Was I wrong about Eckert III this whole time?

[PeteD]

The impression I get that the "nominal" aspect of the scale should not affect the end result, (in which the odd Eckerts are indeed the "average" of the said projections), but the nominal scale is directly relevant to how the distortion gets visualized. For some reason, I was under the impression that distortion visualization was not calculated from nominal scale.

Daan explains this better than I could in this post. Unfortunately, the relevant images now appear as links, so it's not quite as easy to follow as it used to be.

It HAS to be calculated from the scale – how else could you tell that some regions are shown at the "right size" and others are not?

While areal distortion has to be calculated from the scale factor, which depends on the nominal scale, it's also possible use an areal distortion measure that compensates for suboptimal nominal scale such that the final numerical values don't depend on the nominal scale. As far as I know, Goldberg and Gott were the first to do this in 2007, then Györffy did it when optimizing his projections A-F in 2018, and in this paper by Kerkovits from 2020, there's even a derivation of how it's done in case it's not obvious (5.3. Invariance to scaling).

[daan]

The impression I get that the "nominal" aspect of the scale should not affect the end result, (in which the odd Eckerts are indeed the "average" of the said projections), but the nominal scale is directly relevant to how the distortion gets visualized. For some reason, I was under the impression that distortion visualization was not calculated from nominal scale.

Angular deformation is independent of nominal scale. Areal inflation and deflation (flation) have to be referred to something. A way to avoid nominal scale as the reference would be to compute the measure against the greatest or least scale factor in the map. However, the least scale in some maps is zero, so that technique fails there, and it’s infinite in many maps, and so fails in those maps as well. Nominal scale ends up being the usual choice.

Cheers,
— daan

[justlikeoldtimes]

It's been almost a year, and I never finished my little project. I've been distracted by other inane ideas (unrelated to maps).

But this is what I did a year ago before my mind wandered off. I don't feel the need even label these, considering the crowd here.










Realistically, if I were to finish this project, I'd probably just start from the top and remake them in larger resolution. And there's a definitely a lot more I would have liked to have made. I since got a new PC, but it seems like I'll have to stick with my Windows 10 laptop if I want to keep using GeoCart for now. Like I said, I've been distracted, but I haven't forgotten about this.

[daan]

Daan explains this better than I could in this post. Unfortunately, the relevant images now appear as links, so it's not quite as easy to follow as it used to be.

I’m not sure why I put those size constraints in; it was something to do with having to reconfigure everything after a mangled update of phpBB. If your image is too large to be useful, it’s your problem, really. I turned off the limitation. Sorry for the inconvenience in the meantime.

— daan

[daan]

I since got a new PC, but it seems like I'll have to stick with my Windows 10 laptop if I want to keep using GeoCart for now.

Hm. Does Geocart not work on your new PC?

— daan

[Milo]

Angular deformation is independent of nominal scale. Areal inflation and deflation (flation) have to be referred to something. A way to avoid nominal scale as the reference would be to compute the measure against the greatest or least scale factor in the map. However, the least scale in some maps is zero, so that technique fails there, and it’s infinite in many maps, and so fails in those maps as well. Nominal scale ends up being the usual choice.

Or you could use the second-derivative-ish measure of areal distortion that we ended up discussing a few months later.

But this is what I did a year ago before my mind wandered off. I don't feel the need even label these, considering the crowd here.

Haha, nope!

I'm particularly intrigued by the Collignon one. I wouldn't consider either of them to be good projections, and yet they're apparently bad in about the same ways, since the animation shows remarkably little difference between them. I assume this is to the similarity to the sinusoidal projection (which is a little more curvy, but also has angular poles), which is the one projection that, per definition, would end up with a completely static "animation" in this series.

I'm also interested in the Mollweide/Apian one, which, since Mollweide is a projection that I actually like using, and also common in scientific literature, despite having no read theoretical basis for this (no, Earth isn't actually a 2:1 ellipse). The relatively significant differences between the two (particularly over Africa) do highlight the limitations of trying to map Earth as an ellipse, despite it feeling intuitively "right". Then again, it still doesn't look as severe as the azimuthal projections.

[justlikeoldtimes]

I since got a new PC, but it seems like I'll have to stick with my Windows 10 laptop if I want to keep using GeoCart for now.

Hm. Does Geocart not work on your new PC?

— daan

I quickly tried it on Windows 11 with my PC I bought a few months ago.

I think I did the full install. 3.3.6.

I started a new document, which created the canvas as I expected it to.

I then clicked Edit> New. I quickly see the default map for half a second and then the whole app crashes. This software was never explicitly advertised to work on Windows 11, so I wasn't sure what to say. And of course the cause could still be something else with my desktop. I still have ways to use it.

Should I start a thread in Problems?

[daan]

Should I start a thread in Problems?

Yes, please. I haven’t tested on Windows 11. I don’t know why it would be any different for Geocart than Windows 10; unlike Apple, Microsoft works hard to preserve compatibility. Given the complete lack of problems thus far, I did not run out and buy Windows 11 to test against.

Cheers,
— daan