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

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

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. -- Talk by Jürgen Richter-Gebert (TUM) -- 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   -- 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...