What aspect?

General discussion of map projections.
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daan
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What aspect?

Post by daan »

Projection gourmets: What aspect would you call this one? The projection is conformal, by the way.

— daan
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Conformal masque projection
Conformal masque projection
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P.Raposo
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Re: What aspect?

Post by P.Raposo »

How about "blind spot bipolar"? ;)
daan
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Re: What aspect?

Post by daan »

I just might quote you on that!

— daan
quadibloc
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Re: What aspect?

Post by quadibloc »

For some reason, when I attempt to add my web site to my profile, it is rejected. Even though I include the "http://" at the start like it says I must.
The images I have linked were on my web site, though, so people can find it that way.

On that web site, I divide projections into 10 groups. Those groups are:

Cylindrical, Azimuthal, Conic, Pseudocylindrical and Pseudoconic, Polyconic
Conventional
Special conformal projections based on complex numbers
Special equal-area projections
Miscellaneous

I don't even think the Hammer-Aitoff projection has an "aspect" in the sense of cylindrical, azimuthal, or conic (I argue on my web page that true polyconic projections might deserved to be seen as belonging to a fourth aspect). Your example seems to be based on August's conformal or the Eisenlohr - but using some fancy footwork similar to that which gave us Lagrange's projection.

I would categorize it, of course, under "special conformal projections based on complex numbers", like August's or Guyou's.
Last edited by quadibloc on Mon Apr 20, 2020 10:50 pm, edited 1 time in total.
daan
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Re: What aspect?

Post by daan »

quadibloc wrote:For some reason, when I attempt to add my web site to my profile, it is rejected. Even though I include the "http://" at the start like it says I must.
With apologies, that feature is disabled due to its attractiveness for spamming. People register and lurk for some arbitrary amount of time, and then add a spam link to their profile.

— daan
daan
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Re: What aspect?

Post by daan »

quadibloc wrote:I don't even think the Hammer-Aitoff projection has an "aspect" in the sense of cylindrical, azimuthal, or conic
Those would be examples of projection “class”. Aspect refers to… well… something. My point is that it’s not a rigorous concept. Typically noted aspects are:
  • equatorial
  • polar
  • oblique
  • normal
  • transverse
— daan
daan
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Re: What aspect?

Post by daan »

quadibloc wrote:Your example seems to be based on August's conformal or the Eisenlohr - but using some fancy footwork similar to that which gave us Lagrange's projection.
Good call. It is an equatorial Mercator, mapped back onto the sphere via a conformal function, then a spherical transformation to tilt the globe onto its side, then August back to the plane.

— daan
quadibloc
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Re: What aspect?

Post by quadibloc »

daan wrote:Those would be examples of projection “class”. Aspect refers to… well… something.
My first result with a web search confirmed you're right about this: a page on the Mathworks site. But what you describes sounds to me like the case of a projection: convenitonal, oblique, transverse, and so on. I'm going to hunt around a bit more, to find out where, if anywhere, I saw "aspect" used with the meaning I gave it. Looks like a correction to my web page is in order.
daan
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Re: What aspect?

Post by daan »

quadibloc wrote:But what you describes sounds to me like the case of a projection: convenitonal, oblique, transverse, and so on.
Case is usually considered to be a synonym to aspect, but some authors would only use case to refer to normal, transverse, and oblique.

— daan
quadibloc
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Re: What aspect?

Post by quadibloc »

daan wrote:Case is usually considered to be a synonym to aspect, but some authors would only use case to refer to normal, transverse, and oblique.
In my current search, I found plenty of places where it seemed that aspect was restricted to normal, transverse, and oblique: and I'm pretty sure that I saw the term case used earlier where I saw a reference to Thomas Wray's paper. (I note that Thomas Wray's seven cases are all very well for projections with the symmetries of the Mollweide, but you would want to count a 45 degree oblique as special for Guyou, and "Skew Oblique", for example, isn't special for a projection like the Hill Eucyclic.) In any case, I've corrected my page as I must have gotten aspect mixed up with "system" or "class" by carelessly glancing at the text associated with a diagream at one point.
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