Mapthematics Forums

quadibloc wrote: ↑Wed Mar 04, 2026 5:42 pm My efforts have been crowned with success. It took a little while, but that is understandable.

What does the success consist of?

— daan

Good luck!

— daan

A simple blended case, using the “brute-force” PDE. The projections to blend are the sinusoidal S and the cylindric equal-area E projections. [indent=20] S (𝜆, 𝜑) = [𝜆 cos 𝜑, 𝜑] [indent=20] E (𝜆, 𝜑) = [𝜆 cos 𝜑₁, sin 𝜑 ∙sec 𝜑₁] Blending them and keeping just the x coordinate: [indent=20] C (𝜑, 𝜆)[ x...

As a practical matter, what are these other ways of achieving an area-preserving homotopy? I had always thought the “brute-force” method would involve double integrals. As it turns out, it’s not that hard. Messing around with it yesterday yet again, I realized the problem is constrained enough to b...

So long as it unavoidably comes in multiple variations, you can't really claim it's the One True Way of blending maps and that all other ways are obsolete. Which member of the infinite set of symmetric homotopies would achieve the designation of the One True Way? Why is symmetry important in this c...

I’d call it obsolete after my homotopy , letting you blend any two projections. I've read about that one. It's pretty clever, but I do find it a little inelegant due to its lack of symmetry, which prevents a 50% blend of two You know what? I used to agree, but I have wasted far too much time on the...

Provided we do talk about the map I linked to above, it shows – increased spacing of straight parallels towards the poles, – probably equally spaced meridians along the equator (the distance doesn’t seem exactly the same everywhere, but this might be due to the poor accuracy of the drawing), – non-...

Nice find. I did not compare in depth, but this is surely the 等差分纬线多圆锥投影 ( Latitudinally equal-differential polyconic projection ). I’m a bit confused now… No, I’m a bit confused. When I wrote “I did not compare in depth”, I think I meant, “I did not compare even in shallow”, even though I have som...

Nice find. I did not compare in depth, but this is surely the 等差分纬线多圆锥投影 (Latitudinally equal-differential polyconic projection).

— daan