Mapthematics Forums

That’s a thing of beauty! Bravo!

— daan

Happy new year to you, too!

I wish I had something to tell you. I don’t — nothing anyone could act on, anyway. I seem to believe I will adapt the code base to Metal, but I have not started and have no idea how long it will take.

— daan

Ah, right. Sorry; I should have confirmed your conjecture about the usual definition for angular deformation. And yes, using the Jacobian is a pithy path to the solution. Nice to see that explicitly. You might be surprised how uncommon it is in the map projection literature to see the Jacobian used ...

I didn't turn these into angle distortion values because I don't know the typical definition of angle distortion. For angular deformation 𝜔, it is common to use 50 𝜔 = 2 arcsin(𝑏′/𝑎′) where 50 𝑎′ = √( h ² + 𝑘² + 2 h 𝑘 sin 𝜃′) 50 𝑏′ = √( h ² + 𝑘² − 2 h 𝑘 sin 𝜃′) 50 h = √(( ∂ 𝑥/ ∂ 𝜑)² + ( ∂ 𝑦/ ∂ 𝜑)²)...

Welcome to the forums, saga. That’s an interesting inaugural posting. It looks like you’ve put a lot of work into this. I like the Liquid Earth; I could see it being used for maps whose spatial relationships among continents is unimportant. It does a good job of preserving continental shapes on a (n...

Many of the 16th century projections were ad hoc. I don’t know if that exact one shows up in other contexts. I can speculate on what influenced its design, but I don’t know of any description for its construction.

— daan

The variant you link to is something along the lines of the modified ptolemaic projection used by Waldseemüller in his very famous 1507 map of the world as the first showing “America”.

Cheers,
— daan

Apologies for the long delay.

Thank you, Bill, for the solidarity. I still have not settled on a course of action. I’ll note when I do.

— daan

Hello Maezar. You have several choices in Geocart: • Chaise lounge • Dymaxion-like conformal • Polyhedron conformal face • Gnomonic In the case of the dymaxion-like conformal, a couple of the faces have been split and moved; you may need to reassemble them. In the case of the polyhedron conformal fa...

quadibloc wrote: ↑Wed Jun 05, 2024 7:24 pm Oddly, though, you refer to Pafnuty Chebyshev, as if he wasn't the Chebyshev, who hardly needs to be described further, but simply refer to the one who then proved that conjecture simpy as Grave.