1. Towards Topology-Rich Visualization Attila Gyulassy SCI Institute, University of Utah

2. Why Use Topology Representations? Scalar functionStructural representation

3. Topology-based Representations of Scalar Functions 2D Scalar function Reeb Graph/Contour Tree Morse-Smale Complex

4. The state of the art Computation Analysis Visualization

5. Combinatorial Construction Harish Doraiswamy and Vijay Natarajan. Efficient output-sensitive construction of Reeb graphs. Proc. Intl. Symp. Algorithms and Computation, LNCS 5369, Springer-Verlag, 2008, 557-568. Carr H, Snoeyink J, Axen U (2003) 'Computing Contour Trees in All Dimensions'. Computational Geometry, 24 (2):75-94. Harish Doraiswamy and Vijay Natarajan. Efficient algorithms for computing Reeb graphs. Computational Geometry: Theory and Applications, 42, 2009, 606-616. Valerio Pascucci, Kree Cole-McLaughlin, Parallel Computation of the Topology of Level Sets, Algorithmica, v.38 n.1, p.249-268, October 2003 Valerio Pascucci, Giorgio Scorzelli, Peer-Timo Bremer, Ajith Mascarenhas, Robust on-line computation of Reeb graphs: simplicity and speed, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007 Contour TreeReeb Graph Julien Tierny, Attila Gyulassy, Eddie Simon, Valerio Pascucci, Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees, IEEE Transactions on Visualization and Computer Graphics, v.15 n.6, p.1177-1184, November 2009

6. Combinatorial Construction Morse-Smale Complex

7. Data Structures

8. Analysis/Visualization Hamish Carr, Jack Snoeyink, Michiel van de Panne, Simplifying Flexible Isosurfaces Using Local Geometric Measures, Proceedings of the conference on Visualization '04, p.497-504, October 10-15, 2004 Gunther H. Weber, Scott E. Dillard, Hamish Carr, Valerio Pascucci, and Bernd Hamann. Topology-Controlled Volume Rendering, IEEE Transactions on Visualization and Computer Graphics. 13 (2), pp. 330-341. 10.1109/TVCG.2007.47

9. Outline From topology to visualization Modified visualization pipeline? Motivation: as more complex features need to be visualized, more sophisticated classification T Rep is a roadmap to a scalar function What we do with roadmap? Analysis vs vis. Overview of CT and MSC Literature Review Current Work with MSC

10. Background Ct and msc are our roadmaps to compute What is a ct What is an msc Algorithms to compute Ct – carr, reeb graphs – streaming, 2dms – bremer, 3dms – gyulassy Description of result Data structure with nodes, arcs, etc. - discrete can be queried analysis/visualization of result

11. Literature review How has roadmap been used in vis? Vis of the reeb graph? Carr and extracting different isosurfaces Scott's paper using segmentation 2d MS complex – bubbles 3d merge trees – flame 3d MS complex – porous media

12. What we're working on Formalizing the space of visualizations that can be achieved using MS complex Querying Each component – what space of visualizations does this afford?  Vertex, arcs, surfaces, volumes Demo Highlight that it's surfaces we're playing with