<blockquote>
  <p>I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail</p>
</blockquote>

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

<p>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.</p>

<p>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.</p>

CC BY-SA 4.0
2018-06-14T11:17:08.363Z
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.
dtech
CC BY-SA 4.0
2018-06-14T11:23:58.760Z
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 ;)
dtech
CC BY-SA 4.0
2018-06-14T12:41:10.927Z
"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.
Gimelist
CC BY-SA 4.0
2018-06-14T13:42:48.603Z
`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.
dtech
CC BY-SA 4.0
2018-06-14T13:48:34.940Z
The Dymaxion projection was pretty close to what I needed, but I couldn't find one that included the submerged parts of the continental plates, prompting me to make one myself. The Dymaxion map is far more prone to projection distortion, because it projects a sphere onto a very crude low polygon count mesh which significantly deviates from a sphere. In my case the approximation is much better, thus reducing projection related distortion by 6-7 orders of magnitude, far below the threshold eyes can perceive at that target resolution, for all intents and purposes producing a distortion-less map.
dtech
CC BY-SA 4.0
2018-06-14T23:07:39.950Z
@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.
Spencer
CC BY-SA 4.0
2018-06-15T01:12:35.973Z
@dtech as Spencer said, maps (of anything that is not a 2D thing, i.e. Earth) are projections, by definition. And, if you case is 6-7 orders of magnitude better, then it's already pretty good and the distortions are negligible. So - what exactly is your question?
Gimelist
CC BY-SA 4.0
2018-06-25T22:03:03.757Z
Related: https://www.wired.com/2013/11/cahill-butterfly-vs-dymaxion-map/  Also see http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly.html for other polyhedral maps.
mkennedy
CC BY-SA 4.0
2018-06-14T11:07:57.223Z
2018-06-14T11:07:57.223Z
Gimelist
<p>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 <a href="http://blogs.discovermagazine.com/d-brief/2016/11/03/most-accurate-world-map/" rel="nofollow noreferrer">this one</a>, that claims to "not lie" seems rather distorted.</p>

<p>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:</p>

<p><a href="https://i.sstatic.net/QUWfQ.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QUWfQ.jpg" alt="enter image description here"></a></p>

<p>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:
<a href="https://i.sstatic.net/Xg5CA.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Xg5CA.jpg" alt="enter image description here"></a></p>

<p>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.</p>

CC BY-SA 4.0
2018-06-11T23:31:59.913Z
What kind of 3D graphics background are you referring to ?
PROBERT
CC BY-SA 4.0
2018-06-12T03:16:14.050Z
Accurate enough for what? I don't get the question you are asking
Christoph
CC BY-SA 4.0
2018-06-12T06:05:50.517Z
Your basic problem is that you just can't accurately transform a 3D sphere to a 2D plane.
jamesqf
CC BY-SA 4.0
2018-06-12T12:00:57.650Z
Yes @jamesqf, it is theoretically impossible, but this approach attempts to adjust the entire mesh to attain the lowest possible distortion value for every polygon.
dtech
CC BY-SA 4.0
2018-06-12T12:01:13.807Z
Which is also what I mean by "accurate enough" @Christoph - is this as close as it gets?
dtech
CC BY-SA 4.0
2018-06-12T13:12:08.683Z
Better on https://gis.stackexchange.com ?
Communisty
CC BY-SA 4.0
2018-06-12T13:46:07.613Z
I'm voting to close this question as off-topic because it is more suited to  gis.stackexchange.com
Fred
CC BY-SA 4.0
2018-06-12T13:55:46.097Z
Yes it might be a better fit for gis, I asked here mainly because 1 - it is a part of an Earth science study, and 2 - I was already registered with this site.
dtech
CC BY-SA 4.0
2018-06-12T18:26:09.100Z
@BarryCarter you undersold it.
dtech
CC BY-SA 4.0
2018-06-12T21:04:16.687Z
@dtech "Distortion" on a map is a multi dimensional issue that depends on the use case. Do you want equal areas to be equal? Angles to be correctly represented? Measure distances? Navigate a ship? Compare climate zones? These are different goals and give rise to very different notions of distortion. gis.se is probably a better location though
Christoph
CC BY-SA 4.0
2018-06-12T22:50:36.837Z
@Christoph if the entire map is patterned with a 100 mile straight lines, by "no distortion" I mean the flat map having all those lines still straight and equal length, or as close as possible. And if there are any deviations, they should be distributed so that they are mitigated all over the map rather than being localized and heavily pronounced.
dtech
CC BY-SA 4.0
2018-06-13T17:28:00.810Z
@dtech: Sure, but you've traded continental area distortion for distortion in relative position and ocean area.  Which might be ok, depending on what you want to use it for.  (E.g. Mercator projection distorts areas, but is good for navigation...)  And even if you remove all continental distortion at the 100 mile scale, you'll still have some below that scale.
jamesqf
CC BY-SA 4.0
2018-06-13T17:44:00.093Z
@jamesqf as the title indicates, oceans are of no concern here, only the continents, including the submerged parts. Also, I am sure that it is accurate even well below the 100 mile scale, the projection mesh actually has more polygons than the image above has pixels, which only leave room for "way-way-sub-pixel" distortion which is not even visually perceivable. The goal is simply to display the planet's continental plates in 2D space as accurately as humanly (or computerly) possible. Relative position should be just as accurate too, it is only oceans that are completely left out.
dtech
CC BY-SA 4.0
2018-06-20T06:00:30.807Z
[A related GIS question on zero distortion at non-zero latitude](https://gis.stackexchange.com/questions/53410/global-projection-with-zero-scale-distortion-at-non-zero-latitude).
JeopardyTempest
<mapping><continent><projection>
Distortion-free map of all continents
dtech
# Distortion-free map of all continents

