5 ms·
Equally, one could just glue together the edges of a butterfly map, eliminating the boundary penalty. I think this is cheating. The problem statement is: find
by DiogenesKynikos 3y ago
Equally, one could just glue together the edges of a butterfly map, eliminating the boundary penalty. I think this is cheating.
The problem statement is: find a mapping from the surface of a sphere to ℝ² that minimizes a particular penalty function. This paper maps each hemisphere to ℝ², and then argues that the normal boundary penalty term can be ignored.
However, if you just look at what the map does to South America and Africa, where there's a massive discontinuity at the equator, it's absurd to argue that the boundary penalty should be ignored. This map is useless for equatorial regions, and the penalty function should reflect that.
- a1o 3y agoIn the online version you can click and it moves the map so it doesn't have to cut things anywhere specifically - but it will always cut somewhere. https://imgur.com/rgeg1Lc https://imgur.com/rgeg1Lc
- DiogenesKynikos 3y agoYou can always make good local maps of a sphere. I think that's just a basic property of Riemannian manifolds: they locally look like flat space. The problem that this paper is trying to solve, however, is the creation of a minimally distorted (according to some penalty function) global map.