BSFF Winner


A Short Movie about Conformal Maps

The Story

How can you make good flat maps of the round earth?' Our story begins with Mercator's world map of 1569, the first angle-preserving (or 'conformal') world map. His idea fell on fruitful soil, from which a new branch of mathematics has developed. The movie shows some of the highlights of this development, yielding a series of elegant visual forms which arise as 'conformal maps' on a variety of surfaces in 2- and 3-D. Featuring non-technical language, a simple aesthetic, compelling animation, and an original score, the movie builds an accessible bridge from everyday experience to a beautiful but little-known mathematical theory that continues to bear technological fruit today in fields such as computer graphics and architecture.


Mathematics is often considered a dry and abstract subject. Mathematicians, however, know better. This movie arose out of an impulse of Prof. Alexander Bobenko to present the results of his research group at the Technical University Berlin in a form suitable for understanding by interested laymen as well as professional mathematicians. That content bears the general name of conformal maps, and had its start in the cartography of the Age of Exploration. The project began in 2012, when Prof. Bobenko recruited visualization expert Charles Gunn to be in charge of the technical implementation of the movie. They were assisted by a team of experts including Prof. Boris Springborn (theory of conformal maps, script), Stefan Sechelmann (conformal software), Luis Vera (music), and Helene Seidl (sound editor). (For a full listing of credits, see below.)

Work on the movie began in 2012 and was completed in late 2014 (video), February 2015 (English audio), and May 2015 (German audio). The group met weekly to discuss the current state of the project and set goals for the following week. Charles Gunn took the impulses which arose at these meetings and attempted to to design, animate, and render the envisioned animations. (His main software tool was the 3D scene graph jReality (another product of the above-named research group) within the popular Java IDE, Eclipse.) This involved close work with Stefan Sechelmann, who provided the underlying software to calculate the various conformal maps which appear in the movie. At the same time the wording of the script was polished to synchronize with the pictures. Here there were many challenges to avoid technical language while remaining precise and accurate. The images and the narration (as audio file) were then loaded into video editing software (Adobe Premiere Pro CS5), and processed further.

In Spring, 2013, the movie project had the good fortune to recruit Luis Vera, a Master's Student in Math at the TU from Spain, with a musical training, to compose music for the movie. After the text and graphics for a particular scene had reached a finished stage, they were passed to Luis, who in surprisingly short time returned it with a sound track, often incorporating the mathematical ideas directly into the music.

Here would would also like to gratefully acknowledge the funding provided by the Deutsche Forschungsgemeinschaft, Matheon, and SFB Transregio 109: Discretization in Geometry and Dynamics.

Storyboard and Script