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Animation CS 551 / 651

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AnimationCS 551 / 651

Dynamics Modeling and Culling

Chenney, Ichnowski, and Forsyth

- 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 is expensive
- Small timesteps for dynamics computations
- Lots of moving limbs
- Flexible objects like hair/cloth
- Collision checks (n2)

- 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

- Out-of-view

- What simulation fidelity is needed?

- How is simplification constructed?
- Cull DOFs
- Reduce temporal resolution
- Permit more collisions

- Current technology: simplify by hand

- 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

- Suspension of disbelief

- 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?

- Cost of rendering geometry must be justified

Funkhouser and Sequin, 1993

- For each frame
- Compute effect on realism vs. all simplifications
- Set “reality” dial on each object to suit its importance

- 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

- Object’s description is a function of where it is relative to one “cycle”
- Predicting where the blue-line bus is vs. predicting where Osama is

- Where is the car and what is its orientation?

- 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!

- Observe position/orientation ofcar during one cycle

- Using the simplified model
- Replace true dynamics withneural network
- Just keep track of t and increment

- Replace true dynamics withneural network
- A lot like motion capture

- 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

- 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

- People aren’t good at predicting future states
- Examples of these?

- Where are all the cars?
- A chaotic system where physics matters

- Short time lapses
- Use previous state as a basis forprediction of future states
- Extrapolation of accelerations and velocities

- Use previous state as a basis forprediction of future states

- 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

- 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

- Training a neural network

- 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
- …

- 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)

Position after dt

Velocity after dt

True Dynamics

Neural NetApproximation

- Difference image masked by stationary distribution image

- Neural Network Prediction

- 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

- I have a basic model, but no bias to previous states

- 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

- How do I build a basic model?

- 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?

- How do I build a basic model?
- Example: state space of two-joint arm

- 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

- 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

- NN is accurate for designated dt

- Difference image masked by stationary distribution image