13 Projections for 2022 (Part 7)

Fri July 01, 2022 13 Projections for 2022 (Part 7)

A collection of my own experiments
(see Intro for further explanations)

July: Guyou-Wagner

Guyou-Wagner
Original Creator	Emile Guyou (1887) / Karlheinz Wagner (1941)
Group	Miscellaneous
Property	Compromise
Remarks	Weighted arithmetic mean of the Guyou and the Wagner VII projections.
My variation	2018

All projections of this year’s calendar are experimental – but this one is as experimental as it gets. When I created it, I had no specific result in mind. I had no stated goal. I just was curious to see how the arithmetic mean of a conformal and an equivalent projection would look like.

I chose to mix the (conformal) Guyou and the (equivalent) Wagner VII projections, both centered to 15°W^[1]. My first attempt was the ordinary arithmetic mean, but seeing the result I decided to throw in a little weighting: The projection shown above is weighted 2:3 in favor of the Wagner VII. I was pleasantly surprised when I inspected the distortions, because they are mostly pushed into the ocean. Only New Zealand gets inflated quite a bit – and more importantly, the inflations rise significantly within New Zealand’s area: From roughly 2.2 at the northernmost tip to ≈12.6 in the Southwest. That is unfortunate, but on the whole I think that you can call it a favourable distribution of distortions.

Regrettably, the outer form does not allow many practical applications of this projection. It could serve as a wall map that catches attention but still is ordinary enough to pull actual information from it. But apart from that, there’s probably not much left. Nonetheless I like it enough that I will add it to my Projection Collection in a few days.

Next month, we’ll have a projection that is useful – in my opinion. But I don’t think it’ll meet with much approval.

P.S.: In the printed version of the calendar I used a different imagery for the Guyou-Wagner; namely the map image you’ve seen in January on the Wagner IX Autobiographical. Meanwhile, I don’t like that one anymore, so for the image here on the blog I resorted to an old acquaintance, the Natural Earth Cross-blended Hypsometric Tints.

P.P.S.: This isn’t the first public presentation of the Guyou-Wagner, I first showed it in the “Experimental projections” thread of the mapthematics forum. A highly recommendable thread since a few very interesting projections are presented.

P.P.P.S.: And happy birthday, Dad! 🙂

Footnotes

↑ 15°W was chosen as projection center in order to prevent the sliced Europe you get when the projection is centered to the Greenwich meridian. See the image at Wikipedia: Guyou hemisphere-in-a-square projection.