[Proj] Cosmetic latitudes...

Wed Mar 25 03:55:52 EST 2009

daan 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. 

--
Mikael Rittri
Carmenta AB
SWEDEN
www.carmenta.com 

________________________________

From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of strebe
Sent: den 25 mars 2009 02:41
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] Cosmetic latitudes...

On Mar 24, 2009, at 2:19:09 AM, "Mikael Rittri" <Mikael.Rittri at carmenta.com> wrote:  

>I just can't see the logic.

It is a mess, isn't it?

>And aren't there plenty of WKT flavours with different parameter names?

Yes, presumably any projection description is technically free to name its parameters whatever it likes.
>If one prefers a single name for all versions of lat_0, then "latitude_of_origin"
>is not a good name, since it would be misleading for the Hotine Oblique Mercator 
>(the origin is near the equator, not on the central latitude), and for the Krovak 
>(the origin is at the oblique cone apex near Finland, not on the central latitude).  

If the latitude of origin and the central meridian do not, in fact, project to the Cartesian origin, then the term really ought not apply. It is unfortunate that Snyder has used the same symbology (Φ₀) to denote the latitude of the map center in the Hotine as he has elsewhere to denote the latitude of origin. But that is a conflation of symbology, not terminology. His annotations for that projection call Φ₀ the latitude at the center of the map. I can't speak about the Krovac, since I have never studied it.

"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. There are two different principles at play here: a latitude of origin and a latitude of center. They should be distinguished by terminology. It is unfortunate that we must live with legacy conflations and confusions of terminology and symbology, but I do not think the situation would be helped by simply adopting a single term for distinct things.

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?

Regards,
— daan Strebe

On Mar 24, 2009, at 2:19:09 AM, "Mikael Rittri" <Mikael.Rittri at carmenta.com> wrote:

	> Mikael wrote:
	> 
	> >   [-- text deleted --]
	> >
	> > "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.
	>   
	> Please note also that "Latitude of origin" is the  name in the Well
	Known Text 
	> format specification.
	> E.g.,
	> 
	> PARAMETER["latitude_of_origin",49],
	> 
	> Regards,
	> - daan Strebe

	For some projections, yes. Perhaps for the majority. But for some
	projections,
	it is "latitude_of_center".
	And some projections have "central_meridian", while others have
	"longitude_of_center" instead.

	I have tried to figure out the reasons why, by looking at the OGC WKT
	names 
	at http://www.remotesensing.org/geotiff/proj_list , and first I thought
	that
	"central_meridian" is used if and only if the central meridian appears
	as a straight vertical line.  When the meridian is curved, it seems that
	"longitude_of_center" is used instead, and the "center" suffix spills
	over 
	and renames "latitude_of_origin" to "latitude_of_center", even when
	there 
	is no particular reason that it should spill over. 
	   However, things aren't that simple.  The central meridian of Krovak
	appears 
	as a straight vertical line, but it is called "longitude_of_center"
	anyway.  
	And the central meridian of the New Zealand Map Grid is called
	"central_meridian",
	even though it appears as a curved line.
	   I just can't see the logic. And aren't there plenty of WKT flavours
	with different 
	parameter names? 
	   If one prefers a single name for all versions of lat_0, then
	"latitude_of_origin"
	is not a good name, since it would be misleading for the Hotine Oblique
	Mercator 
	(the origin is near the equator, not on the central latitude), and for
	the Krovak 
	(the origin is at the oblique cone apex near Finland, not on the central
	latitude).  

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

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