towards topology-rich visualization attila gyulassy sci institute, university of utah
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Towards Topology-Rich Visualization
Attila GyulassySCI Institute, University of Utah
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Why Use Topology Representations?
Scalar function Structural representation
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Topology-based Representations of Scalar
Functions
2D Scalar function
Reeb Graph/Contour Tree
Morse-Smale Complex
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The state of the art
Computation
Analysis
Visualization
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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 Tree Reeb 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
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Combinatorial Construction
Morse-Smale Complex
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Data Structures
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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
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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
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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
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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
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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