Ideally they'd show a map with a projection based on having the line drawn on it as a straight horizontal or vertical line in the middle of the map. So basically, a Mercator projection with the line being illustrated as its 'equator'.
That would require a custom rendering for each line though.
A single map using that projection calls a lot of attention to the quirks of projecting a sphere onto a plane. A different projection or multiple maps centered on segments of the line would call attention to the straight path you'd take as you graze landmasses.
The maps on the page are not Mercator, but what's the problem with Mercator? It is a perfectly reasonable projection, with some nice properties.
Ideally they'd show a map with a projection based on having the line drawn on it as a straight horizontal or vertical line in the middle of the map. So basically, a Mercator projection with the line being illustrated as its 'equator'.
That would require a custom rendering for each line though.
I like this idea, and they're not in the paper. (The paper shows a globe rotated so the paths are straight, but not a flat mercator projected map).
It should be possible to make one with this tool: http://mrgris.com/projects/merc-extreme/
They have these illustrations in the paper. https://arxiv.org/abs/1804.07389
Given the length of the line over water, that would be a somewhat bizarre map.
See page 9/10 of the source paper.
A single map using that projection calls a lot of attention to the quirks of projecting a sphere onto a plane. A different projection or multiple maps centered on segments of the line would call attention to the straight path you'd take as you graze landmasses.