Topologically Encoded Animation TEA: History

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Topologically Encoded Animation (TEA) History
Future
T. J. Peters Kerner Graphics
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KnotPlot www.knotplot.com Unknot or
Trefoil? Demo A Unknown1 Unknown2   
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Contemporary Computational Influences

• Edelsbrunner geometry topology
• Sethian Marching methods, topology changes
• Blackmore differential sweeps
• Carlsson, Zomordian Algebraic

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Route to KG
May discussion with Norm. NSF SBIR grant for
TEA technology.
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Digital Visual Effects (DVFX)
Plus, we love to blow things up.
Little reuse or modification
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Challenges --- (Audacious?)
Another Inner Life of a Cell XVIVO for Harvard
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TEA dimension-independent technology

• Provably correct temporal antialiasing
• Portability of animation to differing displays
• Efficient compression and decompression

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My Scientific Emphasis
Mappings and Equivalences Knots and
self-intersections Piecewise Linear (PL)
Approximation
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Temporal Aliasing
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Nbhd_1 about curve.
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1.682 Megs
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1.682 Megs
1.682 Megs
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Moore Dissertation 2006
Efficient algorithm for ambient isotopic PL
approximation for Bezier curves of degree 3.
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PL Approximation for Graphics Animation
Visualization
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Unknot
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Bad Approximation! Self-intersect?
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Good Approximation! Respects Embedding Curvatu
re (local) Separation (global) Error bounds!!
gt Nbhd_2 about curve.
But recognizing unknot in NP (Hass, L, P, 1998)!!
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Role of Homotopy
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.
No longer have error bounds.
Proving 1 1 is central.
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Temporal Antialiasing Comparison

• Time to market.
• Produce traditionally.
• Produce with TEA technology.

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Portability for Display

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

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Compression TEA File (lt1KB 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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Compression vs Decompression

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

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UMass, RasMol
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Conclusions

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

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Quotes Interpretation

• You cant rush art., Woody, Toy Story 2
• Time is money.
• Correct math for the most money.

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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

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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.
• Investigators responsibility, not NSF.

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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_sleig
  h.jpg
• www.channel4.com/film/media/images/Channel4/film/B
  /beowulf_xl_01--film-A.jpg
• www.turbosquid.com