t. j. peters university of connecticut, professor tea, knots & molecules in animation,...
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T. J. PetersUniversity of Connecticut,
Professor
TEA, Knots & Molecules in Animation, Simulation & Visualization
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T. J. Peters
Topologically Encoded Animation (TEA)
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Trefoil Knot
3D Rotation
Encode: Rot_0, Rot_1, …, Rot_n
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1.682 Megs
1.682 Megs
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Many Frames
• Not just rigid body motion
• Deform shape
• Preserve crucial characteristics
• Role of 3D and projection
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Temporal Aliasing
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Mappings and Equivalences
Knots and self-intersections
Piecewise Linear (PL) Approximation
My Scientific Emphasis
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Little reuse or modification
“Plus, we love to blow things up.”
Digital Visual Effects (DVFX)
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DVFX vs `Blowing things up’
• Modify & re-use vs destroy.
• But explosions are hard, for now.
• Provide path for integration.
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See EagleEye
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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
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Comparison
• XC, RFR, EC, JD 07
• Singularity
• Solver [GE+97]
• Multiple objects
• KG folk 09
• Critical points (C )
• Newton, PGPU?
• Self-intersection
2
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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.
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Time and Topology
Protein folding Data VolumeVisualize in real time !
Geometry
Slow with errors
Topology
Fast & correct – but scale?
Versus-------- ---------
K. E. Jordan (IBM), L. E. Miller (UConn), E.L.F. Moore (UConn), T. J. Peters (UConn), A. C. Russell (UConn)
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Conclusion
Time can be modeled continuously while frames remain discrete.
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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.”
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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.
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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