Earlier quoted context omitted.
The Isochrones [0] mentioned in the article include basically all the necessary information. I guess a capable GPU-shader programmer could easily render the distortion in real time. (Hint Hint Hacker News for a cool weekend project) [0] https://www.mapbox.com/bites/00156/#10/51.6840/-0.1480
That looks pretty good! It seems like the transformation could be done reasonably quickly, maybe with a two-component texture (not sure how efficient texture sampling in vertex shaders is), in the vertex shader(s) in that Mapbox GL instance right after the basic projection. I might give this a go. It might get a bit weird around the edges though, gotta make sure to have a margin of additional geometry.
On a modern GPU, it's basically just as efficient as in pixel shaders, with two caveats:
1. If you want mip-mapping, you have to do LOD calculations yourself, which is likely a bit slower. (Not an issue in what you have in mind.)
2. There are questions around the locality of your memory accesses. As long as you lay out your vertices more or less along a space-filling curve (which is a good idea for grids anyway, due to vertex reuse) you should be mostly fine. Obviously the details will vary depending on the exact architecture.