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