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I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail. Every map I found was of a particular projection type and as such showed continents out of proportion. Even this one, that claims to "not lie" seems rather distorted.

I am no expert in the area, but I do have some 3D graphics background, so I decided to give it a go. I took a spherical projection map of the continental plates, projected it onto a sphere, then created a polygonal mesh encompassing all continents onto the sphere, then brought that into 2d space and relaxed edge length to correspond to their relative length in 3d space as much as possible and transferred the pixel information to the resulting UV map. Note that I did not account of the planet being an imperfect sphere, so that may be a source of minor inaccuracy. And the result:

enter image description here

It does look a lot like a Dymaxion projection, although my result seems less distorted, probably because the former is project onto a rather low resolution mesh before unfolding: enter image description here

Is my result accurate enough, or is my workflow missing something? And in case of the latter, I'd appreciate a reference to an accurate representation, or at least some info on what I did wrong and how to improve my result.

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closed as off-topic by bon, Fred, arkaia, daniel.neumann, Daniel Griscom Jun 17 '18 at 1:25

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    $\begingroup$ What kind of 3D graphics background are you referring to ? $\endgroup$ – PROBERT Jun 11 '18 at 23:31
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    $\begingroup$ Accurate enough for what? I don't get the question you are asking $\endgroup$ – Christoph Jun 12 '18 at 3:16
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    $\begingroup$ Your basic problem is that you just can't accurately transform a 3D sphere to a 2D plane. $\endgroup$ – jamesqf Jun 12 '18 at 6:05
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    $\begingroup$ Better on gis.stackexchange.com ? $\endgroup$ – Communisty Jun 12 '18 at 13:12
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    $\begingroup$ I'm voting to close this question as off-topic because it is more suited to gis.stackexchange.com $\endgroup$ – Fred Jun 12 '18 at 13:46
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I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail

That's because such a thing does not exist. A projection by definition has distortion, otherwise it would not be a projection.

The only way to have a distortion free view of the planet is by having a physical globe, and looking at it with both eyes so your brain gets the three dimensional perception (assuming going to space is not an option). Anything else will result in distortion.

Now that we have this covered, there are all kinds of projections with all kinds of distortions. Distortions can affect areas, distances, shapes, etc. to various degrees. It's your choice to determine which types of distortions and their magnitudes are acceptable to you, personally. There is no need to reinvent the wheel, there are enough projections out there already.

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  • $\begingroup$ Except that I did not ask for a projection without distortion, what I asked for is a map that is free from the distortion that projection comes with. Which implies that projections are intrinsically distorted, so stressing that is entirely redundant. However, looking with bare eyes at a globe also features a projection all over the globe save for a single hypothetical dot that is normal to the eye sight. We cannot really look at a globe from a 720 degree field of view. $\endgroup$ – dtech Jun 14 '18 at 11:17
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    $\begingroup$ If we are to belabor the point, even looking at a flat surface is distorted to some degree, but that's just due to the human visual apparatus, which the brain has evolved to compensate for to a fair degree, save for certain illusions, particularly crafted to exploit its weak spots. People reinvent wheels all the time, and a lot of the time that's just wasted effort, but there is also this thing called pioneering, thanks to which we have a bunch of purpose specific wheels rather than just slices of tree trunks, and don't dwell in caves and whatnot ;) $\endgroup$ – dtech Jun 14 '18 at 11:23
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    $\begingroup$ "map that is free from the distortion that projection comes with" - but a map is a projection. You're basically asking for a "map-free map". Now, we cannot look at globe from 720 FOV, but your brain understands the distortion because of your 3D vision and mentally "flattens" it. Anyway, if you do want to reinvent the wheel, the map you already produced looks pretty good and the distortions are minimised. I believe that any improvement in one thing (e.g. area) would compromise other things (e.g. shape), so it will not be any better, only different. $\endgroup$ – Gimelist Jun 14 '18 at 12:41
  • $\begingroup$ but a map is a projection - there are many maps that are not projections, and many projections that are not maps. The map is just visual representation. And you cannot print a globe in a text book, or even visually compare features that are not in immediate proximity on the globe, thus the necessity for a map that lays continental plates out in flat 2d space as close to their original shape and proportions as possible. $\endgroup$ – dtech Jun 14 '18 at 13:42
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    $\begingroup$ @dtech Sorry, no, every map involves a projection. It's a fundamental truism of cartography. A theoretical map the size and shape of the Earth, if you could source enough paper and ink to print it, would involve something called the "identity" projection. $\endgroup$ – Spencer Jun 14 '18 at 23:07

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