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

Mikael Rittri Mikael.Rittri at carmenta.com
Mon Mar 23 07:08:11 EST 2009

Gerald wrote:

>    \def\KRO{K\v{r}ov\'{a}k }

Oscar wrote: 

> This is the only correct spelling. - - - 

Thanks, Oscar and Gerald. (Diacritical marks always worry me.) Nice portrait links, too. 

daan wrote (about a central latitude that doesn't affect the shape of the projection): 

> Snyder includes it explicitly in his formulations, referring 
> to it as the "latitude of origin" and denoting it as φ₀.

Yes, now that you mention it. I have never noticed it before, but Snyder 
uses phi_0 when the parameter does not affect the projection shape, but 
otherwise he uses phi_1 (which he often calls the "latitude of the center of 
the projection and origin"), or else phi_1 and phi_2 for two standard parallels.  
This convention is, in fact, stated in his list of symbols on pages viii - ix, 
which I hadn't read carefully enough before.  

"Latitude of origin" sounds fine, but I am not too fond of using 
many different names for what is called lat_0 in Proj.4.  The 
EPSG Guidance Note 7.2 has gone too far in this direction, I think. 
I like "central latitude" as the only name.

To be honest, I was wondering if I ought to implement support for a non-zero 
lat_0 for normal cylindrical projections, just in case others were doing it.

But Gerald wrote:
> In this case [normal cylindrical projections] the use of lat_0 was simple 
> lazyness or the creation by someone completely ignorant of the basics.

which reminded me of an older post by Melita Kennedy on the MetaCRS list: 
> I have had requests to add a latitude of origin parameter to 
> the ESRI Mercator implementation. So far we haven't done it, as 
> you can get the same results through the false northing parameter. 
  ( http://lists.osgeo.org/pipermail/metacrs/2008-November/000178.html )

So, all right. I don't want to be the first to introduce a completely 
useless feature.  (Fourth or fifth would be okay :-> ) 
I guess I should just describe the situation in words for each projection
where it occurs.  There can't be many, without the normal cylindrical ones. 
Thanks for all advice,
Mikael Rittri
Carmenta AB


From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of strebe
Sent: den 21 mars 2009 02:27
To: PROJ.4 and general Projections Discussions; proj at lists.maptools.org
Subject: Re: [Proj] Cosmetic latitudes...

On Mar 20, 2009, at 2:34:00 AM, "Mikael Rittri" <Mikael.Rittri at carmenta.com> wrote:

>		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? 

Being merely a coordinate translation, most of the small-scale map projection literature ignores the "central latitude". Snyder includes it explicitly in his formulations, referring to it as the "latitude of origin" and denoting it as φ₀. See, for example:

Snyder, J.P. 1987. Map Projections — A Working Manual, p. 100. (US Geological Survey Professional Paper 1395). US Government Printing Office, Washington D.C.

Deetz & Adams (Elements of Map Projection) includes what is effectively the radius of the latitude of origin in their formulations of conic projections, but do not attempt to name it.

"Latitude of origin" seems sufficient and unambiguous. The central meridian and latitude of origin project to the cartesian origin. Rather than using the term "cosmetic" I would note that it is just a simple translation that does not bear on the geometry of the projection, and thenceforth label it the "latitude of origin". 

— daan Strebe

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