topologically encoded animation (tea): history & future

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Topologically Encoded Animation (TEA): History & Future. T. J. Peters Kerner Graphics. KnotPlot: Unknot or Trefoil? Demo A: Unknown1 & Unknown2. Contemporary Computational Influences. Edelsbrunner: geometry & topology Sethian: Marching methods, topology changes - PowerPoint PPT Presentation


  • Topologically Encoded Animation (TEA): History & Future T. J. PetersKerner Graphics

  • KnotPlot:

    Unknot or Trefoil?

    Demo A: Unknown1 & Unknown2

  • Contemporary Computational Influences Edelsbrunner: geometry & topology

    Sethian: Marching methods, topology changes

    Blackmore: differential sweeps

    Carlsson, Zomordian : Algebraic

  • Route to KG

    May discussion with Norm.

    NSF SBIR grant for TEA technology.

  • Digital Visual Effects (DVFX)Little reuse or modification

    Plus, we love to blow things up.

  • Challenges --- (Audacious?)Another: Inner Life of a Cell XVIVO for Harvard

  • TEA: dimension-independent technologyProvably correct temporal antialiasing

    Portability of animation to differing displays

    Efficient compression and decompression

  • My Scientific Emphasis

    Mappings and Equivalences

    Knots and self-intersections

    Piecewise Linear (PL) Approximation

  • Temporal Aliasing

  • Nbhd_1 about curve.

  • 1.682 Megs

  • 1.682 Megs1.682 Megs

  • Moore Dissertation 2006Efficient algorithm for ambient isotopic PL approximation for Bezier curves of degree 3.

  • PL Approximation for Graphics Animation & Visualization

  • Unknot

  • BadApproximation!


  • Good Approximation!

    Respects Embedding:

    Curvature (local) &Separation (global)

    Error bounds!! =>Nbhd_2 about curve.But recognizing unknot in NP (Hass, L, P, 1998)!!

  • Proving 1 1 is central.If c is a non-self-intersecting curve and F is a homotopy of c such that each homotopic image of c is non-self-intersecting, then F is an ambient isotopy.Role of HomotopyNo longer have error bounds.


  • Temporal Antialiasing Comparison

    Time to market.

    Produce traditionally.

    Produce with TEA technology.

  • Portability for Display

    Ipod to Big Screen by parameters.

    3D TV. (Prototype shown today.)

  • Compression: TEA File (
  • Compression vs Decompression

    Compression, Phase I.

    Decompression, Phase II.

  • UMass, RasMol

  • Conclusions

    Time can be modeled continuously while frames remain discrete.

    Difference between

    Perturb then approximate versus

    Approximate then perturb.

  • Quotes & Interpretation

    You cant rush art., Woody, Toy Story 2Time is money.

    Correct math for the most money.

  • Overview References

    Modeling Time and Topology for Animation and Visualization, [JMMPR], pre-print

    Computation Topology Workshop, Summer Topology Conference, July 14, 05, Special Issue of Applied General Topology, 2007

    Open Problems in Topology II, 2007

    NSF, Emerging Trends in Computational Topology, 1999,

  • Acknowledgements: NSF

    SBIR: TEA, IIP -0810023 .SGER: Computational Topology for Surface Reconstruction, CCR - 0226504.Computational Topology for Surface Approximation, FMM - 0429477.

    Investigators responsibility, not NSF.

  • Acknowledgements: Images\_g/


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