Tea knots molecules in animation simulation visualization
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TEA, Knots & Molecules in Animation, Simulation & Visualization. T. J. Peters Kerner Graphics, Inc., CTO; University of Connecticut, Professor . Topologically Encoded Animation (TEA). T. J. Peters Kerner Graphics. Trefoil Knot 3D Rotation Encode: Rot_0, Rot_1, …, Rot_n.

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Tea knots molecules in animation simulation visualization
TEA, Knots & Molecules in Animation, Simulation & Visualization

T. J. Peters

Kerner Graphics, Inc., CTO;

University of Connecticut, Professor


Topologically encoded animation tea
Topologically Encoded Animation (TEA) Visualization

T. J. Peters

Kerner Graphics


Trefoil Knot Visualization

3D Rotation

Encode: Rot_0, Rot_1, …, Rot_n


More aggressive moves
More Aggressive Moves Visualization

  • Not just rigid body motion

  • Deform shape

  • Preserve crucial characteristics


KnotPlot: Visualizationwww.knotplot.com

Unknot or Trefoil?

Demo A: Unknown1 & Unknown2


1.682 Megs Visualization

1.682 Megs


Homeomorphism is Visualizationnot enough

  • F : X  Y,

  • such that F is

  • continuous,

  • 1 – 1

  • onto

  • and has a continuous inverse.




Contemporary computational influences
Contemporary Computational Influences Visualization

  • Edelsbrunner: geometry & topology

  • Sethian: Marching methods, topology changes

  • Blackmore: differential sweeps

  • Carlsson, Zomordian : Algebraic


Isotopy & Animation Visualization

F : X x [0,1]  Y,

such that for each

t in [0,1]

F : X x t is a homeomorphism.

We take Y to be 3D space.


Kerner graphics digital visual effects dvfx

KERNER OPTICAL Visualization

Kerner Graphics: Digital Visual Effects (DVFX)

KERNEROPTICAL

“Plus, we love to blow things up.”

Little reuse or modification


Dvfx vs blowing things up
DVFX vs `Blowing things up’ Visualization

  • Modify & re-use vs destroy.

  • But explosions are hard, for now.

  • Provide path for integration.


EagleEye Visualization


Unknot Visualization


Bad Visualization

Approximation!

Self-intersect?


Good Visualization

Approximation!

Respects Embedding:

Curvature (local) &

Separation (global)

Error bounds!! =>

Nbhd_2 about curve.

But recognizing unknot in NP (Hass, L, P, 1998)!!


Compression: TEA File (<1KB vs 1.7 Megs) Visualization

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 vs Decompression Visualization

  • Compression, Phase I.

  • Decompression, Phase II.

  • Phase IB Project with Kerner Technologies??


Dimension independence
Dimension Independence Visualization

  • Compute

    • Minimum separation distance.

    • Minimum radius of curvature.

    • Take minimum.

  • Tubular neighborhood:

    • Constant radius = limit.

    • Adaptive options?


Computing
Computing Visualization

  • Curvature – calculus problem

  • Minimum Separation Distance:

    • Candidate line segments.

    • Nearly normal at both ends.

    • Newton’s Method to converge.



Symmetry performance
Symmetry & Performance Visualization

  • Important for animation.

  • Not used in initial test cases.

  • Role for PGPU’s (updates!!)

  • Pre-print 09

    • www.cse.uconn.edu/~tpeters


Comparison
Comparison Visualization

  • KG folk 09

  • Critical points (C )

  • Newton, PGPU?

  • Self-intersection

  • XC, RFR, EC, JD 07

  • Singularity

  • Solver [GE+97]

  • Multiple objects

2


Tea authoring tools for dvfx
TEA Authoring Tools for DVFX Visualization

  • Time-checker like spell-checker

    • runs in background; not intrusive!

    • very expensive if missed.

  • Parametric re-design; similar to CAGD PTC

  • Integrate with VFX.


Visualization for simulations
Visualization for Simulations Visualization

  • Animation `on-the-fly’.

  • No human in the loop.

  • Recall update issue (fast!!).


Time and topology
Time and Topology Visualization

Data Volume

Protein folding

Visualize in real time !

--------

---------

Geometry

Versus

Topology

Slow with errors

Fast & correct – but scale?

K. E. Jordan (IBM), L. E. Miller (UConn), E.L.F. Moore (UConn), T. J. Peters (UConn), A. C. Russell (UConn)


Similarity
Similarity? Visualization

  • 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.”


Conclusions
Conclusions Visualization

  • Time can be modeled continuously while frames remain discrete.

  • Difference between

    • Perturb then approximate versus

    • Approximate then perturb.


Overview references

  • Modeling Time and Topology for Animation and Visualization …., [JMMPR], TCS08

  • Computation Topology Workshop, Summer Topology Conference, July 14, ‘05, Special Issue of Applied General Topology, 2007

  • Open Problems in Topology II, 2007 [BP]

  • NSF, Emerging Trends in Computational Topology, 1999, xxx.lanl.gov/abs/cs/9909001

Overview References


Acknowledgements nsf
Acknowledgements: NSF …., [JMMPR], TCS08

  • 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
Acknowledgements: Images …., [JMMPR], TCS08

  • 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


Challenges --- (Audacious?) …., [JMMPR], TCS08

Another: Inner Life of a Cell – XVIVO for Harvard


Tea dimension independent technology
TEA: dimension-independent technology …., [JMMPR], TCS08

  • Provably correct temporal antialiasing

  • Portability of animation to differing displays

  • Efficient compression and decompression


Nbhd_1 about curve. …., [JMMPR], TCS08


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