Conformal Octahedron World Map

[Luca_bat_map]

Hello,
I am looking from a looooong time for a software able to do this projection

http://www.csiss.org/map-projections/Po ... formal.pdf

Unfortunately the mathematic of this map is too complicated for me. I know that it uses Lee's ellipctic functions to map an octant into an equilateral triangle. Cahill did the first version of this map, then Lee, then others...

http://www.genekeyes.com/Cahill-Projections-pt.2.pdf

Actually I did my own rearrangment of the octants and I am working on a bat-shaped map. I'm manually manipulating every single geocell in a 10° graticule to obtain my map so it's a huge work (I'll post it when finished). I think this is the best world map possible (from my point of view )...

Is it possible to include that kind of conformal projection (octant into equilateral triangle) in Geocart?

Thanks for the reply.

Ciao!

[daan]

Hello Luca_bat_map, and welcome to the forums!

Thanks for the inquiry. I will look into the octahedral format for conformal maps. I may end up just putting in a general regular polygon engine, depending on details. It’s high time Geocart had some of these conformal regular polygons beyond squares. Of course I would include a specialization for the configuration Cahill promoted. I can’t say when this might happen, unfortunately.

Regards,
— daan

[Luca_bat_map]

Hi Daan, thank you!

That would be great. Just be patient and I'll show you my rearrangment. It's slightly different from Cahill due to my choice of central meridian and of course it looks totally different due to my rearrangment of the parts. I hope to finish my job in one month or less, I'll post it there!

[Luca_bat_map]

Hi all, I finally finished my own conformal bat-shaped projection! Please take a look and tell me what you think about it!

If you can put in next version of Geocart this version I hope you'll use my name! (Ask me in private in the case... )



Greetings to all!

[Atarimaster]

Please take a look and tell me what you think about it!

I just have to say: I really like it, looks great!

[daan]

Hello, Luca_bat_map.

That’s a novel and useful arrangement. Nice job!

How did you generate the coordinates for it?

— daan

[Luca_bat_map]

It's been quite a big work with graphic tools. I started generating gnomonic projections with a free trial of a competitor software of Geocart. Then I used a graphic software to generate the conformal grid in a vectorial way and finally I manually transformed every single 10° geocell. I analyse deeply the grid used by Cahill to build the one used here.

So you can understand that the result is not "really" conformal everywhere because the inside of a geocell, in truth, is a manual transformation of the gnomic projection of that area.

Still I believe that the difference between this image and one "computer generated" is not noticeable due to the 10° dense graticule.

However, as I told in my first post, the mathematics for this projection is well know since Lee wrote this book

http://www.amazon.com/Conformal-project ... 0919870163

Do you think that this "Cahill-Concialdi bat projection" (Concialdi is my surname... ) can be placed in next version of Geocart???

[daan]

Just finished this for the new year. It was annoyingly complicated to develop, but here is Cahill’s in all its glory. I haven’t looked at details of the Concialdi variant yet.

Cahill's conformal butterfly

Cahill small.jpg (270 KiB) Viewed 7564 times

Cheers for the new year!
— daan

[Atarimaster]

Oh, great! Thanks, daan!
Could you also post the distortion visualization, please?

[daan]

As you wish.

Cahill distortion small.jpg (150.71 KiB) Viewed 7560 times

— daan