0977: "Map Projections"

[steve waterman]

I have decided to place these new projections onto my site instead of here in this forum...
After failing to have the first graphic above, not show up in the previous post...I believe, for sure, that file is sitting there yet just is being ignored.

These will take a couple of days to complete and I will post that address here at this forum where all new projections
can be better organized and formatted than here.

[esperanto41]

I have just posted a 40 MB pdf version of the Cahill-Keyes Megamap, 1/1,000,000 and 132' x 65' (40 m x 20 m), which can be easily opened and scrolled if you use the Chrome browser. It can be zoomed in pre-set increments, from 9% to 100% and beyond. (When first opening the giant pdf, you must scroll it down and to the right.) Available for free from this page on my website:
http://www.genekeyes.com/MEGAMAP-BETA-1/Megamap-Beta-1.html
PS: esperanto41 is Gene Keyes, and vice versa.

[PM 2Ring]

Thanks, PM 2Ring. I have just posted an explanation here:
http://mapthematics.com/forums/viewtopic.php?f=8&t=223

Thanks again. That "projection of a projection" technique is a neat idea; I guess it could be used to make vast numbers of variant projections. And you could do all sorts of weird & wonderful things if you use a different surface for the intermediate stage, rather than using a sphere. Reading your explanation in the above link reminded me of a projection technique that I read about a few years ago, which involved a couple of stereographic projections, but using a pseudosphere as the intermediate surface. But I can't for the life of me remember what the application was.

BTW, there seems to be a minor typo in your LaTeX. On line 2, you've used \phi_p instead of \varphi_p.

[Idhan]

The idea of applying the Mollweide-to-Hammer transformation is interesting. I wonder what a "double-Hammer" map, with the Mollweide-to-Hammer transformation applied to a map that's already in Hammer, or a "double-Mollweide" map, with the Hammer-to-Mollweide transformation applied to a Mollweide map, would be like. The "double-Mollweide" would be especially interesting, I think -- it would be an equal area map where the parallels are actually further apart along the prime meridian and converge toward the boundary.

[Strebe]

I wonder what a "double-Hammer" map, with the Mollweide-to-Hammer transformation applied to a map that's already in Hammer, or a "double-Mollweide" map, with the Hammer-to-Mollweide transformation applied to a Mollweide map, would be like.

Hi, Idha. I posted images of the projections you suggested here:

Code: Select all

http://mapthematics.com/forums/viewtopic.php?f=8&t=223

Enjoy! And feel free to comment in that forum.

Regards,
— daan Strebe

[Strebe]

Thanks again. That "projection of a projection" technique is a neat idea; I guess it could be used to make vast numbers of variant projections. And you could do all sorts of weird & wonderful things if you use a different surface for the intermediate stage, rather than using a sphere. Reading your explanation in the above link reminded me of a projection technique that I read about a few years ago, which involved a couple of stereographic projections, but using a pseudosphere as the intermediate surface. But I can't for the life of me remember what the application was.

BTW, there seems to be a minor typo in your LaTeX. On line 2, you've used \phi_p instead of \varphi_p.

PM 2Ring, thanks for the kind comments and the correction. I have posted the corrected formulæ.

There are a lot of research papers that deal with stereographic projections on pseudospheres for various applications in physics, so it turned out to be a chore to track down the one you might have been referring to. Do let me know if you remember it!

Thanks & regards,
— daan Strebe

[homunq]

You worry about the quality of rationalist fanfic for My Little Pony.

[dmswart]

What projection would be a favorite for those who favor novelty? As in "You like They Might Be Giants, Wierd Al Yankovic and Sir Mix-a-lot. The best thing about Chess is it's many novel variations that come out every year. You wonder why they don't use gimmicky Statue of Liberty plays in the NFL more often."
--
David Swart

[dmswart]

What happened to the Aitoff projection? I was disappointed to see it wasn't represented here...

The fairly similar Hammer projection gets more use in practice than Aitoff.

Brett, I'd say that depends. At my work, Aitoff plots are used almost exclusively to represent layouts of immersive displays from the observer's point of view.

[steve waterman]

re - waterman projection

2012 satellite imaged versions now available
http://www.watermanpolyhedron.com/maps.html

A write-up upon the mathematics/derivation of this projection
http://www.watermanpolyhedron.com/methodp.html

and a "rebuttal" poster regarding the mathematical derivation
of numerous polyhedral projections
http://www.watermanpolyhedron.com/projectionAA.html
[ only low res shown...but use the magnifier to get better look ]

and what others have said about this projection/math
http://www.watermanpolyhedron.com/commentsall.html

[helo darqness]

This is old, I know. But new to me. There are still images of these maps, but the animation makes it better...

http://www.graflexdirections.com/projec ... index.html (wish this was a GIF)