Skip to main content
View expanded cover

International Congress on Mathematical Software

ICMS 2016: Mathematical Software – ICMS 2016 pp 359–365Cite as

CindyGL: Authoring GPU-Based Interactive Mathematical Content

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9725)

Abstract

CindyJS is a framework for creating interactive (mathematical) content for the web. The plugin CindyGL extends this framework and leverages WebGL for parallelized computations.

CindyGL provides access to the GPU fragment shader for CindyJS. Among other tasks, the plugin CindyGL is used for real-time colorplots.

We introduce the main principles, concepts and application of CindyGL and describe the encountered technical challenges. Special focus is put on a novel visualization scheme that uses feedback loops, which were among the motivating forces of developing CindyGL. They can be used for a wide range of applications. Some of them are numerical simulations, cellular automatons and fractal generation, which are described here.

Keywords

  • Interactive visualization
  • Web technologies
  • WebGL
  • Transpiler
  • CindyScript
  • GLSL
  • OpenGL
  • Shader based colorplots
  • Feedback loops on GPU
  • Fractals
  • Limit sets
  • IFS
  • Kleinian groups

J. Richter-Gebert—Supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics”.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-42432-3_44
  • Chapter length: 7 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   79.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-42432-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   99.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

References

  1. Barnsley, M.F.: Fractals Everywhere. Academic Press, Boston (2014)

    MATH  Google Scholar 

  2. Montag, A.: Interactive image sequences converging to fractals. Bachelors Thesis. http://aaron.montag.info/ba/main.pdf

  3. Mumford, D., Series, C., Wright, D.: Indra’s Pearls: The Vision of Felix Klein. Cambridge University Press, Cambridge (2002)

    CrossRef  MATH  Google Scholar 

  4. Richter-Gebert, J., Kortenkamp, U.: The power of scripting: DGS meets programming. Acta didactica Napocensia 3(2), 67–78 (2010)

    Google Scholar 

  5. Richter-Gebert, J., Kortenkamp, U.: The Cinderella.2 Manual: Working with the Interactive Geometry Software. Springer, Heidelberg (2012)

    CrossRef  MATH  Google Scholar 

  6. Stussak, C.: Echtzeit-Raytracing algebraischer Flächen auf der GPU. Ph.D. thesis, Diploma thesis, Martin Luther University Halle-Wittenberg (2007)

    Google Scholar 

  7. von Gagern, M., Kortenkamp, U., Richter-Gebert, J., Strobel, M.: CindyJS - Mathematical visualization on modern devices. Submitted to ICMS 2016 Berlin (unpublished)

    Google Scholar 

  8. von Gagern, M., Mercat, C.: A library of OpenGL-based mathematical image filters. In: Fukuda, K., Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 174–185. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  9. Wegert, E.: Visual Complex Functions: An Introduction with Phase Portraits. Springer Science & Business Media, Berlin (2012)

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Munich, Munich, Germany

    Aaron Montag & Jürgen Richter-Gebert

Authors
  1. Aaron Montag
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jürgen Richter-Gebert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aaron Montag .

Editor information

Editors and Affiliations

  1. Universität Kaiserslautern , Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Zuse Institute Berlin , Berlin, Germany

    Thorsten Koch

  3. Johannes Kepler University Linz , Hagenberg, Austria

    Peter Paule

  4. University of Notre Dame , Notre Dame, Indiana, USA

    Andrew Sommese

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Montag, A., Richter-Gebert, J. (2016). CindyGL: Authoring GPU-Based Interactive Mathematical Content. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42432-3_44

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42431-6

  • Online ISBN: 978-3-319-42432-3

  • eBook Packages: Computer ScienceComputer Science (R0)