[Proj] Cosmetic latitudes, and the diacritics of Josef Krovak and others

[Mikael Rittri]

Gerald,
you wrote:

> The only legitimate use of lat_0 is when the location of mathematical
> origin is necessary to determine the overall character of the projection ... 

Yes, I agree.

> In the case of normal cylindrical projections the "natural origin" is *always*
> at the equator and thus lat_0 is always 0 and omitted.

Yes, I think you are right. At least, I hope so, and I think EPSG Guidance Note 7.2
agrees with you. 

But there are other kinds of projections where the lat_0 is cosmetic,
although it is common practice to let it be non-zero anyway.

For example, lat_0 is cosmetic in 

 * Gauss-Krüger Transverse Mercator (I am not sure about Gauss-Schreiber),
 * Lambert Conformal Conic (2SP) (but not in Lambert Conformal Conic (1SP), EPSG-style).

(For LCC, I think lat_0 is cosmetic in Proj.4 with +proj=lcc, even in 
 the one-standard-parallel case, since both lat_1 and lat_2 must be given 
 even if they are equal. Right?)

In common practice, lat_0 is usually non-zero for LCC(2SP), and sometimes 
non-zero for Transverse Mercator, too.  (I am not saying this is good, 
just that many people are doing it.) 

In EPSG terminology, lat_0 for Transverse Mercator is called "Latitude of Natural Origin",
while lat_0 for Lambert Conformal Conic (2SP) is called "Latitude of False Origin". 
In Carmenta Engine, the lat_0 is always called the "CentralLatitude".

Your term "geographical origin offset" is perhaps better than "cosmetic", though. 
Thanks! 

Best Regards,
--
Mikael Rittri
Carmenta AB
SWEDEN
www.carmenta.com

-----Original Message-----
From: Gerald I. Evenden [mailto:geraldi.evenden at gmail.com] 
Sent: den 20 mars 2009 15:27
To: proj at lists.maptools.org
Cc: Mikael Rittri
Subject: Re: [Proj] Cosmetic latitudes, and the diacritics of Josef Krovak and others

On Friday 20 March 2009 5:34:00 am Mikael Rittri wrote:
> Hello,
> I lump together some unrelated light-weight questions here:
>
> A) For some projections, a parameter for central latitude can be 
> given, but it does not really affect the shape of the map - it just 
> creates an extra offset in the northing values (in addition to the 
> offset due to the FalseNorthing).
>     My question: is there an established terminology for such a 
> central latitude?
>     When documenting projections, I would like to write something like 
> "the central latitude can be specified but is just cosmetic", with a 
> link to a glossary entry for "cosmetic central latitude".
>     But is "cosmetic" the best word?

This is a case of deja vu all over again.  ;-)

Not long ago I went through a debate with someone who wanted a "lat_0" for a cylindrical projection.  As commented above, I responded that y_0 would do the job and that lat_0 was totally unnecessary.  In this case the use of lat_0 was simple lazyness or the creation by someone completely ignorant of the basics.

Note: lat_0 in the above case had nothing to do with the lat_ts or true scale specification.

The only legitimate use of lat_0 is when the location of mathematical origin is necessary to determine the overall character of the projection such as in the azimuthal projections where it determines the point of tangency of the projection plane with the earth (when k_0=1).  I would tend to call it the "natural" orgin.

In the case of normal cylindrical projections the "natural origin" is *always* at the equator and thus lat_0 is always 0 and omitted.  If a lat_0 is present in the cylindrical projections, it might be called a "geographical origin offset" as contrasted to the the Cartesian origin offset of the false eastings and northings.

Much of this argument can also be carried over to lon_0.

I would tend to call it "geographical origin offset."

--
The whole religious complexion of the modern world is due to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist