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A Library of OpenGL-Based Mathematical Image Filters

  • Martin von Gagern
  • Christian Mercat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

Abstract

There are a lot of transformations that can turn one raster image into a derived one in a mathematically interesting way. This article describes a collection of such filters, implemented in OpenGL in order to use the high degree of parallelism modern GPUs provide, thereby providing performance required to process e.g. live camera images in real-time. The filters contained in this library include wallpaper groups, conformal maps described by meromorphic functions, as well as hyperbolic symmetry groups. Using examples of increasing complexity, several key implementation techniques are explained, including texture wrap configurations, user-configurable control points, and custom fragment shader programs. This work might exhibit aesthetic aspects of mathematics to the masses and provide useful building blocks for scientists as well as artists.

Keywords

Transformation tiling wallpaper group conformal map meromorphic function hyperbolic geometry GPU parallelism webcam 

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References

  1. 1.
    Mercat, C.: Conformal webcam, Images des Math., CNRS (March 2009), http://images.math.cnrs.fr/Applications-conformes.html
  2. 2.
    Conway, J.H., Burgiel, H., Goodman-Strauss, C.: The Symmetries of Things. A.K. Peters, Wellesley (2008)zbMATHGoogle Scholar
  3. 3.
    von Gagern, M., Richter-Gebert, J.: Hyperbolization of Euclidean Ornaments. Electronic Journal of Combinatorics 16(2), R12 (2009)Google Scholar
  4. 4.
    Springborn, B., Schröder, P., Pinkall, U.: Conformal equivalence of triangle meshes. In: ACM SIGGRAPH (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Martin von Gagern
    • 1
  • Christian Mercat
    • 2
  1. 1.Zentrum Mathematik (M10)TU MünchenGarchingGermany
  2. 2.I3M/LIRMM, cc 51Université Montpellier 2France

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