Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration

1. Front Matter

   Pages 1-8

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2. Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees

   • Peer-Timo Bremer, Valerio Pascucci, Bernd Hamann

   Pages 1-18

3. The TOPORRERY: computation and presentation of multi-resolution topology

   • Valerio Pascucci, Kree Cole-McLaughlin, Giorgio Scorzelli

   Pages 19-40

4. Isocontour based Visualization of Time-varying Scalar Fields

   • Ajith Mascarenhas, Jack Snoeyink

   Pages 41-68

5. DeBruijn Counting for Visualization Algorithms

   • David C. Banks, Paul K. Stockmeyer

   Pages 69-88

6. Topological Methods for Visualizing Vortical Flows

   • Xavier Tricoche, Christoph Garth

   Pages 89-107

7. Stability and Computation of Medial Axes - a State-of-the-Art Report

   • Dominique Attali, Jean-Daniel Boissonnat, Herbert Edelsbrunner

   Pages 109-125

8. Local Geodesic Parametrization: an Ant’s Perspective

   • Lior Shapira, Ariel Shamir

   Pages 127-137

9. Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces

   • Ingrid Hotz, Louis Feng, Bernd Hamann, Kenneth Joy

   Pages 139-155

10. Flow Visualization via Partial Differential Equations

    • Tobias Preusser, Martin Rumpf, Alex Telea

    Pages 157-189

11. Iterative Twofold Line Integral Convolution for Texture-Based Vector Field Visualization

    • Daniel Weiskopf

    Pages 191-211

12. Constructing 3D Elliptical Gaussians for Irregular Data

    • Wei Hong, Neophytos Neophytou, Klaus Mueller, Arie Kaufman

    Pages 213-225

13. From Sphere Packing to the Theory of Optimal Lattice Sampling

    • Alireza Entezari, Ramsay Dyer, Torsten Möller

    Pages 227-255

14. Reducing Interpolation Artifacts by Globally Fairing Contours

    • Martin Bertram, Hans Hagen

    Pages 257-269

15. Time- and Space-efficient Error Calculation for Multiresolution Direct Volume Rendering

    • Attila Gyulassy, Lars Linsen, Bernd Hamann

    Pages 271-283

16. Massive Data Visualization: A Survey

    • Kenneth I. Joy

    Pages 285-302

17. Compression and Occlusion Culling for Fast Isosurface Extraction from Massive Datasets

    • Benjamin Gregorski, Joshua Senecal, Mark Duchaineau, Kenneth I. Joy

    Pages 303-323

18. Volume Visualization of Multiple Alignment of Large Genomic DNA

    • Nameeta Shah, Scott E. Dillard, Gunther H. Weber, Bernd Hamann

    Pages 325-342

19. Model-based Visualization - Computing Perceptually Optimal Visualizations

    • Jarke J. van Wijk

    Pages 343-350

The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

• 3D
• Alignment
• algorithms
• computer
• computer graphics
• mathematical modeling
• modeling
• rendering
• sets
• stability
• visualization

• School of Computing Science, Simon Fraser University, Burnaby, Canada

  Torsten Möller, Robert D. Russell

• Department of Computer Science, University of California, Davis, Davis, USA

  Bernd Hamann

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