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TEA, Knots & Molecules in Animation, Simulation & Visualization

TEA, Knots & Molecules in Animation, Simulation & Visualization. T. J. Peters Kerner Graphics, Inc., CTO; University of Connecticut, Professor . Topologically Encoded Animation (TEA). T. J. Peters Kerner Graphics. Trefoil Knot 3D Rotation Encode: Rot_0, Rot_1, …, Rot_n.

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TEA, Knots & Molecules in Animation, Simulation & Visualization

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  1. TEA, Knots & Molecules in Animation, Simulation & Visualization T. J. Peters Kerner Graphics, Inc., CTO; University of Connecticut, Professor

  2. Topologically Encoded Animation (TEA) T. J. Peters Kerner Graphics

  3. Trefoil Knot 3D Rotation Encode: Rot_0, Rot_1, …, Rot_n

  4. More Aggressive Moves • Not just rigid body motion • Deform shape • Preserve crucial characteristics

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

  6. 1.682 Megs 1.682 Megs

  7. Homeomorphism is not enough • F : X  Y, • such that F is • continuous, • 1 – 1 • onto • and has a continuous inverse.

  8. Two Frames with Different Topology

  9. Instantaneous Self-intersection

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

  11. Isotopy & Animation F : X x [0,1]  Y, such that for each t in [0,1] F : X x t is a homeomorphism. We take Y to be 3D space.

  12. KERNER OPTICAL Kerner Graphics: Digital Visual Effects (DVFX) KERNEROPTICAL “Plus, we love to blow things up.” Little reuse or modification

  13. DVFX vs `Blowing things up’ • Modify & re-use vs destroy. • But explosions are hard, for now. • Provide path for integration.

  14. EagleEye

  15. Unknot

  16. Bad Approximation! Self-intersect?

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

  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. • Phase IB Project with Kerner Technologies??

  20. Dimension Independence • Compute • Minimum separation distance. • Minimum radius of curvature. • Take minimum. • Tubular neighborhood: • Constant radius = limit. • Adaptive options?

  21. Computing • Curvature – calculus problem • Minimum Separation Distance: • Candidate line segments. • Nearly normal at both ends. • Newton’s Method to converge.

  22. Infinitely many good seeds

  23. Symmetry & Performance • Important for animation. • Not used in initial test cases. • Role for PGPU’s (updates!!) • Pre-print 09 • www.cse.uconn.edu/~tpeters

  24. Comparison • KG folk 09 • Critical points (C ) • Newton, PGPU? • Self-intersection • XC, RFR, EC, JD 07 • Singularity • Solver [GE+97] • Multiple objects 2

  25. TEA Authoring Tools for DVFX • Time-checker like spell-checker • runs in background; not intrusive! • very expensive if missed. • Parametric re-design; similar to CAGD PTC • Integrate with VFX.

  26. Visualization for Simulations • Animation `on-the-fly’. • No human in the loop. • Recall update issue (fast!!).

  27. Time and Topology Data Volume Protein folding Visualize in real time ! -------- --------- Geometry Versus Topology Slow with errors Fast & correct – but scale? K. E. Jordan (IBM), L. E. Miller (UConn), E.L.F. Moore (UConn), T. J. Peters (UConn), A. C. Russell (UConn)

  28. Similarity? • The Need for Verifiable Visualization • Kirby and Silva, IEEE CG&A, 08 • What confidence (or error measures) can be assigned to a computer-based prediction of a complex event? • CFD: colorful faulty dynamics • “First, do no harm” • “Primarily, don’t introduce artifacts.”

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

  30. Modeling Time and Topology for Animation and Visualization …., [JMMPR], TCS08 • Computation Topology Workshop, Summer Topology Conference, July 14, ‘05, Special Issue of Applied General Topology, 2007 • Open Problems in Topology II, 2007 [BP] • NSF, Emerging Trends in Computational Topology, 1999, xxx.lanl.gov/abs/cs/9909001 Overview References

  31. Acknowledgements: NSF • SBIR: TEA, IIP -0810023. • SGER: Computational Topology for Surface Reconstruction, CCR - 0226504. • Computational Topology for Surface Approximation, FMM - 0429477. • IBM Faculty & Doctoral Awards • Investigator’s responsibility, not sponsor’s.

  32. Acknowledgements: Images • http://se.inf.ethz.ch/people/leitner/erl_g • www.knotplot.com • http://domino.research.ibm.com/comm/pr.nsf/pages/rscd.bluegene-picaa.html • www.bangor.ac.uk/cpm/sculmath/movimm.htm • blog.liverpoolmuseums.org.uk/graphics/lottie_sleigh.jpg

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

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

  35. Nbhd_1 about curve.

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