[Proj] Cosmetic latitudes...
strebe at aol.com
Wed Mar 25 12:12:07 EST 2009
I think that sorts it out well, and I agree that "center" is harder to pinpoint, as well as having less precedence in the literature, and therefore less desirable when latitude of origin and latitude of center coincide.
I realized after I sent my last response that I had not addressed your original inquiry, which is the category term for what you have proposed "cosmetic latitudes". I have never seen such a term in the literature, so I don't think you would be causing trouble by inventing your own term. If I were to do it (which I might!), I would use something like "positioning latitude", in the sense that the latitude contributes to the graticule's position on the Cartesian plane, but nothing else.
>Disclaimer: these are not official opinions of Carmenta AB. But I can work on it.
— daan Strebe
On Mar 25, 2009, at 1:55:52 AM, "Mikael Rittri" <Mikael.Rittri at carmenta.com> wrote:
> "Latitude of center" seems even more problematic for the same reason:
> unless the projection is vertically symmetrical, the "latitude of center"
> generally is not at the center of the projection.
That's true. If nothing else, the "latitude of center" can be far
outside the area of interest. (For example, the traditional
Swedish Grid is based on a Transverse Mercator with origin
at the equator, far from Sweden. I admit that "center" is not a
very good term for this point. I could argue that this projection
in theory extends to Antarctica, but on the other hand its associated
datum RT90 is not defined outside Sweden.)
> Hence, if it is the latitude of the projection's "center", then should we not call
> it the latitude of center (or central latitude)? (In point of fact, since Hotine is
> infinite in extent there is no mathematical "center", but at least symmetry allows
> a reasonable choice for a center.) If it is the latitude at the origin, then should
> we not call it the latitude of origin?
Well, that makes sense. It could be both, of course, but I suppose
you prefer the term "latitude of origin" in that case. It should be easy
to determine whether a point projects to the Cartesian origin. It seems
harder to define "center" in a formal way, so we could resort to the
"center" term only when necessary. If so, I know only two or three projections
where "center" would be necessary: Krovak, Hotine Oblique Mercator (with
origin at the natural origin near the equator), and possibly EPSG's
Polar Stereographic Variant C, depending on which parameters
that are used to define it. Do you know any more examples?
Disclaimer: these are not official opinions of Carmenta AB. But I can work on it.
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