Gott-Goldberg-Vanderbei may have a lower error, but its usefulness is also significantly reduced.
My favourite for world maps is still Winkel Tripel (https://en.wikipedia.org/wiki/Winkel_tripel_projection). Winkel-Tripel was given one of the best ranks by Gott and Goldberg, before they developed the projection in the OP.
Winkel Tripel used to be the standard until Google Maps came along and pushed everyone back to using Mercator for data visualization and political maps.
My favourite for "local area" usage was the old New Zealand Map Grid .. not a polyconic projection, rather a custom complex polynomial optimised to reduce grid error in toto (by multiple metrics) for the North and South Islands of New Zealand.
As a topographic grid projection it was aligned with the "spine of best fit" of the two islands, rather than stright up North|South aligned, and weighted to minimise the N|S and E|W distortion within the land region of interest as distance from the centre zone increased.
There were very few (three ?) in use about the world pre WGS84 .. and like many things went the way of the Dodo, the Krasovsky 1940 ellipsoid, the Bessel 1841, and all those tens and tens of other ellipsoids, datums, and projections of days yore.
> My favourite for "local area" usage was the old New Zealand Map Grid .. not a polyconic projection, rather a custom complex polynomial optimised to reduce grid error in toto (by multiple metrics) for the North and South Islands of New Zealand.
My personal favorite map projection is the Equal Earth projection (https://en.wikipedia.org/wiki/Equal_Earth_projection) but it seems like it is relatively unknown. Though in general I have a soft spot for all equal-area projects, except the abomination Gall-Peters.
To me, Kavrayskiy VII still feels like the most balanced compromise among general-purpose pseudocylindrical projection - more so than Winkel Tripel, and of course miles ahead of Mercator but that isn't even a contest.
Agreed. The only thing i have against Kavrayskiy VII is that i learned about it from the XKCD about map projections, which makes me feel like a complete fraud.
> The ideal projection is simply 3D, as it accounts for all scales
Unless you have 3D display that is not really true, it is still projected to 2D; perspective projection is still projection and it is not obvious that it's in any way "ideal" for maps
I'm assuming someone has made a graph of error versus utility in map projections? Not being able to draw straight lines is a fairly useful thing to do.
If you want accurate, it is also silly to insist on it being a static 2d projection? Having a globe is not exactly difficult.
If we're doing strangely discontinuous maps, I'd like to submit Fuller's Dymaxion Map [1] -- at least that one keeps the continents contiguous, while truly minimizing deformations.
If strange discontinuities are not a problem, what about the Euler spiral?
Okay in the limit it has no area, but if you see it as a limiting process of arbitrarily thin strips then the distortion goes to 0 as the width decreases.
Their justification for no boundary cut error is kinda dodgy.. they say they have none because this projection is really two discs back to back, 'you can just stretch a string over the edge of the disk'.
That's cool but by that argument can't i just fold a Mercator map in half and also have no boundary cut?
I would say worse than "kinda dodgy" - it's completely intellectually dishonest, and their paper should not have got past peer review if it claims this has no boundary cut but the Mercator projection has a big one.
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.
Yes, dodgy. Same argument could be made for the dymaxion map, which can be folded into an icosahedron, then you can easily stretch the string over the polyhedron.
I've seen maps of the heavens using this projection, with the added stipulation of the celestial equator being on a separate bar. So the two circles would represent e.g. +45 degrees north and south of the celestial equator, and the bars would represent from 45 north to 45 south (or thereabout, I'm not sure about the actual degrees).
Is there any reason why the rotation animation doesn't just use CSS rotation? The code looks rather complicated and this old laptop seems to really be unhappy to do what appears to just be two images doing a standard rotation.
Yeah sure, that feature makes sense. But when you start rotating it by pressing the spin/pause button in the interface, don't things become much simpler?
Maybe the answer is "no" but I really can't understand why.
Before I pushed the rotate button, I expected the rotation to be along a different axis, not the one aligned with the projection. i didn't look at the code, does it support that?
It's probably increased accessibility of applied map projection plotting libraries vs. the knowledge of theory and history as formal requirement for making up stuff like this.
See also Gall-Peters. Formalizing and marketing Map Projectsions are two separate skill sets.
Physplaining [2] describes this quite well, if there is an established body of resarch and astrophysic specialist
"rediscover" a specialist area that got reduced exposure with in the era of digital print and publishing.
Readit News
My favourite for world maps is still Winkel Tripel (https://en.wikipedia.org/wiki/Winkel_tripel_projection). Winkel-Tripel was given one of the best ranks by Gott and Goldberg, before they developed the projection in the OP.
Winkel Tripel used to be the standard until Google Maps came along and pushed everyone back to using Mercator for data visualization and political maps.
My favourite for "local area" usage was the old New Zealand Map Grid .. not a polyconic projection, rather a custom complex polynomial optimised to reduce grid error in toto (by multiple metrics) for the North and South Islands of New Zealand.
As a topographic grid projection it was aligned with the "spine of best fit" of the two islands, rather than stright up North|South aligned, and weighted to minimise the N|S and E|W distortion within the land region of interest as distance from the centre zone increased.
https://www.linz.govt.nz/guidance/geodetic-system/coordinate...
There were very few (three ?) in use about the world pre WGS84 .. and like many things went the way of the Dodo, the Krasovsky 1940 ellipsoid, the Bessel 1841, and all those tens and tens of other ellipsoids, datums, and projections of days yore.
Paper link: https://www.linz.govt.nz/resources/research/conformal-mappin...
[0]https://en.wikipedia.org/wiki/Peirce_quincuncial_projection
The ideal projection is simply 3D, as it accounts for all scales, and the geoid if so inclined.
Unless you have 3D display that is not really true, it is still projected to 2D; perspective projection is still projection and it is not obvious that it's in any way "ideal" for maps
If you want accurate, it is also silly to insist on it being a static 2d projection? Having a globe is not exactly difficult.
https://en.wikipedia.org/wiki/General_Perspective_projection
Deleted Comment
1: https://en.wikipedia.org/wiki/Dymaxion_map
The blog series I was reading: https://blog.plover.com/aliens/dd/intro.html
The Cosmic Call map was specifically pages 19-20: https://blog.plover.com/aliens/dd/p19.html
Okay in the limit it has no area, but if you see it as a limiting process of arbitrarily thin strips then the distortion goes to 0 as the width decreases.
That's cool but by that argument can't i just fold a Mercator map in half and also have no boundary cut?
https://i.stack.imgur.com/UhosY.jpg
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.
As far as I can tell its not published anywhere nor received any peer review.
https://xkcd.com/2304/
https://en.wikipedia.org/wiki/Dymaxion_map
You need to both fold it in half and glue the ends together, basically creating a torus (or two-sided cylinder) shape
Here's one that I just found online:
https://fineartamerica.com/featured/vintage-stars-map-celest...
I agree with the other commenter that this would be a good default.
Is it not that?
Maybe the answer is "no" but I really can't understand why.
(but envisioned as being glued to opposite sides of a single disk)
It's probably increased accessibility of applied map projection plotting libraries vs. the knowledge of theory and history as formal requirement for making up stuff like this. See also Gall-Peters. Formalizing and marketing Map Projectsions are two separate skill sets.
https://twitter.com/mxfh/status/1363807641932337153
Physplaining [2] describes this quite well, if there is an established body of resarch and astrophysic specialist "rediscover" a specialist area that got reduced exposure with in the era of digital print and publishing.
[1] https://www.mappingasprocess.net/blog/2021/2/17/a-radically-...
[2] https://www.mappingasprocess.[net/blog/2021/2/21/perfecting-...