Flat Map of a Sphere via Stress Minimization

Abstract

In this paper we describe a mathematically interesting but relatively minor improvement to the Gott-Goldberg-Vanderbei (GGV) map projection. This new projection can be described as what one would get by making a spherical rubber ball representation of the Earth and then stretching the ball circularly around the equator until the Northern and Southern hemispheres flatten to a disk. It is interesting that this new projection is very similar to but not exactly the same as the GGV projection. And, the mathematics required to solve this flattening problem is a very nice example of using the calculus of variations to solve an infinite dimensional optimization problem.