(Asked by: username_0 on 2018-06-11)

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](http://blogs.discovermagazine.com/d-brief/2016/11/03/most-accurate-world-map/), 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](https://i.sstatic.net/QUWfQ.jpg)](https://i.sstatic.net/QUWfQ.jpg)

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](https://i.sstatic.net/Xg5CA.jpg)](https://i.sstatic.net/Xg5CA.jpg)

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.

**Tags:** mapping, continent, projection

> **Comments:**
> **username_1**: What kind of 3D graphics background are you referring to ?  
> **username_2**: Accurate enough for what? I don't get the question you are asking  
> **username_3**: Your basic problem is that you just can't accurately transform a 3D sphere to a 2D plane.  
> **username_0**: Yes @username_3, it is theoretically impossible, but this approach attempts to adjust the entire mesh to attain the lowest possible distortion value for every polygon.  
> **username_0**: Which is also what I mean by "accurate enough" @username_2 - is this as close as it gets?  
> **username_4**: Better on https://gis.stackexchange.com ?  
> **username_5**: I'm voting to close this question as off-topic because it is more suited to  gis.stackexchange.com  
> **username_0**: Yes it might be a better fit for gis, I asked here mainly because 1 - it is a part of an Earth science study, and 2 - I was already registered with this site.  
> **username_0**: @BarryCarter you undersold it.  
> **username_2**: @username_0 "Distortion" on a map is a multi dimensional issue that depends on the use case. Do you want equal areas to be equal? Angles to be correctly represented? Measure distances? Navigate a ship? Compare climate zones? These are different goals and give rise to very different notions of distortion. gis.se is probably a better location though  
> **username_0**: @username_2 if the entire map is patterned with a 100 mile straight lines, by "no distortion" I mean the flat map having all those lines still straight and equal length, or as close as possible. And if there are any deviations, they should be distributed so that they are mitigated all over the map rather than being localized and heavily pronounced.  
> **username_3**: @username_0: Sure, but you've traded continental area distortion for distortion in relative position and ocean area.  Which might be ok, depending on what you want to use it for.  (E.g. Mercator projection distorts areas, but is good for navigation...)  And even if you remove all continental distortion at the 100 mile scale, you'll still have some below that scale.  
> **username_0**: @username_3 as the title indicates, oceans are of no concern here, only the continents, including the submerged parts. Also, I am sure that it is accurate even well below the 100 mile scale, the projection mesh actually has more polygons than the image above has pixels, which only leave room for "way-way-sub-pixel" distortion which is not even visually perceivable. The goal is simply to display the planet's continental plates in 2D space as accurately as humanly (or computerly) possible. Relative position should be just as accurate too, it is only oceans that are completely left out.  
> **username_6**: [A related GIS question on zero distortion at non-zero latitude](https://gis.stackexchange.com/questions/53410/global-projection-with-zero-scale-distortion-at-non-zero-latitude).  

---

## 1 answers

### Answer by username_7 on 2018-06-14. Score: 2

> 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.

> **Comments:**
> **username_0**: 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.  
> **username_0**: 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 ;)  
> **username_7**: "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.  
> **username_0**: `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.  
> **username_0**: The Dymaxion projection was pretty close to what I needed, but I couldn't find one that included the submerged parts of the continental plates, prompting me to make one myself. The Dymaxion map is far more prone to projection distortion, because it projects a sphere onto a very crude low polygon count mesh which significantly deviates from a sphere. In my case the approximation is much better, thus reducing projection related distortion by 6-7 orders of magnitude, far below the threshold eyes can perceive at that target resolution, for all intents and purposes producing a distortion-less map.  
> **username_8**: @username_0 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.  
> **username_7**: @username_0 as username_8 said, maps (of anything that is not a 2D thing, i.e. Earth) are projections, by definition. And, if you case is 6-7 orders of magnitude better, then it's already pretty good and the distortions are negligible. So - what exactly is your question?  
> **username_9**: Related: https://www.wired.com/2013/11/cahill-butterfly-vs-dymaxion-map/  Also see http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly.html for other polyhedral maps.  

---

