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Topologically Encoded Animation (TEA): History and Future Trends

Explore the evolution and future prospects of topologically encoded animation (TEA), featuring a blend of computational influences and advancements in digital visual effects (DVFX). Discover the applications of TEA technology, efficient compression methods, and the interplay of topology and geometry in animation. Delve into the use of piecewise linear (PL) approximation for graphics and visualization, along with the challenges and innovative solutions in the field. Join the discourse on knot theory, self-intersections, and temporal antialiasing techniques for enhanced animation quality. Uncover how TEA technology enables dimension-independent animation with provably correct temporal antialiasing, offering portability across various display platforms.

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Topologically Encoded Animation (TEA): History and Future Trends

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  1. Topologically Encoded Animation (TEA): History & Future T. J. Peters Kerner Graphics

  2. KnotPlot: www.knotplot.com Unknot or Trefoil? Demo A: Unknown1 & Unknown2

  3. Contemporary Computational Influences • Edelsbrunner: geometry & topology • Sethian: Marching methods, topology changes • Blackmore: differential sweeps • Carlsson, Zomordian : Algebraic

  4. Route to KG May discussion with Norm. NSF SBIR grant for TEA technology.

  5. Digital Visual Effects (DVFX) “Plus, we love to blow things up.” Little reuse or modification

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

  7. TEA: dimension-independent technology • Provably correct temporal antialiasing • Portability of animation to differing displays • Efficient compression and decompression

  8. My Scientific Emphasis Mappings and Equivalences Knots and self-intersections Piecewise Linear (PL) Approximation

  9. Temporal Aliasing

  10. 1.682 Megs 1.682 Megs

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

  12. PL Approximation for Graphics – Animation & Visualization

  13. Unknot

  14. Bad Approximation! Self-intersect?

  15. Good Approximation! Respects Embedding: Curvature (local) & Separation (global) Error bounds!! => Nbhd_2 about curve. But recognizing unknot in NP (Hass, L, P, 1998)!!

  16. Temporal Antialiasing Comparison • Time to market. • Produce traditionally. • Produce with TEA technology.

  17. Portability for Display • Ipod to Big Screen by parameters. • 3D TV. (Prototype shown today.)

  18. Compression: TEA File (<1KB vs 1.7 Megs) Bezier degree = 3, with Control points 0.0 0.0 0.0 4.293 4.441 0.0 8.777 5.123 1.234 12.5 0.0 0.0 Perturbation vectors; constraint on each vector 1 24.1 0.0 0.0 ; 26.4 1 -12.5 0.0 5.0 ; 18.1 2 -2.1 -2.4 -3.1 ; 9.0 1 -11.6 0.0 -1.9 ; 14.0

  19. Compression vs Decompression • Compression, Phase I. • Decompression, Phase II.

  20. UMass, RasMol

  21. Conclusions • Time can be modeled continuously while frames remain discrete. • Difference between • Perturb then approximate versus • Approximate then perturb.

  22. Quotes & Interpretation • “You can’t rush art.”, Woody, Toy Story 2 • “Time is money”. • Correct math for the most money.

  23. 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 Overview References

  24. Acknowledgements: NSF • SBIR: TEA, IIP -0810023. • SGER: Computational Topology for Surface Reconstruction, CCR - 0226504. • Computational Topology for Surface Approximation, FMM - 0429477. • Investigator’s responsibility, not NSF.

  25. Acknowledgements: Images • http://se.inf.ethz.ch/people/leitner/erl\_g/ • www.bangor.ac.uk/cpm/sculmath/movimm.htm • www.knotplot.com • blog.liverpoolmuseums.org.uk/graphics/lottie_sleigh.jpg • www.channel4.com/film/media/images/Channel4/film/B/beowulf_xl_01--film-A.jpg • www.turbosquid.com

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