2023
The Clebsch Surface with 27 Distinguished Lines
App: clebsch-surf
Author: Ricardo Waibel
Mentor: Diaaeldin Taha
Deforming a Rectangle to a Torus
App: rectangle-to-torus
Author: Ricardo Waibel
Mentor: Diaaeldin Taha
Pascal’s theorem and Poncelets Porism
App: Pascal’s theorem, Poncelets Porism
Author: Lukas Schmidt, Miriam Compton, Adrian Becker
Mentor: Diaaeldin Taha
Blog post: link
Quasicrystals
App: link
Author: Noah Koopmann, Ingmar Lowack
Mentor: Diaaeldin Taha
Blog post: link
Root Systems and their Weyl Groups
App: link
Author: Amelie Strupp
Mentor: Diaaeldin Taha
Description: Explore root systems and their transformations in 2 and 3 dimensions, and gain insight into root systems in higher dimensions through projections.
2022
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
Mentor: Diaaeldin Taha
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.
Apps:
- Translation Surfaces: double-pentagon, L-shape
- Mirror rooms: double-pentagon, L-shape
- Polyhedra: cube
Hyperbolic Asteroids
App: link 1 (1vs1), link 2 (single player)
Authors: Ines Bultmann, Filippa Piazolo
Mentor: Diaaeldin Taha
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
Mentor: Diaaeldin Taha
Grandma’s Recipe
App: link
Authors: Alassane Diagne, Aysegül Peközsoy
Mentor: Diaaeldin Taha
2021
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.
2019
flagtrafo
App: link
Author: Lukas D. Sauer
Mentor: Anna Wienhard
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.