The Liquid Earth projection

[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 in analysis. Laskowski’s 1989 The Traditional and Modern Look at Tissot's
Indicatrix is the first mention that I can recall off the top of my head.

— daan

[Milo]

With that in mind, a simpler way to write this calculation would be

"Simpler" if you remember by heart what Jacobian matrices and Frobenius norms are

[quadibloc]

I am highly impressed by the Liquid Earth projection, as it is beautiful in appearance, showing the continents with very little distortion.
Doing that, and also having the projection approximately equal-area is quite an achievement.
I don't know enough about how to work with meshes to do anything like that, but I did do something far simpler in an attempt to get all the continents depicted with reasonably accurate shapes:

Oh, dear, the image won't show now, because the site isn't in https instead of http.

It's at
http://www.quadibloc.com/maps/images/conhem.gif

visible from the page

http://www.quadibloc.com/maps/mapint.htm

It's just the two hemispheres, each depicted in a conformal conic.

[saga]

@quadliboc Thank you!

That link still doesn't work. Did you mean to post http://www.quadibloc.com/maps/images/conhem2.gif?

[Milo]

I wanted to say that doesn't look like a conic projection, but then I realized it is, just in transverse aspect.

[quadibloc]

@quadliboc Thank you!

That link still doesn't work. Did you mean to post http://www.quadibloc.com/maps/images/conhem2.gif?

Oops, yes, that definitely is the diagram I wanted to point you to. But the other link, to the page, should have worked.