T. J. PetersUniversity of Connecticut,

Professor

TEA, Knots & Molecules in Animation, Simulation & Visualization

T. J. Peters

Topologically Encoded Animation (TEA)

Trefoil Knot

3D Rotation

Encode: Rot_0, Rot_1, …, Rot_n  

1.682 Megs

1.682 Megs

Many Frames

• Not just rigid body motion

• Deform shape

• Preserve crucial characteristics

• Role of 3D and projection

Temporal Aliasing

Mappings and Equivalences

Knots and self-intersections

Piecewise Linear (PL) Approximation

My Scientific Emphasis

Little reuse or modification

“Plus, we love to blow things up.”

Digital Visual Effects (DVFX)

DVFX vs `Blowing things up’

• Modify & re-use vs destroy.

• But explosions are hard, for now.

• Provide path for integration.

See EagleEye

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

Comparison

• XC, RFR, EC, JD 07

• Singularity

• Solver [GE+97]

• Multiple objects

• KG folk 09

• Critical points (C )

• Newton, PGPU?

• Self-intersection

2

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.

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)

Conclusion

Time can be modeled continuously while frames remain discrete.

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.”

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.

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