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Comment by GavinMcG | Hacker News Reader

> "AuthaGraph... faithfully represents all oceans and continents"

What does this mean? Literally, that is impossible, so what's it actually preserving and distorting?

It looks like angle is distorted. Is that it?

It looks like this is just another "equal area" projection. Many of these exist. Map projections are design to minimize certain distortions but at the expense of additional other distortions. Obviously since the world is round, you cannot minimize all of them. Other examples of distortions that a projection can aim to minimize are: distance, direction, scale, angle.

An example of another existing equal area projection is the Mollweide projection: [1] which you may have seen before.

1: https://en.wikipedia.org/wiki/Mollweide_projection

Correct, but this is one that has two important properties: It tiles, so it can be used for web maps, and you only need to rotate it to always have it point north, so it can be used for mobile maps.

Google Maps, and similar tile systems, can’t have the local area undistorted and pointed in the right direction without these properties – and this map fulfills them.

The AuthaGraph map is an equal area map, not a conformal map, so its local maps are distorted. For example, you can see that the meridians and parallels fail to meet at right angles.

The similar Lee Conformal Tetrahedric projection (http://www.csiss.org/map-projections/Miscellaneous/Lee_Confo...) has undistorted local maps, at the expense of somewhat large area differences for different regions (though perhaps not as bad as Mercator).

For one thing there is massive distortion of relative distances in southern parts... New Zealand or Australia to Antarctica is something like 4 hours flight, not halfway across the planet.

Except for the fact that it tessellates so all you need to do is make the map a bit bigger and that distortion goes away (seen in [0]).

0. http://www.spoon-tamago.com/wp-content/uploads/2016/10/autha...

A map shouldn't need an infinite series of other maps to be useful.

But if you have an infinite series of maps (e.g. google maps) then using a projection that takes advantage of that is indeed useful.

You're looking for a map where a straightish line gives you the direct path between two points? That's completely impossible. Flying from LA to Tokyo will take you over Alaska. Try to work that one out on a map.

(Yeah, you can make a map where straight lines work, but only for a chosen point of origin or antipodes around that point.)

Then why are you labeling it "completely impossible"? Here's a perfectly sensible straightish-line path between LAX and NRT, using a polar-aspect orthographic projection:

http://www.gcmap.com/mapui?P=LAX-NRT&MS=wls&MP=p&DU=mi

Yes, if you cherry pick the right projection for a particular route you'll get something like that, which is exactly what I said. But plot Johannesburg to Sydney on the same map.

What I said is impossible is to have a map where all routes between pairs of points look sensible. It gets worse if you optimize for other factors, like making maps equal-area, conformal, rectilinear, etc.

http://www.gcmap.com/mapui?P=JNB-SYD&MP=polar&DU=mi ?

There's an easy way to make all routes between pairs of points look sensible at once: plot them on a 3D globe ;)

You can see at the bottom of the second poster that the same projection admits different framings of the tesselation plane to reflect different purposes. The one in the triangle seems ideal to reflect a focus on Antarctica and indeed conveys the fact you mention.

Not once you tesselate the maps

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