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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T. J. Peters
Kerner Graphics, Inc., CTO;
University of Connecticut, Professor
T. J. Peters
Trefoil Knot Visualization
Encode: Rot_0, Rot_1, …, Rot_n
Unknot or Trefoil?
Demo A: Unknown1 & Unknown2
1.682 Megs Visualization
Homeomorphism is Visualizationnot enough
Two Frames with Different Topology Visualization
Instantaneous Self-intersection Visualization
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 VisualizationKerner Graphics: Digital Visual Effects (DVFX)
“Plus, we love to blow things up.”
Little reuse or modification
Curvature (local) &
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
Infinitely many good seeds Visualization
Visualize in real time !
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)
Challenges --- (Audacious?) …., [JMMPR], TCS08
Another: Inner Life of a Cell – XVIVO for Harvard
Nbhd_1 about curve. …., [JMMPR], TCS08