TU Berlin Fakultät II
Institut für Mathematik

Mathematische Visualisierung



Geometry Group






Vorlesungen Prof. Dr. John Sullivan Tuesday 10-12 MA 313
Thursday 10-12 MA 313
Übung Charles Gunn Wednesday 14-16 MA 313


  • [19.4.7] At the Thursday meeting (19 April) we set the time of the Übung for Wednesday afternoon, 2-4 pm.
  • [19.4.7] If you have problems running Java webstart, please contact me (Charles Gunn).
  • [23.4.7] There were some bad links in Assignment 1, which have now been repaired (thanks to Thorsten Matje!).
  • [23.4.7] The accounts on the math network computers are now ready. Stop by MA 319 to activate your account.
  • [9.5.7] Next week, 16.5.7, I will not be here and Professor Francis from the Univ. of Illinois will lead the Uebung, with a demo and discussion of "CAVE toys" (CAVE is an acronym for a virtual reality installation similar to the PORTAL; Prof. Francis has developed many applications for the CAVE which are both mathematically interesting and fun to use, hence the name "toy").
  • [23.5.7] I've added some web resources related to wallpaper groups under the links section below.


Miscellaneous Downloads

Contents and Tasks

  • The focus of the practical sessions (the ''Übung'') will be designing and implementing an interactive 3D application combining mathematical content with interactive finesse. This mathematical content of the application can be chosen from the mathematical themes of the lectures (or with agreement with the instruction); the design and implementation will be guided by both mathematical rigor and an appealing, easily-understood user interface. By the end of the semester these applications will be tested out in the PORTAL, a virtual reality theater attached to the Visualization Group here.
  • Students enrolling in the practice seminar will be expected to be proficient in Java, as the semester project will be based upon the jreality Java package developed within the Visualization Group at TU.
  • At the beginning of the semester, there will be some weekly assignments designed to develop proficiency in jReality (see above), so that students can begin to work on their projects.
  • The central themes of the lecture include symmetry groups, discrete groups in euclidean and non-euclidean 2- and 3-dimensions, applications of quaternions, and optimal curves and surfaces. Potential themes for projects can be drawn from the wide range of themes included in these topics:
    • Symmetry groups of euclidean and non-euclidean plane and 3-space, including as special cases
    • Euclidean point, band, wallpaper, and crystallographics groups,
    • Visualization of projective geometry (included as the "mother" geometry of euclidean and non-euclidean geometries),
    • Optimal curves and surfaces, especially those with symmetry,
    • Topological visualization (inside vs. outside views of manifolds, complex surfaces, parameter spaces),
    • Visualization of complex numbers, quaternions, and other number systems,
    • Visualization of dynamical systems related to the above themes (such as flows in space or on surfaces)
    • ...

Software tools

Projects will be developed using tools developed here at the TU Visualization Group: to begin with, primarily jReality. Students whose projects involve use of numerics are advised to check out the jtem project also. As a Java programming environment, we encourage using the Eclipse open source project from IBM (see links below). The applications themselves can also be then experienced in the Virtual Reality theatre in this building: Portal.


  • To obtain a passing grade for the Übung, a student is expected to actively take part in it.
  • The assistant is glad to speak German as much as possible, although he generally chooses to write in English.


  • Software
  • Office hours Sullivan Thursday 13:30-14:30 MA 318
    Gunn make appt. MA 319
    Samples of wallpaper symmetries from WS04

    Charles Gunn . 30.05.2007.