity after dt

True Dynamics

Neural NetApproximation

medium time lapses1
Medium time lapses
  • Difference image masked by stationary distribution image
results
Results
  • Neural Network Prediction
tilt a whirl6
Tilt-a-whirl
  • Long time lapses
    • Previous state is not a startingpoint for prediction… stochastic
    • What does the traffic on I-29 look like at 5:00 this afternoon?
      • I have a basic model, but no bias to previous states
        • Obviously if an accident happened at 4:00, my prediction would be wrong
tilt a whirl7
Tilt-a-whirl
  • Long time lapses
    • How do I build a basic model?
      • Based on observations
      • I am more likely to expect system states that occurred frequently in my observations
      • Some system states will be implausible because of limits on feasibility that I determine
tilt a whirl8
Tilt-a-whirl
  • Long time lapses
    • How do I build a basic model?
      • State of world is defined by DOFs
      • DOFs define n-dimensional space
      • Reduce the space to a finite volume
        • Limits on feasibility
        • What are min/max for each DOF?
  • Example: state space of two-joint arm
tilt a whirl9
Tilt-a-whirl
  • Long time lapses
    • Discretize state-space volume intocells
    • Run the simulation for a while
      • At each timestep, record which cell system is in
      • Accumulate counters in each cell
    • Each cell is a assigned a value corresponding to the probability system is in that state
which model do we use
Which model do we use?
  • Extrapolation vs. NN vs. Stochastic
    • NN is accurate for designated dt
      • Start using NNs at smallest dt
    • At some point, knowing exact state at time t doesn’t help
      • As time passes, state of system begins to match the basic prediction of stationary distribution
medium time lapses2
Medium time lapses
  • Difference image masked by stationary distribution image
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