Good mathematicians visualize everything, including algebra

Working group on geometry


Geometry Group



Past semesters


Images, Videos, and Games

Virtual Math Labs




Mathematical visualization I (winter 2009/10)


Jens-Peter Rohrlack: "Cardan Suspension"

run as java web start

This project provides the ability to visualize 'Euler' angles (order is ZX'Z '') via a 'Cardan' suspension utilizing the jreality and jrealityBullet libraries. Furthermore a free movement mode is available, so one can lean back and just watch.

While it moves freely you can stop & drag (left mouse button) the rings and cone or apply an impulse to them (double click right mouse button). Additionally you can turn on / off gravity or the colorful disco mode by pressing the according buttons.
Move around on the plane by using the arrow keys or WASD. Jump or fly upwards by pressing the space bar a few times. To lock and unlock your current height press 'G'. To look around move your mouse while holding the right mouse button. If you do not see the utility window on the left side, hold and and press .

additional Information...

Eike Verdenhalven: "Vector fields"

start as java web start

In addition to the main application, there is also an application into which you can load your own vector fields packed in .jar files. There is an example file here that also contains the source code for the examples.

additional Information...

Benjamin Kutschan: "Discrete elastic surfaces - an experiment"

Version 1: start as java web start

additional Information...

Version 2: start as java web start

Alexander Bauer: "Darboux Transformation"

start as java web start

The SVN repository of the event can be accessed with an institute account:

svn + ssh: //

(Perhaps you have to replace the computer name "rockafellar" with another switched-on institute computer).

The contents of the SVN repository as a jar archive MathVisWS2009.jar (sources and compiled classes) together with the libraries used are available at: ws / jars /.

Mini projects


  • April 20: Exercise certificates are available for everyone who has submitted mini-projects to Ms. Gillmeister (Mon, Tue, Thu, Fri 9:30 a.m. - 11:30 a.m., MA 320).
  • April 13th: The project presentations will take place on Friday, April 23rd, 2010 from 1 p.m. in MA 313.
  • 21.1: The first web starts from the exercises are online.
  • 16.12: Please choose a project. From now on, the exercises will focus on the projects.
  • 3.12: Tomorrow we're going to look at a few things in the portal (MA 205a).
  • 23.11 .: Your assistant (Paul) will not be present for his office hours or for practice this week due to illness.
  • November 19: Projects, material and interesting links.
  • November 12th: 4th exercise.
  • November 5th: 3rd exercise.
  • 21.10 .: 2nd exercise.
  • 15.10 .: 1st exercise.
  • 14.10 .: One-time exchange of VL and O: On Thursday,15.10., the lecture takes place in MA 542 from 10-12. On Friday,16.10., the exercise takes place from 10-12 in MA 313.

Material and interesting links

  • Ulrich Pinkall, Boris Springborn, Steffen Weissmann: A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow
  • Matthias Müller, Jos Stam, Doug James, Nils Thürey: SIGGRAPH 2008 Realtime Physics Course Notes
  • Dolphin play bubble rings.
  • Miklos Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, Eitan Grinspun: "Discrete Elastic Rods".
    [pdf], [video].


An important trend in computer graphics in both film production and game development is the real-time simulation of physical processes.

TU smoke (Click on a picture to start the associated film.)

The requirements for real-time simulations differ significantly from the requirements for "conventional" numerical simulations:

  • 100 time steps per second.
  • Qualitatively correct behavior over long periods of time is more important than the accuracy of the details.
  • Possibility of increasing the accuracy in detail with constant qualitative long-term behavior but longer computing time.

The lecture uses examples to show that it is possible to develop mathematical algorithms that separate the simulation of the qualitative long-term behavior from the detailed calculations and thus meet the requirements mentioned. These algorithms, their roots in discrete differential geometry and other algorithms for real-time simulation of physical processes are described in the lecture.

Exercises and sham criteria:

In the exercises, physical real-time simulations are implemented in Java in mini-projects or existing ones are changed. We will work with the Java development environment Eclipse and use the Java libraries jBullet for physical simulations, jReality for 3D representation and some projects from jTEM.

The training certificate is given to those who successfully implement the mini-projects on the scheduled dates.