1. Viz, A Personal Overview Shapes vs Data
T. J. Peters

2. G. Carlsonn “Data has shape and shape has meaning.”

3. Shared: Not just 1. pie charts, 2. bar graphs, 3. glyphs

5. Unknot

6. Bad
Approximation!
Self-intersect?

7. Why Bad? No
Intersections!
Changes
Knot Type
Now has 4
Crossings

8. Good Approximation! Respects Embedding Via Curvature (local)
Separation (global)
But recognizing unknot in NP (Hass, L, P, 1998)!!

9. Perturb within tube
How far?
Can I go outside?
Show pre-print.

20. Overview References
Computation Topology Workshop, Summer Topology Conference, July 14, ‘05, Denison,
planning with Applied General Topology
NSF, Emerging Trends in Computational Topology, 1999, xxx.lanl.gov/abs/cs/
Open Problems in Topology 2 (problems!!)
I-TANGO,Regular Closed Sets (Top Atlas)

21. Credits & Citations Citations ROTATING IMMORTALITY   
Citations
Isotopic equivalence from Bezier curve subdivisionfor application to high performance computing, K. E. Jordan, J. Li, T. J. Peters and J. A. Roulier,CAGD, 31, , 2014
Topological subtleties for molecular movies, J. Li, T. J. Peters, K. Marinelli, E.Kovalev, K. E. Jordan, Top& Appl , in press.

22. Acknowledgements, NSF
I-TANGO: Intersections --- Topology, Accuracy and Numerics for Geometric Objects (in Computer Aided Design), May 1, 2002, #DMS
SGER: Computational Topology for Surface Reconstruction, NSF, October 1, 2002, #CCR
Computational Topology for Surface Approximation, September 15, 2004,
#FMM