Animation cs 551 651
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Animation CS 551 / 651 PowerPoint PPT Presentation


  • 37 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Animation CS 551 / 651

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


Tilt a whirl10

Tilt-a-whirl


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


Tilt a whirl11

Tilt-a-whirl


Medium time lapses2

Medium time lapses

  • Difference image masked by stationary distribution image


Results1

Results


  • Login