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.
That's the paper alright, I've got a physical copy in a filing cabinet somewhere :-)
IIRC, for anyone else looking for a curio, there was one state|county|region in the USofA that used a custom conformal projection for a local grid system pre 1980s .. somewhere outside the regular PLA mapping grids.
I don't think this is the one you're thinking of, but in NYC the subway maps (which are not particularly geographically accurate) are drawn with Manhattan vertical, rather than on its 20-something degree tilt.
subway maps (which are not particularly geographically accurate)
Subway maps and bus maps in cities are very typically not geographically accurate map projections .. the focus tends to be on a compact stylisation that represents connections for travel plans.
Historically Roman Road maps were on a scroll and very linear, today the UK underground tube maps are displayed in a manner that aids commuters in making connections.
I'm not all that familiar with NYC subway maps (only there for a short time in the 80s .. and who can recall their youth?) but I remember them being more "graphic" rather than "geographic".
I'm thinking more of a local land projection map that would have been used for local surveying in the days prior to global GPS .. but thanks for the thought all the same!
The NYC MTA map is pretty geographic by metro map standards. There are some obvious distortions, like Manhattan being wider than it actually is and it's not actually vertical as noted before. It also includes a lot of surface street and neighbourhood references. Most metro maps just focus on station names.
Compared with something like the London Tube map or Paris Metro map it's extremely geographic.
My comments above were referring to the axis alignment used in a projection transformation that takes 3D points wrapped about a sphere and maps them to a flat 2D plane.
Most of the common global world projections use conic projections that have a major axis aligned NS and conic slices that are orthogonal to the cone major axis mapped to latitude lines that are East-West.
There are many other types of projections, the older NZ map grid is an unusual one.
Once a projection is used to make a flat map, that map can be rotated about in any direction .. but that's another thing altogether.
You may, or not, enjoy looking through a free USGS projection reference of note:
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
Sure, but it can be projected in a way that minimizes distortion of the current region you're looking at. 3D effectively allows you to choose the best projection from an infinite family of projections, while 2D restricts you to a single projection regardless of your location of interest.
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.
Comments
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.
The triple was|is a damn fine world projection.
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...
That's the paper alright, I've got a physical copy in a filing cabinet somewhere :-)
IIRC, for anyone else looking for a curio, there was one state|county|region in the USofA that used a custom conformal projection for a local grid system pre 1980s .. somewhere outside the regular PLA mapping grids.
I don't think this is the one you're thinking of, but in NYC the subway maps (which are not particularly geographically accurate) are drawn with Manhattan vertical, rather than on its 20-something degree tilt.
Subway maps and bus maps in cities are very typically not geographically accurate map projections .. the focus tends to be on a compact stylisation that represents connections for travel plans.
Historically Roman Road maps were on a scroll and very linear, today the UK underground tube maps are displayed in a manner that aids commuters in making connections.
I'm not all that familiar with NYC subway maps (only there for a short time in the 80s .. and who can recall their youth?) but I remember them being more "graphic" rather than "geographic".
I'm thinking more of a local land projection map that would have been used for local surveying in the days prior to global GPS .. but thanks for the thought all the same!
The NYC MTA map is pretty geographic by metro map standards. There are some obvious distortions, like Manhattan being wider than it actually is and it's not actually vertical as noted before. It also includes a lot of surface street and neighbourhood references. Most metro maps just focus on station names.
Compared with something like the London Tube map or Paris Metro map it's extremely geographic.
https://new.mta.info/map/5256
Tilt relative to what? Rotating a map doesn't make it inaccurate.
My comments above were referring to the axis alignment used in a projection transformation that takes 3D points wrapped about a sphere and maps them to a flat 2D plane.
Most of the common global world projections use conic projections that have a major axis aligned NS and conic slices that are orthogonal to the cone major axis mapped to latitude lines that are East-West.
There are many other types of projections, the older NZ map grid is an unusual one.
Once a projection is used to make a flat map, that map can be rotated about in any direction .. but that's another thing altogether.
You may, or not, enjoy looking through a free USGS projection reference of note:
Map projections: A working manual Synder (1987) https://pubs.usgs.gov/publication/pp1395
The Plate 1 link is to a handy wall poster of a limited number of common projections: https://pubs.usgs.gov/pp/1395/plate-1.pdf
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.
I'm partial to the Pierce Quincuncial [0] projection myself. Actually, any conformal projection that tiles really.
[0]https://en.wikipedia.org/wiki/Peirce_quincuncial_projection
Technically Mercator tiles.
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.
IIRC the use of Web Mercator is primarily for ease of generating 256×256 tiles.
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
Sure, but it can be projected in a way that minimizes distortion of the current region you're looking at. 3D effectively allows you to choose the best projection from an infinite family of projections, while 2D restricts you to a single projection regardless of your location of interest.
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.
A globe is just using physics to create a perspective projection on your retina.
https://en.wikipedia.org/wiki/General_Perspective_projection
Not quite, you have two retina and local light sources. So you get more information from a globe than any 2d projection.
However by rotating a perspective projection your brain can better recreate the underlying 3D nature of earth.
Right? And that isn't hard and can get you accurate images.
I get that this was a lot harder in the past. But today, this isn't difficult at all.
Oblig: https://xkcd.com/977/
And West Wing: https://www.youtube.com/watch?v=vVX-PrBRtTY