[Proj] Terminology for origins

Mikael Rittri Mikael.Rittri at carmenta.com
Fri Oct 3 04:34:36 EDT 2008

Is there a simple and accepted standard terminology for the various kinds of projection origins?  

Gerald wrote:
> First, I detest the term "natural origin."  

Me too. 

> It seems to be synonymous with the basic mathematical origin. "Natural" is an unnecessary adjective 

I agree that it is the wrong adjective. 

> and just the term origin should suffice.

Should suffice, but doesn't, since the point with Easting and Northing both zero is also a kind of origin. 
I think there used to be a simple and wide-spread terminology before EPSG became so influential, like this:

  * False Origin: the point whose projected coordinates are both zero.  
  * True Origin: the point whose projected coordinates are False Easting and False Northing.

The words "True" and "False" are perhaps somewhat strange, but this terminology is used, for example, by:
  - http://www.mered.org.uk/mike/gps/gps_usergrid_more.htm
  - http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidecontents/guide7.html
  - http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys.html
  - http://home.clear.net.nz/pages/paulcatc/nzgrid1.htm
  - http://www.dartmouth.edu/~remsense/1-10%20Projections.htm

On the other hand, we have a single but influential source, 

  - http://www.epsg.org/guides/docs/G7-2.pdf (EPSG (or OGP) Guidance Note 7.2)

which makes subtle (I say hair-splitting) distinctions. It defines (section 1.2)

  * Grid Origin: the point whose projected coordinates are both zero.

which I can accept, but also that 

  * The point whose projected coordinates are False Easting and False Northing should be called 
    o "Natural Origin" if it is natural enough in an undefined way, or 
    o "False Origin" if it is less natural, or 
    o "Projection Centre", if it is not very natural, but not very false either,
    o "Grid Origin", but in a different meaning from the usual EPSG Grid Origin, 
         if the other alternatives are not sufficiently confusing ;-) 

In practice, it seems that this point is called 

    o "Natural Origin" in most projections, but 
    o "False Origin" in a Lambert Conformal Conic (2SP) and in a Polar Stereographic Variant C,
    o "Projection Centre" in an Oblique Mercator (plain or non-Hotine variant),
    o "Grid Origin" in a Krovak Oblique Conformal Conic. 

The first three lines above follows mostly from Table 3 on page 14. 
Krovak is forgotten in Table 3, but in section 1.3.2 on Krovak names the parameters
    FE = Easting at grid origin,
    FN = Northing at grid origin,
even though according to section 1.2, the Easting and Northing at a Grid Origin 
have to be zero and are not free to vary.  (In earlier versions of Guidance Note 7.2,
these parameters for Krovak were called Easting/Northing at Projection Centre, but this was 
wrong.  In the usual instance of projection, the Projection Centre is east of Slovakia, 
but the point with coordinates FE and FN is the oblique cone apex near Helsinki.)

Personally, I prefer the old, simple terminology, but since EPSG has hijacked the 
old term "False Origin" to mean "True Origin" now and then, the old terminology 
can be misunderstood.  

Grid Origin is OK by me, since it cannot be misunderstood (except for Krovak!).  
For the point with coordinates (FE, FN), I don't know a really good name.  
However, the site http://www.sco.wisc.edu/pubs/wiscoord/summary.php uses 
the term 

    "Actual Origin" 

for this point, which does not conflict with any EPSG term.  

Does anyone agree that Grid Origin and Actual Origin are good names?  

Mikael Rittri
Carmenta AB
Box 11354
SE-404 28 Göteborg
Visitors: Sankt Eriksgatan 5
Tel: +46-31-775 57 37
Mob: +46-703-60 34 07 
mikael.rittri at carmenta.com

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