A Geometrical Representation and Visualization of Möbius Transformation Groups

Kento Nakamura and Kazushi Ahara
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 159–166 Regular Papers


In this paper, we propose a system which enables us to create computer graphics arts originating from Kleinian groups easily and intuitively. Using this system, we can realize various types of Möbius transformations by arranging some circles and lines on the plane. The system uses the efficient rendering algorithm called IIS, introduced in the previous paper by the authors. In the 3D space, making a change circles and lines into spheres and planes, we extend the system to the 3D graphics of Kleinian groups.