topologically encoded animation (tea): history & future

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

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

  • KnotPlot: www.knotplot.com

    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!

    Self-intersect?

  • 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.

    CONTACT

  • 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, xxx.lanl.gov/abs/cs/9909001

  • 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

    http://se.inf.ethz.ch/people/leitner/erl\_g/ www.bangor.ac.uk/cpm/sculmath/movimm.htmwww.knotplot.comblog.liverpoolmuseums.org.uk/graphics/lottie_sleigh.jpgwww.channel4.com/film/media/images/Channel4/film/B/beowulf_xl_01--film-A.jpgwww.turbosquid.com

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