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TEA, Knots & Molecules in Animation, Simulation & VisualizationPowerPoint Presentation

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

T. J. Peters

Kerner Graphics, Inc., CTO;

University of Connecticut, Professor

More Aggressive Moves Visualization

- Not just rigid body motion
- Deform shape
- Preserve crucial characteristics

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.

Two Frames with Different Topology Visualization

Instantaneous Self-intersection Visualization

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 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’ Visualization

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

EagleEye Visualization

Unknot Visualization

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 Visualization

- Compression, Phase I.
- Decompression, Phase II.
- Phase IB Project with Kerner Technologies??

Dimension Independence Visualization

- Compute
- Minimum separation distance.
- Minimum radius of curvature.
- Take minimum.

- Tubular neighborhood:
- Constant radius = limit.
- Adaptive options?

Computing Visualization

- Curvature – calculus problem
- Minimum Separation Distance:
- Candidate line segments.
- Nearly normal at both ends.
- Newton’s Method to converge.

Infinitely many good seeds Visualization

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 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 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

- Animation `on-the-fly’.
- No human in the loop.
- Recall update issue (fast!!).

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? 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 Visualization

- Time can be modeled continuously while frames remain discrete.
- Difference between
- Perturb then approximate versus
- Approximate then perturb.

- 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

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 …., [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 …., [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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