explain xkcd - User contributions [en]

Talk:2951: Bad Map Projection: Exterior Kansas

2024-06-27T13:48:40Z

172.71.99.32: /* How would the rest of the world look? */

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.[[Special:Contributions/162.158.158.61|162.158.158.61]] 03:20, 27 June 2024 (UTC)

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

Including Hawaii would have been the cherry on the cake. [[Special:Contributions/198.41.242.174|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). --[[Special:Contributions/162.158.86.100|162.158.86.100]] 05:58, 27 June 2024 (UTC)

:: Admittedly, I guessed where they would be. [[Special:Contributions/172.71.174.139|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'. [[User:Jaap-Jan|Jaap-Jan]] ([[User talk: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. [[Special:Contributions/162.158.78.73|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... ;) [[Special:Contributions/172.70.163.120|172.70.163.120]] 09:23, 27 June 2024 (UTC)

: Check out the Wikipedia article "Azimuthal equidistant projection" and scroll to "Sample azimuthal equidistant projection maps". There is an inverse example, that puts California at the center of a world map. Now imagine everything else in the "great sea" of Randall's map, using a similar projection. [[Special:Contributions/172.71.99.32|172.71.99.32]] 13:48, 27 June 2024 (UTC)

==Adding an image?==
Is it possible to add an image to the description? I'm looking at the Wikipedia article "Azimuthal equidistant projection" and the "external Antarctica" map is relevant. https://en.wikipedia.org/wiki/File:Azimuthal_equidistant_projection_SW.jpg Thanks! [[Special:Contributions/172.71.99.32|172.71.99.32]] 13:43, 27 June 2024 (UTC)

Talk:2951: Bad Map Projection: Exterior Kansas

2024-06-27T13:43:17Z

172.71.99.32: Section: Adding an image?

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.[[Special:Contributions/162.158.158.61|162.158.158.61]] 03:20, 27 June 2024 (UTC)

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

Including Hawaii would have been the cherry on the cake. [[Special:Contributions/198.41.242.174|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). --[[Special:Contributions/162.158.86.100|162.158.86.100]] 05:58, 27 June 2024 (UTC)

:: Admittedly, I guessed where they would be. [[Special:Contributions/172.71.174.139|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'. [[User:Jaap-Jan|Jaap-Jan]] ([[User talk: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. [[Special:Contributions/162.158.78.73|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... ;) [[Special:Contributions/172.70.163.120|172.70.163.120]] 09:23, 27 June 2024 (UTC)

==Adding an image?==
Is it possible to add an image to the description? I'm looking at the Wikipedia article "Azimuthal equidistant projection" and the "external Antarctica" map is relevant. https://en.wikipedia.org/wiki/File:Azimuthal_equidistant_projection_SW.jpg Thanks! [[Special:Contributions/172.71.99.32|172.71.99.32]] 13:43, 27 June 2024 (UTC)

2951: Bad Map Projection: Exterior Kansas

2024-06-27T13:39:20Z

172.71.99.32: /* Explanation */ Added reference to polar projection and external Antarctica

{{comic
| number = 2951
| date = June 26, 2024
| title = Bad Map Projection: Exterior Kansas
| image = bad_map_projection_exterior_kansas_2x.png
| imagesize = 740x706px
| noexpand = true
| titletext = Although Kansas is widely thought to contain the geographic center of the contiguous 48 states, topologists now believe that it's actually their outer edge.
}}

==Explanation==
{{incomplete|Created by a TOPOLOGICAL CORNFIELD - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This is the seventh comic in the series of [[:Category:Bad Map Projections|Bad Map Projections]] displaying Bad Map Projection #45: Exterior Kansas.

This comic portrays an unusual projection of a map of the contiguous United States. Maps of individual countries are common, especially in academic settings. It is typical for such maps, which only display a limited area of the globe, to use a projection that does not severely distort the shape of the country or its internal borders, but a country that is large enough (as with the United States) will always noticably suffer from certain distortions of at least one element chosen from distances, areas or angles. This usually occurs at its extremities (though some projections can be made more faithful to its extremities at the expense of distorting its interior).

Here, however, Randall has opted for a much different projection. Rather than placing the geographical center of the country in the middle and the borders on the outside, this map has gone the opposite direction, with the border of the US toward the center, and the geographical center of the US (Kansas) and surrounding states distorted to surround the entire map. This, understandably, results in the shape of both the national and state borders being largely unrecognizable as it effectively puts ''every'' bit of the chosen map features out towards the distorted extremities. Much of the internal area of Kansas itself (should one wish to display further internal features) may be located far beyond the comic's edges, perhaps even to infinitely far away on the projected plane.

If Alaska and Hawaii were present in this map and represented in geographically accurate locations (as opposed to inset, as is common in many maps of the United States), Alaska would be near the top of the empty space "inside" the border, while Hawaii would be near the center, if even visible. Both would be rather small, with Hawaii particularly compressed (to an extent dictated to by the exact projection method used).

This map is of the same polar-style projection that one sees on the flag of the United Nations. Some maps of that style depict an "external Antarctica".

==Transcript==
{{incomplete transcript|Missing map description. Do NOT delete this tag too soon.}}

:[Caption below the panel:]
:Bad Map Projection #45:
:Exterior Kansas

{{comic discussion}}

[[Category:Bad Map Projections]]
[[Category:US maps]]