Conformal polyhedral maps

[daan]

I’m putting all the Platonic solids into Geocart as conformal projections. As a single map, you will have just one face of the polyhedron, but you can specify which face. Here is my “chaise lounge” icosahedron conformal map as a demonstration.

Arabia is unfortunate. Most of the rest shows good continuity. I’m not sure you can get better than this using completely regular faces with no duplications.

Best for the new year,
— daan

[Luca_bat_map]

So you can also create a conformal Fuller map... You're doing something amazing here Daan!

[daan]

Aaaaand there you have it.

Best,
— daan

[Luca_bat_map]

Much better than the original one! Conformality makes everything look better

[daan]

I agree: there are few good reasons to use gnomonic instead of conformal in polyhedral maps. Who needs the kinks?

— daan

[Atarimaster]

I also agree that the dymaxion-like conformal looks better than Fuller’s original!

How about also adding conformal versions of Wijk’s “Optimal fold-outs of Platonic solids”? (See Fig. 8 in Unfolding the Earth: Myriahedral Projections)

I see that it’s probably not very helpful to add a distinct menu entry for each and every possible layout there is but these are, in my opinion, very nice and could be grouped, either in a submenu or even as a single projection with parameters.
And of course, I don’t know if these “optimal fould-outs” are still optimal when they’re conformal…

Kind regards,
Tobias

[Luca_bat_map]

Check out also this intersting paper about polyhedral maps!

https://inspire.redlands.edu/cgi/viewco ... s_gradproj

Even if I don't like so much the result, the idea is very good and I guess that using the conformal engine that Daan developed it's possible to obtain great maps!

[Atarimaster]

… aaand I’d also like the “M-shaped” variant of the Cahill conformal butterfly – maybe as a parameter? (Just like you can select various variants for e.g. the Wagner VIII.)
Although it’s of course fairly easy to create it in a graphic application using an export of the butterfly variant. But hey, I’m lazy and like to let other people do the dirty work for me.


… two hours later:
I just realized that it’s even easier than I figured earlier. So maybe there’s really no need to add it to Geocart.

[daan]

Check out also this intersting paper about polyhedral maps!

Even if I don't like so much the result, the idea is very good and I guess that using the conformal engine that Daan developed it's possible to obtain great maps!

I was a committee member for that thesis.

Unfortunately, conformal maps are not possible for two different shapes if they must match along an edge. The only exceptions are:
• The shapes are rotations and/or reflections of each other; or
• One shape is just a piece of the other shape.

— daan

[Atarimaster]

Talking about polyhedral maps – would it be tough to integrate some equal-area polyhedral maps using the van Leeuwen projection?
For example, maybe a dymaxion-like equivalent map, or configurations similar to Wijk’s “optimal fold-outs”?