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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)

T. J. Peters

Kerner Graphics

slide4

Trefoil Knot

3D Rotation

Encode: Rot_0, Rot_1, …, Rot_n

more aggressive moves
More Aggressive Moves
  • Not just rigid body motion
  • Deform shape
  • Preserve crucial characteristics
slide6

KnotPlot: www.knotplot.com

Unknot or Trefoil?

Demo A: Unknown1 & Unknown2

slide7

1.682 Megs

1.682 Megs

slide8

Homeomorphism is not enough

  • F : X  Y,
  • such that F is
  • continuous,
  • 1 – 1
  • onto
  • and has a continuous inverse.
contemporary computational influences
Contemporary Computational Influences
  • Edelsbrunner: geometry & topology
  • Sethian: Marching methods, topology changes
  • Blackmore: differential sweeps
  • Carlsson, Zomordian : Algebraic
slide12

Isotopy & Animation

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

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’
  • Modify & re-use vs destroy.
  • But explosions are hard, for now.
  • Provide path for integration.
slide17

Bad

Approximation!

Self-intersect?

slide18

Good

Approximation!

Respects Embedding:

Curvature (local) &

Separation (global)

Error bounds!! =>

Nbhd_2 about curve.

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

slide19

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 vs Decompression
  • Compression, Phase I.
  • Decompression, Phase II.
  • Phase IB Project with Kerner Technologies??
dimension independence
Dimension Independence
  • Compute
    • Minimum separation distance.
    • Minimum radius of curvature.
    • Take minimum.
  • Tubular neighborhood:
    • Constant radius = limit.
    • Adaptive options?
computing
Computing
  • Curvature – calculus problem
  • Minimum Separation Distance:
    • Candidate line segments.
    • Nearly normal at both ends.
    • Newton’s Method to converge.
symmetry performance
Symmetry & Performance
  • Important for animation.
  • Not used in initial test cases.
  • Role for PGPU’s (updates!!)
  • Pre-print 09
    • www.cse.uconn.edu/~tpeters
comparison
Comparison
  • 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
  • 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
  • Animation `on-the-fly’.
  • No human in the loop.
  • Recall update issue (fast!!).
time and topology
Time and Topology

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?
  • 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
  • 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
  • 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
  • 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
slide37

Challenges --- (Audacious?)

Another: Inner Life of a Cell – XVIVO for Harvard

tea dimension independent technology
TEA: dimension-independent technology
  • Provably correct temporal antialiasing
  • Portability of animation to differing displays
  • Efficient compression and decompression