topologically encoded animation (tea): history & future
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DESCRIPTIONTopologically Encoded Animation (TEA): History & Future. T. J. Peters Kerner Graphics. KnotPlot: www.knotplot.com Unknot or Trefoil? Demo A: Unknown1 & Unknown2. Contemporary Computational Influences. Edelsbrunner: geometry & topology Sethian: Marching methods, topology changes - PowerPoint PPT Presentation
Topologically Encoded Animation (TEA): History & Future T. J. PetersKerner Graphics
Unknot or Trefoil?
Demo A: Unknown1 & Unknown2
Contemporary Computational Influences Edelsbrunner: geometry & topology
Sethian: Marching methods, topology changes
Blackmore: differential sweeps
Carlsson, Zomordian : Algebraic
Route to KG
May discussion with Norm.
NSF SBIR grant for TEA technology.
Digital Visual Effects (DVFX)Little reuse or modification
Plus, we love to blow things up.
Challenges --- (Audacious?)Another: Inner Life of a Cell XVIVO for Harvard
TEA: dimension-independent technologyProvably correct temporal antialiasing
Portability of animation to differing displays
Efficient compression and decompression
My Scientific Emphasis
Mappings and Equivalences
Knots and self-intersections
Piecewise Linear (PL) Approximation
Nbhd_1 about curve.
1.682 Megs1.682 Megs
Moore Dissertation 2006Efficient algorithm for ambient isotopic PL approximation for Bezier curves of degree 3.
PL Approximation for Graphics Animation & Visualization
Curvature (local) &Separation (global)
Error bounds!! =>Nbhd_2 about curve.But recognizing unknot in NP (Hass, L, P, 1998)!!
Proving 1 1 is central.If c is a non-self-intersecting curve and F is a homotopy of c such that each homotopic image of c is non-self-intersecting, then F is an ambient isotopy.Role of HomotopyNo longer have error bounds.
Temporal Antialiasing Comparison
Time to market.
Produce with TEA technology.
Portability for Display
Ipod to Big Screen by parameters.
3D TV. (Prototype shown today.)
- Compression: TEA File (
Compression vs Decompression
Compression, Phase I.
Decompression, Phase II.
Time can be modeled continuously while frames remain discrete.
Perturb then approximate versus
Approximate then perturb.
Quotes & Interpretation
You cant rush art., Woody, Toy Story 2Time is money.
Correct math for the most money.
Modeling Time and Topology for Animation and Visualization, [JMMPR], pre-print
Computation Topology Workshop, Summer Topology Conference, July 14, 05, Special Issue of Applied General Topology, 2007
Open Problems in Topology II, 2007
NSF, Emerging Trends in Computational Topology, 1999, xxx.lanl.gov/abs/cs/9909001
SBIR: TEA, IIP -0810023 .SGER: Computational Topology for Surface Reconstruction, CCR - 0226504.Computational Topology for Surface Approximation, FMM - 0429477.
Investigators responsibility, not NSF.