Request for feedback on my map projection paper

[justinkunimune]

So this might be a weird request, but here goes:

The last year or so, as a hobby, I've been developing some map projections by modelling the Earth as an elastic mesh. Here's one of the more visually distinctive ones:

The "Danseiji IV" projection

danseijiIV.png (175.74 KiB) Viewed 2107 times

I've gotten them to where I think they're worthy of publishing in a peer-reviewed journal, and wrote a paper to submit accordingly. Since I worked on them alone and none of my friends are into cartography (and it's 20 pages long), though, I don't have anyone to proofread it. I've read over and revised it myself, but I have a feeling that it's severely flawed in ways that only someone other than me will be able to see.

I don't suppose anyone here would want to read a draft of a map projection paper and send feedback on it? I'm mostly looking for feedback on the writing and whether it's comprehensible, but if anyone has strong opinions on the process or the projections, I'd love to hear those, too!

https://drive.google.com/file/d/177BSNn ... sp=sharing

[daan]

Not a weird request at all.

Do you want comments here or in private?

If I critique this, it might disqualify me from the formal peer review, depending on journal, though I haven’t had that happen yet.

I like your sample there. Pretty low distortion over land.

Danseiji = 団 精二 = 荒俣 宏様?

— daan

[justinkunimune]

Thank you! I suppose in private would avoid spamming others who follow these forums with comments that are too specific to interest them.

I'm currently aiming for the International Journal of Cartography and GIS.

It's actually from 弾性 for "elasticity" and 地 for "earth", though I like "body sprite two" as well!

[quadibloc]

I can say immediately that the Danseiji IV projection looks very nice, as it does seem to provide low distortion for all the major continental areas, which is something few, if any, other projections achieve.

As to the writing, in general, it is very good. But I found one nitpick. The sentence

Since each element has nodes for vertices, the elements’ states are completely defined
by the nodes’.

makes sense only if what is meant is that the states of the elements are completely defined by the states of the nodes. In the previous text, the notes are only noted as having positions.

The Danseiji III projection is also very attractive. The last two, shrinking the oceans instead of eliding them, are perhaps too unconventional for most people even in the present day.

[Atarimaster]

I'm mostly looking for feedback on the writing and whether it's comprehensible, but if anyone has strong opinions on the process or the projections, I'd love to hear those, too!

Regarding the writing:
Well, as usual I’ve got no chance to understand the mathematic parts – but at least I can say that I understand what you are doing here, so it’s got to be comprehensible.

Regarding the projections:
I like Danseiji N and I to IV, although personally, I think that N, I and II might look better using a horizontal stretching, for example something like this, which is the Danseiji I, horizontally stretched by a factor of 1.1 while vertically compressed by 0.9091 in order to keep the property of being almost-equal-area:

Danseiji-1_x1.1.png (60.6 KiB) Viewed 2082 times

Danseiji IV: Nice work! And since you mention the Dymaxion map, I prefer your work, because of its “organic” shapes (the outer shape of the projection and the graticule lines) and because I find it much easier to project it back to the globe in my mind.

Danseiji V: Hmmm. While I agree very much to the idea of keeping distortions away from the continents, I’m not very fond of shrinking down the Atlantic Ocean because in my opinion it changes the relative position of the continents towards each other too much. However it may be interesting for certain thematic maps, e.g. land use maps.

Danseiji VI: That’s funny, because only recently I was struggling with the problem that on a world map with lots of labels for cities, you always have to discard large cities from densely populated areas because there’s simply not enough space to keep them all, while on the other hand you can add very small cities in sparsely populated areas just in order to have anything there. At some point, I was thinking that it might be helpful to have a map that enlarges the densely populated areas, but to a lesser extent than maps that I’ve seen before.
And, well, here it is!
I have to admit that aesthetically speaking, I don’t find it very attractive, but it surely can be useful – although I guess I still wouldn’t be able to cram all the labels into Germany that I’d like to add…

Kind regards,
and good luck with your paper!
Tobias Jung

[justinkunimune]

Thanks for all the feedback! I'll definitely rework the sentence Quadibloc pointed out.

I'm glad ye like Danseiji III and IV; those are certainly my favorites of the group. I like V as well despite it's strangeness---I guess I just have a taste for unorthodox maps. I agree with Tobias that Danseiji VI is not very pretty looking, but I still think it's a fun idea, and hope that someone may make good use of it someday.

[quadibloc]

I guess I just have a taste for unorthodox maps.

I've noticed that from the selection of projections in MapDesigner. Myself, I have an interest in the mildly esoteric among map projections, seeking to know more about ones that are out of the way, but I'm definitely inclined towards the orthodox, at least in some senses, as you might find should you chance to visit my web page, http://www.quadibloc.com/maps/mapint.htm.

[Luca_bat_map]

Hi Justin!

I have read all the paper. It sounds pretty clear to me even if I'm not so much into that level of mathematics. To be honest I already noticed the Danseiji maps in your MapDesigner and I find Danseiji IV absolutely great. The base idea is great, I totally like it. The only thing I would try to improve is the "conformality closeness". In effect I found out that a very similar map to the Danseiji IV can be obtained playing with the conformal projection on a cube in the latest Geocart (I played with the demo version and I obtained a very nice map, I'll post it as soon as I'm home): you get more or less the same shape and interruptions.

However, back to your work, let me ask you one thing. As I understood, you minimized the elastic force while "stretching" the triangular mesh on plane. What if you try to do the same adding one constraint: each of the 3 sides of each mesh triangle must be stretched as the other sides of the same triangle within a defined tolerance. In this way the result will be much more "conformal-like" and I believe that the overall look would be even better.

Is that a nonsense or do you think it can be effectively done?

Ciao from Italy, Luca

[quadibloc]

I tried to make a fully conformal projection with fairly low distortion of area and general shape using just the Lambert conic conformal:



Nowadays, though, of course the biggest demand is for projections that are fully equal-area.

[justinkunimune]

Hi, Luca,

I think that can be done. Probably the way I would go about it would be to replace the elastic energy function with something like lambda*log(a*b)^2 + mu*log(a/b)^2. Then, if I crank mu way up or lambda way down, like I did with Danseiji II, the result would be basically conformal. The main reason I didn't pursue it was that when I tried the same thing with equal mu and lambda, I got the broken-looking mesh in figure 7. I actually tried the same thing with lambda=100, and a similar thing happened, but the super stretched interruption regions got sucked into the crack to maintain the equal area. It still didn't look very nice. I just assumed a similar thing would happen with lambda=.01.

The other reason I didn't feel compelled to pursue conformality is that I think there are more efficient ways to create conformal projections. If I'm not mistaken, a conformal projection is completely defined by its boundary (i.e. Adams's is the only elliptical conformal projection, and August's is the only epicycloidal one). So I felt like if I was going to optimize conformal maps, I should optimize the boundary and then solve for the conformal map projection that fills it. Except I don't know how to do that.

Maybe it would be worthwhile, though, even if it was with a mesh. I am curious to see your cube projection.