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Towards Topology-Rich Visualization

Towards Topology-Rich Visualization. Attila Gyulassy SCI Institute, University of Utah. Why Use Topology Representations?. Scalar function. Structural representation. Topology-based Representations of Scalar Functions. Reeb Graph/Contour Tree. 2D Scalar function. Morse-Smale Complex.

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Towards Topology-Rich Visualization

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

  2. Why Use Topology Representations? Scalar function Structural representation

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

  4. The state of the art Computation Analysis Visualization

  5. Combinatorial Construction Contour Tree Reeb Graph 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 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. 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. 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

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