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

  • Torsten Möller
  • Bernd Hamann
  • Robert D. Russell

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Peer-Timo Bremer, Valerio Pascucci, Bernd Hamann
    Pages 1-18
  3. Valerio Pascucci, Kree Cole-McLaughlin, Giorgio Scorzelli
    Pages 19-40
  4. Ajith Mascarenhas, Jack Snoeyink
    Pages 41-68
  5. David C. Banks, Paul K. Stockmeyer
    Pages 69-88
  6. Xavier Tricoche, Christoph Garth
    Pages 89-107
  7. Dominique Attali, Jean-Daniel Boissonnat, Herbert Edelsbrunner
    Pages 109-125
  8. Lior Shapira, Ariel Shamir
    Pages 127-137
  9. Tobias Preusser, Martin Rumpf, Alex Telea
    Pages 157-189
  10. Wei Hong, Neophytos Neophytou, Klaus Mueller, Arie Kaufman
    Pages 213-225
  11. Alireza Entezari, Ramsay Dyer, Torsten Möller
    Pages 227-255
  12. Martin Bertram, Hans Hagen
    Pages 257-269
  13. Attila Gyulassy, Lars Linsen, Bernd Hamann
    Pages 271-283
  14. Kenneth I. Joy
    Pages 285-302
  15. Benjamin Gregorski, Joshua Senecal, Mark Duchaineau, Kenneth I. Joy
    Pages 303-323
  16. Nameeta Shah, Scott E. Dillard, Gunther H. Weber, Bernd Hamann
    Pages 325-342

About this book


Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized.

For these reasons a workshop was organized at the Banff International Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the mathematical areas relevant to the recent advances in order to discuss the research challenges facing this field in the next several years. The workshop was organized into five different thrusts:

- Topology and Discrete Methods

- Signal and Geometry Processing

- Partial Differential Equations

- Data Approximation Techniques

- Massive Data Applications

This book presents a summary of the research ideas presented at this workshop.


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

Editors and affiliations

  • Torsten Möller
    • 1
  • Bernd Hamann
    • 2
  • Robert D. Russell
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceUniversity of California, DavisDavisUSA

Bibliographic information