great work!

Although I find the hype about the AuthaGraph map rather… disturbing, I tried to come up with an »Authagraph lookalike«, too. Since developing formulae is way beyond my knowledge of the mathematics, I used the van Leeuwen projection (which is probably unknown to most people unless you happen to work with a certain map projection software).

It’s truly equal-area but of course that comes at a price, namely a higher distortion of the shapes. In case you’re interested:

https://blog.map-projections.net/an-equal-area-projection-in-the-fashion-of-the-authagraph-map

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]]>Any idea how I could use this projection in QGIS or other mapping software?

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]]>`augr`

, and a bunch of parameters with sensible defaults: `lat_1= lon_1= alpha= xshift= yscale= bb= cc= roundness=`

. Did you mean something else?Please also be wary that the projection is imperfect/buggy/unfinished — more details here.

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]]>At the authagraph (dot com) website, page 4 shows a picture of “the World without Ends”. It is that picture that makes me so excited: “[A tessellated] world map without gaps and overlaps”. I want to scroll it, rotate and zoom in and out of it, and if possible (as it seems with gnomonic projection), chose my own distortions and so on! 🙂

Can you tessellate the map made with your third method in the same way?

It’s the flattening of the earth from any point of view that is mind-boggling.

Thanks again.

//Erik

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]]>I’m not that good at this so I’m not sure I understand what you mean with “four spherical triangles”. What I meant with the 4 “o”‘s was something like this (apologies, this can be embarrassing…):

If the tetrahedron and the circle would have the same volume, then the relation between the diameter of the sphere and the length of the edge of the tetrahedron would be a/d=2^(1/6) and their bodies would both be inside and outside each other, right? Then the body intersections would be circles, both leaving “marks” on the sphere and on the tetrahedron, no?

What I mean is that there should be no distortion at all along the circumference of those circles.

A regular tetrahedron can be “unfold” onto a rectangle: |/\/\|

With the circles above inserted, it becomes: p/o\o/o\d (well, with some imagination 🙂 )

If the volume of the sphere is either much bigger or much smaller than the tetrahedron, then there would be distortions everywhere except in the four points where the surface of the sphere is exactly parallel to the 4 surfaces of the tetrahedron.

So it should be possible to make the size of those circles fit where it makes most sense to minimise distortion.

Well, this is why I want to be a real programmer in my next life! 🙂

Best regards.

//Erik

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]]>As for the screensaver, it must show *vector* maps since the rendering of a single high-resolution *raster* map takes tens of seconds. Also, the point of AuthaGraph is hiding its distortions by the ocean. The configurations of vertices that yield AuthaGraphs with land-avoiding distorted areas are rare. IMHO, other projections suit a screensaver better. See e.g. https://bl.ocks.org/mbostock/1e10b76becaa4ea4471262bcae619dae or https://www.jasondavies.com/maps/transition/.

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