论文标题
通过应力最小化球形的平坦地图
Flat Map of a Sphere via Stress Minimization
论文作者
论文摘要
在本文中，我们描述了对Gott-Goldberg-Vanderbei（GGV）地图投影的数学有趣但相对较小的改进。这个新的投影可以描述为通过制作球形橡胶球的代表，然后将球绕在赤道周围，直到北半球和南半球将球呈圆形，从而将球伸向磁盘。有趣的是，这种新投影与GGV投影非常相似，但并不完全相同。而且，解决这个扁平问题所需的数学是使用变化的计算来解决无限尺寸优化问题的一个很好的例子。
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.
