Some speculations about Dietrich-Kitada

[daan]

I do wish I owned a copy of Maurer’s text. Will there be images forthcoming?

— daan

[quadibloc]

Not at the moment, but I still have other good news for you. A thesis, consisting mostly of a literal translation of Maurer's text, is online:

https://apps.dtic.mil/dtic/tr/fulltext/u2/675812.pdf

and also here

https://archive.org/details/DTIC_AD0675812/

[daan]

Ah ha! Snyder mentions this translation in his Bibliography, but I had never seen a printed copy (or electronic). Retrieved, thank you.

Seems not to be a thesis, but some sort of collaboration or contract between Harvard Center for Environmental Design Studies and Office of Naval Research?

— daan

[quadibloc]

You're right, I didn't look carefully enough at the title page.

[Atarimaster]

I have now learned that H. Maurer, in addition to devising an equal-area polyconic, and a few other projections, was also the author of a book in which he attempted to provide a classification scheme for all the projections known at the time (1935). At first, it seemed to me that S. 164 might have been the projection we know as the Dietrich-Kitada, making that a projection that was known in Germany previously, and simply used by Bruno Dietrich, but a closer look has led me to put aside that exciting possibility.

Oh, damn. I agree it would have been nice to find a source for that projection.
However I don’t quite understand how you came to the “projection that was known previously and simply used by Bruno Dietrich” conclusion, since Maurer’s book was published 8 years after Dietrich’s. So even if Maurer’s No. 164 would have been identical to the Dietrich-Kitada, it still could mean that Maurer did the same thing that Kitada did later, namely developing a formula for a projection that was published without presenting the formula…

[quadibloc]

My memory played tricks on me, so I placed Bruno Dietrich's book in 1937 instead of 1927. But Maurer described and illustrated a projection that wasn't exactly equal-area; apparently, someone had gotten half-way to the Dietrich-Kitada by putting the meridians in the right place, but using circular arcs for parallels.

With circular arcs for parallels, but still fully equal-area, and resembling a squashed (by the Bromley-Mollweide factor!) Dietrich-Kitada, there would be Maurer's own equal-area polyconic, also mentioned.

[Atarimaster]

Speaking of “resembling Dietrich-Kitada”: This is my own attempt.
The outer shape is somewhat similar, and it is fully equal-area, but the graticule (and there, the distribution of distortion) is totally different. So in fact… it’s not very much like Dietrich-Kitada.
(As some of you might guess, it’s a Wagner VII variant.)

[daan]

Tobias: I like the differential behavior of this Wagner parameterization more than I do Dietrich–Kitada (= it is a “smoother” projection), but I like the overall distribution of distortion better on Dietrich–Kitada.

— daan

[quadibloc]

but I like the overall distribution of distortion better on Dietrich–Kitada.

You do? I find the Dietrich-Kitada interesting, and so I toyed with extracting a useful projection from its central hemisphere, but in general I've found "the general distribution of distortion" of the Dietrich-Kitada to be its greatest flaw, making it almost impossible to find an orientation of the world on that projection that makes an attractive map, with the high distortion all dumped in the middle of the ocean.

(As some of you might guess, it’s a Wagner VII variant.)

I would never have guessed that. Since it doesn't have pole lines, like the Eckert-Griefendorff projection, I would call it a Hammer variant.

Apparently, instead of using a latitude compression factor of 2, like the Hammer, or 4, like the Eckert-Griefendorff, you had to lower the compression factor all the way to 1.2 in order to obtain the apple shape:

[Atarimaster]

but I like the overall distribution of distortion better on Dietrich–Kitada.

Yes, I like how the angular deformation isocols almost run along the meridians (edit:) and the fact that the distortion doesn’t as high at the edges of the map. (New Zealand!)

I would never have guessed that.

Well, you’re new in the forum. If you’d had been here some time longer, you’d know that when it comes from me, it’s almost always something with Wagner.

Since it doesn't have pole lines, like the Eckert-Griefendorff projection, I would call it a Hammer variant.

Oh, well, the Wagner is a Hammer variant, too (speaking chronologically), or the Hammer is a special case of Wagner (speaking mathematically), so, yes, it kind of IS a Hammer variant. I was calling it Wagner variant because I created it with Geocart’s generalized Wagner.