Talk:2951: Bad Map Projection: Exterior Kansas

Seems weird that it's just the contiguous US, with "hints" about what lies within. I hope Randall will release another version with the rest of the world included.162.158.158.61 03:20, 27 June 2024 (UTC)

Would the center be both poles and Kansas's antipode? --172.68.27.150 03:58, 27 June 2024 (UTC)

Including Hawaii would have been the cherry on the cake. 198.41.242.174 05:42, 27 June 2024 (UTC)

As the center of the map corresponds to Kansas' antipode (Kerguelen in the Indian Ocean https://www.geodatos.net/en/antipodes/united-states/kansas-city), Hawaii isn't really "near the center", but rather to the right of the center (in the direction of the "Pacific Ocean" tag). --162.158.86.100 05:58, 27 June 2024 (UTC)

Admittedly, I guessed where they would be. 172.71.174.139 06:09, 27 June 2024 (UTC)

I don't think the middle part is meant to be seen as 'water', just 'out of scope'. Jaap-Jan (talk) 07:44, 27 June 2024 (UTC)

Yeah, this is similar to a map like https://suncatcherstudio.com/uploads/patterns/us-maps/pdf-png/usa-map-states-names-color-010101.png In that map, Canada and Mexico aren't "rendered as water", they're not rendered at all, and neither are the oceans. I'm going to edit that. 162.158.78.73 13:34, 27 June 2024 (UTC)

How would the rest of the world look?

Currently the center is all water. If I understand correctly the rest of the world could be added, but how would it look? For example, would Europe and Asia cover a good part of the water or would they be tiny specs in the middle (almost making this a world map already)

My impression (without measuring/replicating) is that this is mathematically (or whatever) a gnomonic projection (which can only show half the world, anyway, even on a sheet stretching up to infinity) radially inverted. As such quite a lot of features that aren't shown ('beyond/within' the 'coastline'/borders) couldn't be, anyway, as more than half the world away. Map-centre would be the compressed singularity of the Great Circle exactly 90° off the 'centre of Kansas' that itself now exists at infinite-radius-every-angle far off the page.

Though it could just be stereographic with any negatively positioned projection origin. Instead of -1, for gnomonic, with a -2 radii origin you would get the whole surface (at infinity!) in ways that whatever you do to radially invert (probably the direct reciprocal) and otherwise scale (clearly choosing the additional 'zoom level' factor that neatly brings the Kansas border more or less into frame) to compress all offshore/over-border territories into the 'oceanic' centre. Or it could just be a useful rescale of a -2r projection of the Kansas-antipode, such that all borders of Kansas are pulled into frame.

(Regarding Hawaii, if quick googling is right about Hawaii being 3,600km from Kansas(-centre?), then that puts it at various preskewed factors towards the 'hemispherical horizon' of ~10,000km or the antipodal point at ~20,000km, before then being further squashed by the particular coordinate conversion system in use. If it's a near-side orthographic projection and, say approaching +1 radii up from the surface-tangent, then it could perhaps be 'over the horizon' in the direct projection and thus 'beyond the singularity' of the inverted-radius version.)

I'd have to mess with some map data, to be sure the existing features fit either idea of projection (or find the actual one (ab)used), but this'd probably be what I'd do, straight off the bat. And then I could apply it to extraterratorial features, also. I've got some of the necessary data and mungable code handily sitting on a machine that I am unhandily not going to next use until at least the weekend, and reimplimenting it on this tablet would mean starting from first principles again/testing/etc... ;) 172.70.163.120 09:23, 27 June 2024 (UTC)