1. Towards Topology-Rich Visualization/Analysis
Attila Gyulassy
SCI Institute, University of Utah
Co-laborers: Peer-Timo Bremer, Valerio Pascucci

2. Why topology-based analysis?
Experts think: Topology-based analysis is good!
Structural multi-resolution representation of a function
Combinatorial algorithms for its computation
Extracting features = querying structure

3. Why topology-based analysis?
Josh is ugly!!

4. The Morse-Smale Complex

5. Topology simplification

6. Idealized Topological Analysis Pipeline
Compute
topology
representation
Data
acquisition
Filtering/
simplification
Final analysis

7. Closing the loop What am I looking for?
Hypothesis of feature definition

8. Closing the loop What am I looking for?
Hypothesis of feature definition

9. Basis for Feature Space

10. Intrinsic Features (1)
Critical Points

11. Intrinsic Features (2)
Arcs

12. Intrinsic Features (3)
Basins/Mountains

13. Intrinsic Features (4)
Separatrices

14. Feature Visualization
Critical points / Arcs
Spheres/Tubes where color/radius can be specified
2-Manifolds
Locally rescaled transfer functions
3-Manifolds
Segment space, local transfer functions possible

15. MSC DS & Queries

16. Examples