Online Apps


Deforming a Rectangle to a Torus

App: rectangle-to-torus
Author: Ricardo Waibel

Pascal’s theorem and Poncelets Porism

App: Pascal’s theorem, Poncelets Porism
Author: Lukas Schmidt, Miriam Compton, Adrian Becker
Blog post: link


App: link
Author: Noah Koopmann, Ingmar Lowack
Blog post: link

Root Systems and their Weyl Groups

App: link
Author: Amelie Strupp
Description: Explore root systems and their transformations in 2 and 3 dimensions, and gain insight into root systems in higher dimensions through projections.


Disc and Annulus Deformations

App: link
Author: Ricardo Waibel
Instructions: Deform the disc and annulus; try to retract it to a point.
Blog post: link

Ellis Wormhole

App: link
Author: Ricardo Waibel
Instructions: Simply view and play with the Ellis wormhole and some simple geodesics.
Blog post: link

Random Walks in the Poincaré Disk

App: link
Author: Paul Martin
Instructions: Refresh the page to start a new random walk.

Ray Marching in Flat Surfaces

Note: The ray marching apps run better on more powerful graphics cards. For higher frame rates, choose a small browser window or reduce the resolution (for example, zoom by pressing CTRL while scrolling up).

Authors: Fabian Lander, Mara-Eliana Popescu
Instructions: Drag with the mouse to rotate the scene, and use the mouse wheel to zoom in and out. The keys W/A/S/D translate the camera. Note that the rotation is applied to the rooms themselves and not the camera.

Hyperbolic Asteroids

App: link 1 (1vs1), link 2 (single player)
Authors: Ines Bultmann, Filippa Piazolo
Instructions: Player 1: LEFT/RIGHT/FORWARD and SPACE, Player 2: A/D/W and SHIFT
Blog post: link

Möbius Paint

App: link
Authors: Mouna Dorothea Deubler, Yunus Sahin, Juliane Stehle

Grandma’s Recipe

App: link
Authors: Alassane Diagne, Aysegül Peközsoy


Hyperbolic Ping-Pong

App: link
Author: Ricardo Waibel, based on work by Isabel Giray, Karina Kniel and Phil Neitzel
Description: This game is a hyperbolic version of the classic Pong game, taking place in the Poincaré disc. The ball and paddles move on geodesics, a generalized version of straight lines from Euclidean geometry.
The original code was developed by the above-mentioned seminar students, check out this blog post for more information. The python code was transcribed to javascript using transcription software. For more information, check out the blog post or this GitHub repository with the rewritten python and javascript code.



App: link
Author: Lukas D. Sauer
Description: Interactively experience transformations in the real projective plane using the flagtrafo web application. Transform tuples of flags using the eruption flow, the bulge flow, and the shear flow. Learn how the inscribed polygons are affected by the transformations.