Which projections you favor?

[PeteD]

Personally, I think that if you're trying to make the cylindrical equal-area and equirectangular projections look as good as possible over the whole globe, then 42.63° or 43° seems about right.

On the other hand, you could say that it's an impossible task to make these projections look good over the whole globe. This is most obviously the case for the cylindrical equal-area but is arguably true for any cylindrical projection, including the equirectangular, which is in my opinion the least bad of the bunch for a general-purpose world map (of course, other cylindrical projections may be more appropriate for specific purposes). In that case, it might make more sense to make the projection look reasonably good over as much of the globe as possible instead and just accept that it looks bad beyond this region*.

Taking the Winkel tripel to represent the limit of what looks reasonably good for Africa gives phi0 = arccos((pi + 2) / (2*pi)) = 35.08° for the equirectangular and somewhere around 30° for the cylindrical equal-area.


*This is the approach of Capek's Q, but the fact that the Gall-Peters is considered to have acceptable distortion everywhere between 60.32° N and 60.32° S suggests to me that Capek's threshold for acceptable maximum angular deformation is significantly too high.

[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.

[mapnerd2022]

I would only use the Cylindrical Equal Área on the original version with the standard Equator, but only showing the Equatorial Latitudes for a map of distributions of anything that comes from those latitudes, Coffee, Rubber, Sugar Cane...

[mapnerd2022]

And I would use the Equidistant Cylindrical for measuring distances and bearings from, in my country's case, Lisbon. Of course Lisbon would be grossly distorted in shape and area, as well as being stretched from a Pointed Meta-Pole to a Meta-Pole Line, but that would outweigh that application.

[Milo]

I would only use the Cylindrical Equal Área on the original version with the standard Equator, but only showing the Equatorial Latitudes for a map of distributions of anything that comes from those latitudes, Coffee, Rubber, Sugar Cane...

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.)

And I would use the Equidistant Cylindrical for measuring distances and bearings from, in my country's case, Lisbon. Of course Lisbon would be grossly distorted in shape and area, as well as being stretched from a Pointed Meta-Pole to a Meta-Pole Line, but that would outweigh that application.

Cylindrical equidistant projection only preserves distances from the equator (or poles). Lisbon conspiciously does not lie on the equator. To measure distances from Lisbon, you absolutely want the azimuthal equidistant projection (in oblique aspect).

[mapnerd2022]

I mean I would use the cylindrical equidistant in oblique aspect. I mean, in 1951, Botley did use it in that aspect to measure distances and bearings from London...

[mapnerd2022]

So in his example of his proposal of that application of the oblique aspect of the projection, London becomes the North Pole, so it's greatly distorted and becomes a line, but distances and bearings can be directly read from London.

[Milo]

Hmm... yeah, that would work. Feels weird to use a projection where the point of interest is the most distorted, though.

[mapnerd2022]

I know, right?

[PeteD]

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?