t. j. peters kerner graphics, inc., cto; university of connecticut, professor tea, knots &...
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T. J. PetersKerner Graphics, Inc., CTO;
University of Connecticut, Professor
TEA, Knots & Molecules in Animation, Simulation & Visualization
T. J. PetersKerner Graphics
Topologically Encoded Animation (TEA)
Trefoil Knot
3D Rotation
Encode: Rot_0, Rot_1, …, Rot_n
More Aggressive Moves
• Not just rigid body motion
• Deform shape
• Preserve crucial characteristics
1.682 Megs
1.682 Megs
Homeomorphism is not enough
F : X Y,
such that F is
1. continuous,2. 1 – 13. onto4. and has a continuous inverse.
Two Frames with Different Topology
Instantaneous Self-intersection
Contemporary Computational Influences
• Edelsbrunner: geometry & topology
• Sethian: Marching methods, topology changes
• Blackmore: differential sweeps
• Carlsson, Zomordian : Algebraic
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.
Little reuse or modification
“Plus, we love to blow things up.”
Kerner Graphics: Digital Visual Effects (DVFX)
KERNER OPTICALKERNER OPTICAL
DVFX vs `Blowing things up’
• Modify & re-use vs destroy.
• But explosions are hard, for now.
• Provide path for integration.
EagleEye
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)!!
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.
• Phase IB Project with Kerner Technologies??
Dimension Independence
• Compute – Minimum separation distance.
– Minimum radius of curvature.
– Take minimum.
• Tubular neighborhood:– Constant radius = limit.
– Adaptive options?
Computing
• Curvature – calculus problem
• Minimum Separation Distance:– Candidate line segments.
– Nearly normal at both ends.
– Newton’s Method to converge.
Infinitely many good seeds
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
• 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.
Visualization for Simulations
• Animation `on-the-fly’.
• No human in the loop.
• Recall update issue (fast!!).
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)
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
• 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
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
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
Nbhd_1 about curve.