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Z02
Web based visualization of mathematics


Many projects in the SFB/TRR 109 use computational experiments. This project provides a visualization platform that can be commonly used. For instance CindyJS is used as a viewer for 3D models and other interactive models in the DGD Gallery

Mission-

We have implemented Cinderella as an authoring system and CindyJS as a web viewer for visualization and real-time interactive simulation. We are now developing a software platform and its mathematical foundationto  allow a versatile and fast prototyping of mathematical experiments and visualizations which can be used for research and demonstration.

Scientific Details+

Visualization and real-time interactive simulation play an important role both in mathematical research and in mathematical communication. We aim at the development of a software platform and its mathematical foundation that allows a versatile and fast prototyping of mathematical experiments and visualizations which can be used for research and demonstration. The project attacks both the mathematical and the software related aspects of such a platform. In particular, the system should be usable as a flexible authoring system for providing mathematical content that can run in contemporary web browsers, taking advantage of modern hardware and software technologies.

We specifically emphasise (on the mathematical side) on the creation of a system that provides a high mathematical consistency and expressiveness. Another focus (on the computer science side) is to provide an intuitive authoring system that can in particular be used for the creation of web based demonstrations and microlaboratories that run within a browser and on mobile devices. The system among other aims should provide an easy access to an interactive geometry viewing environment (2D and 3D), to a versatile scripting language and to a reliable physics simulation engine.

To understand the relevance and current challenges of the creation of such a visualization system in the current decade one has to take into account recent developments in the landscape of browser based interaction possibilites. The recent past showed a dramatic change in the possible environments for such a general math visualization system. Since 2012 the language Java showed a massive decline in its support within browsers. Currently only few (but very powerful) possibilities exist that make the authoring of interactive web based mathematical content possible including CindyJS.  The focus within this project is to establish the CindyJS project aims to be one of the first medium to large scale mathematical visualization projects based on an HTML5 frame- work.

 

Publications+

Papers
  • Michael Strobel.
    Non-standard Analysis in Dynamic Geometry.
    Journal of Symbolic Computation: Special Issue on Dynamic Geometry and Automated Reasoning, 2019.
    arXiv:1801.10507, doi:10.1016/j.jsc.2018.12.006.
  • Aaron Montag and Jürgen Richter-Gebert.
    Bringing Together Dynamic Geometry Software and the Graphics Processing Unit.
    preprint, August 2018.
    arXiv:1808.04579.
  • Michael Strobel.
    First Steps in Non-standard Projective Geometry.
    Preprint, March 2018.
    arXiv:1804.01850.
  • Aaron Montag and Jürgen Richter-Gebert.
    CindyGL: Authoring GPU-Based Interactive Mathematical Content.
    ICMS 2016: Mathematical Software – ICMS 2016 pp 359-365, July 2016.
    doi:10.1007/978-3-319-42432-3_44.

PhD thesis

Team+

Prof. Dr. Dr. Jürgen Richter-Gebert   +

University: TU München, Zentrum Mathematik, M10, 02.06.054
Address: Boltzmannstr. 3, 85748 Garching bei München, GERMANY
Tel: +49 89 28918354
E-Mail: richter[at]ma.tum.de
Website: http://www-m10.ma.tum.de/bin/view/Lehrstuhl/RichterGebert

Aaron Montag   +

University: TU München
E-Mail: aaron.montag[at]tum.de

Michael Strobel   +

University: TU München
E-Mail: strobel[at]ma.tum.de