Timeline for Which world map projection allows comparing countries by shape and size?
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| Mar 6, 2012 at 16:52 | comment | added | whuber | Thank you for clarifying that! New projections are created every day. We all have the computational power to invent projections to optimize map-making criteria, much like the one you previously expressed ("a projection that maps a sphere onto a solid figure with the lowest standard deviation of an error"). Restricting the solutions to an "existing" projection considerably simplifies life. You should let us know, though, what projections are available to you, because not all software supports all projections :-). | |
| Mar 6, 2012 at 16:47 | comment | added | crenate | @whuber I am asking about a currently existing projection - one you can buy in the shop (e.g. like the mentioned Dymaxion), not about how much fun would there be in cutting and pasting ;) | |
| Mar 6, 2012 at 15:40 | comment | added | whuber | That's a good point. However, you can make the cuts within the oceans--or, almost equivalently, let the projection distort however it wants within the oceans--and do you best to preserve the shapes of individual countries. Indeed, why not make the cuts around all the country boundaries? It would be like cutting pieces out of a jigsaw puzzle and spreading them around the table. This is a practicable solution: just use a collection of country-specific projections and display them all at the same scale. | |
| Mar 6, 2012 at 12:17 | comment | added | crenate | @whuber yes you are right, but if you cut the map too much you won't be able to compare much :). I think I outlined pretty precisely what I want to achieve. | |
| Mar 6, 2012 at 10:07 | comment | added | MappaGnosis | Exactly, hence the pedantry alert :). <Pedantry Alert #2> By 'flat' I presume you mean after unwrapping from some other shape such as a cone, cylinder, icosahedron etc. because projections to flat surfaces are less common than projections to an 'easily unwrapped' 3D shape, like the cone and cylinder especially.</Pedantry Alert #2> | |
| Mar 5, 2012 at 17:52 | comment | added | whuber | +1 You're quite right; mathematically, mapping the earth onto a globe is a projection. But (outside of mathematics) the term "projection" is usually reserved for projections onto developable surfaces: that is, flat map sheets. | |
| Mar 5, 2012 at 17:50 | comment | added | whuber | Mithy, you can bring the SD of the error arbitrarily close to zero by interrupting the map along lots of lines. Think of peeling an orange into segments: when the segments are narrow, there is little distortion. Although the cuts across segments introduce "infinite" terms into the SD, because the cuts have measure zero, they don't affect the SD (averaged over all points of the globe). Thus, you need to be more careful about your criteria for a good projection. | |
| Mar 5, 2012 at 12:46 | comment | added | crenate | Interrupted projections are ok as I only want to compare countries visually. The question that remains is which one gives the most uniform distortions. I think that in terms of mathematics we should be looking for a projection that maps a sphere onto a solid figure with the lowest standard deviation of an error. | |
| Mar 5, 2012 at 12:34 | history | edited | MappaGnosis | CC BY-SA 3.0 |
added 115 characters in body
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| Mar 5, 2012 at 12:28 | history | answered | MappaGnosis | CC BY-SA 3.0 |