Which projections you favor?

[mapnerd2022]

They are 3 projections I've devised recently (meaning last year).

[mapnerd2022]

The Canana Projections: (Canana is my last name)

[mapnerd2022]

Oops, there's this one left:

[PeteD]

For the cylindrical equal-area projection, setting the standard parallel at the equator is actually suboptimal for any possible region you might want to map. Even for an equator-straddling region (like Africa, or even Indonesia), you'll have lower overall distortion if you set the standard parallel just slightly off the equator.

(On the other hand, an equatorial standard parallel is advisable for a cylindrical equidistant map, where it maximizes resolution-efficiency.)

Your resolution efficiency is a very interesting parameter, especially regarding its equal values for dual (or whatever term was settled on) projections. However, in terms of conventional angular deformation, isn't it also true for the equirectangular projection that setting the standard parallel at the equator is suboptimal for any possible region you might want to map? It seems to me that you would want to minimize angular deformation in more situations than you would want to minimize resolution efficiency.

[Milo]

Your resolution efficiency is a very interesting parameter, especially regarding its equal values for dual (or whatever term was settled on) projections. However, in terms of conventional angular deformation, isn't it also true for the equirectangular projection that setting the standard parallel at the equator is suboptimal for any possible region you might want to map? It seems to me that you would want to minimize angular deformation in more situations than you would want to minimize resolution efficiency.

I guess so. Maybe I got a little carried away with my own invention.

I wanted to say that because it's a compromise projection, the angular fidelity comes at the cost of areal fidelity, but that isn't correct. For cylindrical projections, the relative flation between two points is independent of the choice of standard parallel.

The actual cost you pay is either increasing the overall size of the map, or making the equator more cramped (so distances that are large on the the actual globe are harder to make out). If you have space to spare, it's a non-issue. And if you just want a wall map showing the general shape of Africa as a whole, rather than making out the fine detail of local landforms, it's not an issue either. (And in any case it'll only make like a 10% difference either way.)

I do think that resolution-efficiency is relevant for the applications where people are most likely to use the cylindrical equidistant projection in the first place. But if you're just using it as a generic compromise projection, maybe not so much.

[PeteD]

For cylindrical projections, the relative flation between two points is independent of the choice of standard parallel.

Isn't this also true for pseudocylindricals? In general, the relative flation between two points is invariant under any uniform stretching or compression of the projection.

[Milo]

Isn't this also true for pseudocylindricals?

Well, pseudocylindricals don't have a "standard parallel" in the same sense cylindricals or conics do. Zero distortion can only be achieved at the equator and/or the central meridian (well, unless you do something really weird), rather than two whole parallels. Although many pseudocylindrical projections (such as Mollweide) achieve zero distortion at two specific points on the central meridian, so I suppose you could call the latitudes those points happen to be on the standard parallels. (On the other hand, the sinusoidal projection has zero distortion along the full central meridian as well as the equator, making the concept of a standard parallel even more meaningless for that one.)

In general, the relative flation between two points is invariant under any uniform stretching or compression of the projection.

Yeah, so essentially what I'm saying is that changing the standard parallel is always just a matter of uniform stretching, rather than a more involved modification.

Although a simple result that you were probably already aware of, it isn't completely trivial, since conic projections do have standard parallels that are more than just stretching.

[PeteD]

Although many pseudocylindrical projections (such as Mollweide) achieve zero distortion at two specific points on the central meridian, so I suppose you could call the latitudes those points happen to be on the standard parallels.

I have been and didn't realize this was wrong. I'll stop.

[mapnerd2022]

I agree, because I'd rather use one of the Canana projections or the Robinson, or any of the Winkel Tripel versions, the Mollweide, the Hammer, the Aitoff and so on.

I haven't heard of the Canana projections. Do you have a link or formulae?

I've already presented them in the experimental projections thread as well as here recently. Since I'm no mathematician, I haven't got any formulae for any of them.

[PeteD]

Yes, I saw them. Thanks for sharing your work!