T. J. PetersKerner Graphics
Topologically Encoded Animation (TEA): History & Future
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.
Little reuse or modification
“Plus, we love to blow things up.”
Digital Visual Effects (DVFX)
Challenges --- (Audacious?)
Another: Inner Life of a Cell – XVIVO for Harvard
TEA: dimension-independent technology
• Provably correct temporal antialiasing
• Portability of animation to differing displays
• Efficient compression and decompression
Mappings and Equivalences
Knots and self-intersections
Piecewise Linear (PL) Approximation
My Scientific Emphasis
Temporal Aliasing
1.682 Megs
1.682 Megs
Moore Dissertation 2006
Efficient 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)!!
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 (<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
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 can’t rush art.”, Woody, Toy Story 2
• “Time 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.
• Investigator’s responsibility, not NSF.
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
