T. J. PetersKerner Graphics

Topologically Encoded Animation (TEA): History & Future

KnotPlot: www.knotplot.com

Unknot or Trefoil?

Demo A: Unknown1 & Unknown2  

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