The challenge of real time symmetry drawing (Jürgen Richter-Gebert, DMV Mathart 2022)

Описание: Symmetric patterns and ornamental structures are a great topic to communicate about the beauty of mathematics. The topic even attracts laypersons. it becomes even more interesting if people can create such patterns themselves by drawing on a tablet computer, or similar device. This talk will report about the mathematical and computer science challenges behind the project iOrnament (iornament.com), a symmetry drawing app for iOS that is used by many people worldwide. Besides the underlying theory of the overall system that covers topics, like symmetry, crystallographic groups, non-euclidean geometries and conformal mappings we will focus on the following topics:
– overall system architecture
– fast stroke drawing
– implementation of effects like glitter and gold pens
– deformation algorithms for hyperbolic tesselations
– the special role of the GPU (graphical processing unit) for fast rendering
– real time requirements
Since each of the topics might easily fill the entire talk, I will give flashlights about several highlights.

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Talk by Jürgen Richter-Gebert (TUM)

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Talk given at: Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 12. - 16. September 2022 (https://ms-math-computer.science/proj...)
Organized by: Milena Damrau and Martin Skrodzki (https://ms-math-computer.science/)
Twitter:   / msmathcomp  

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See also:

Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 14-17 September 2020 (https://ms-math-computer.science/proj...)
Playlist:    • DMV Minisymposium "Mathematics and Arts" 2020  

Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 27 September - 1 October 2021 (https://ms-math-computer.science/proj...)
Playlist:    • Jigsaw puzzles, bell ringing, and Hamilton...