Plausible motion simulation

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Plausible motion simulation

• Ronen Barzel (on leave from PIXAR)
• John Hughes (on sabbatical from Brown)

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Goals

• Set context for the work to be presented in the
  course.
• Correct some misimpressions that people have
  gotten from our 1996 paper.

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How can you do goal-directed (physical) animation?

• Make your bed!

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Engineers Approach
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Mid-Late 1980s
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Reconcile realism with control.
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Plausible Animation
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Exactness?
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Result B
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Plausible Animation (2)
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Three versions of physical motion

• Nature
• Model
• Numerics

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Natures solution

• What really happens in the world
• What would really happen in the world if we tried
  it
• Important question Tried what? Whats the
  situation were asking nature about?

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Model solution

• Might say Mathematical model
• A simplification of the real world
• e.g. rigid body model
• e.g. Newton vs. Einstein
• Chosen to capture interesting or relevant
  properties
• Expressed as equations of motion

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Numerical solution

• Approximation to analytic solution of model
  equations
• Given numbers describing objects state, returns
  numbers describing their motion.

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Examine what we mean by the correct result

• What result should we be willing to accept? Why?
• Is there a single correct result?

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Graphics models only describe an approximation

• Have already made a somewhat arbitrary choice
• No need to be too insistent on it
• But lets say its as good as we can get

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Numerical solution is always a cloud

• All values within the cloud are equally accurate
• Traditional view solver computes best answer
• the cloud can be made arbitrarily small
• cloud converges on the correct answer.
• but is this always true?

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The model may be unstable

• Consider a ball that lands exactly on the fence,
  can fall on either side
• Numerical cloud is disjoint
• Decreasing tolerance parameter doesnt cause
  cloud to converge.
• Solver chooses one side or the other arbitrarily
• Either side is equally correct
• A more honest solver would offer both sides,
  let us choose between them

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How good are our input values?

• Often describe object as sphere or plane,
  etc.
• Real-world objects are never exactly spherical or
  planar
• Texture mapping, microfacets, etc. known in
  rendering to get more realistic results
• Similarly we need texturing in simulation to
  get more realistic results

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Consider input as a range/distribution

• Yields distribution of results
• If model is stable
• Results may vary slightly
• But may be observable
• If model is unstable
• Results may vary almost arbitrarily
• Honest solver would offer range of results

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In some sense, were saying

• Because of limitations of computing
• We cant really compute Natures solution anyway
• There are always many results that are equally
  appropriate w.r.t. model and inputs
• We may as well choose the one we want

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But even more

• In principle we cant know inputs with analytic
  accuracy
• Natures solution isnt unique.
• The real world includes instability
• Random-number generators dice
• Chaos

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Ultimate claim

• In no case can we compute a single correct
  solution
• We can therefore choose among them.

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Preceding is physics, not cheating
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Coming up

• Stephen Chenney
• Jovan Popovic
• Ron Fedkiw