Experimental projections

General discussion of map projections.
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Piotr
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Experimental projections

Post by Piotr »

This topic is for custom-made projections. Experiment and create new projections! Who knows, maybe your projections will have smallest distortion!
This projection is Sinusoidal mixed with Tobler's World In A Square (can be made by stretching Smyth by 2 vertically), then after the mix, it's stretched horizontally by 1.22222222.
Image
If any area distortion, then close to poles.
daan
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Re: Experimental projections

Post by daan »

You can see the distortion for your custom projection in Geocart. Choosing to see the areal distortion specifically will tell you how much your blend deviates from equal-area.

I was not able to replicate your projection with the instructions you gave. I got something similar, but distinctly different.

— daan
Piotr
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Re: Experimental projections

Post by Piotr »

What I actually did is stretch horizontally by 1.1 and vertically by 0.9. Smyth is stretched horizontally by sqrt(0.5) and vertically by sqrt(2).
Piotr
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Re: Experimental projections

Post by Piotr »

Extreme Cylindrical projection is a projection that has accurate shapes for low-mid latitudes and gives up shapes for sizes at high latitudes. I made this projection because Antarctica in Cylindrical Equal-Area looks nice to me for some reason.
Image
Piotr
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Re: Experimental projections

Post by Piotr »

Point-pole Winkel Tripel

This is generated by averaging Aitoff and loximuthal (loximuthal standard parallel is 0, and loximuthal horizontal factor is 0.70710678 (square root of 0.5)). I chose loximuthal because it's a nice point-pole pseudocylindrical projection that bends sharply at outer meridians and has equally spaced parallels making it more similar to equirectangular than say, Mollweide is and this configuration because North/South symmetry makes sense (therefore 0 standard parallel) and just like you can shrink equirectangular horizontally for higher standard parallels, a similar effect can be done in loximuthal (therefore the horizontal shrink). The square root of 0.5 factor is just a number that I arbitrarily chosen; it appears to work well (as in very similar to original Winkel Tripel) because the standard parallel for equirectangular in Winkel Tripel is about 50.47°, this factor on equirectangular corresponds to 45° standard parallel and the narrower higher latitudes tend to make "real standard parallel" larger on loximuthal than in equirectangular.

Top: Political
Bottom: Tissot indicatrix
Left: Winkel Tripel
Right: Point-pole Winkel Tripel

Image
daan
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Re: Experimental projections

Post by daan »

That’s pretty good for an oval-ish projection. The regions in the high latitudes, outer meridians, are worse than Winke tripel, but not horribly worse. The rest of the map is quite similar, and even better at the highest latitudes toward the middle.

— daan
Piotr
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Re: Experimental projections

Post by Piotr »

Which is about what you would expect from a point-pole projection. If you have any experimental projections, you can post them here.
Piotr
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Re: Experimental projections

Post by Piotr »

Rounded Mercator

Image

Consists of 2 parts — Mercator (0 to 45) and edited azimuthal equidistant (45 to 90). Edited azimuthal equidistant is generated by doubling latitudes from the pole included, multiplying the map vertically by 0.70710678 and taking the north/south half of the east/west hemisphere.
daan
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Re: Experimental projections

Post by daan »

That’s an interesting presentation.

As a variation, maybe consider setting 11° as the central meridian, and then interrupting asymmetrically at 12°W.

— daan
Atarimaster
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Re: Experimental projections

Post by Atarimaster »

Piotr wrote:This topic is for custom-made projections. Experiment and create new projections! Who knows, maybe your projections will have smallest distortion!
In this experiment, I didn’t care about distortions, I was just curious to see the result of blending two certain projections.
Well, it looks… interesting. :lol:
Probably something you’d use only for purely decorative maps. However, the distortions on most landmasses aren’t even that bad after all (with a few exceptions). So, which projections were blended here? – I’m not telling that now. I think one of them isn’t that hard to guess, and the other one… well, probably not hard to guess either in case you remember from my previous postings which projections I like a lot… ;)

So, here it is:
physical.jpg
The blended projection
(216.54 KiB) Downloaded 1739 times
Angular distortion
Angular distortion
angular.png (25.75 KiB) Viewed 1749 times
Areal distortion
Areal distortion
areal.png (29.21 KiB) Viewed 1749 times
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