[MetaCRS] Equirectangular / Equidistant Cylindrical Parameters

[Frank Warmerdam]

Didier and Trent,

Setting the stage
-----------------

At Even's suggestion I have reviewed:

   http://trac.osgeo.org/gdal/ticket/2478

The core of the ticket relates to straightening out how to handle the
Equirectangular (also known as Plate Caree or Equidistant Cylindrical)
projection.

Traditionally OGRSpatialReference, and libgeotiff have assumed that
Equirectangular has four parameters, central meridian, latitude of origin,
false easting and false northing.  This was presumably based on an examination
of the EPSG documents.  The dilemma relates to the handling of
latitude of origin.

The EPSG documents (ie. section 1.3.14 of guidance note 7-2) talk about
a standard parallel as being the latitude at which the scale is true.  The
actual equations use the symbol (?O), and refer to this parameters as the
latitude of natural origin.  Based on this (and the use of EPSG parameter
8801 - latitude of natural origin) I have designed the geotiff projection,
and OGR to have just this one latitude parameter.

The ESRI PE approach to Equidistant Cylindrical has only one latitude
parameter, which is called Standard_Parallel_1.  Melita at ESRI has
indicated that this is based on Snyder and Voxland's _An Album of
Map Projections_.

Over the GDAL/OGR 1.6 release cycle Didier (IGN) has extended Equirectangular
in OGR to include two latitude parameters - latitude_of_origin, and
pseudo_standard_parallel_1.

Traditionally OGR mapped the latitude_of_origin parameter in WKT to
the PROJ.4 parameter lat_ts (latitude of true scale).  The lat_0 (latitude
of origin) value was not set.  After Didier's changes the PROJ.4 translation
sets both the lat_ts (from pseudo_standard_parallel_1 if available, otherwise
from latitude_of_origin) and the lat_0 from latitude_of_origin.

Core Question(s)
----------------

1) Is latitude of origin a distinct concept from latitude of true scale
(aka standard parallel)?

2) If we have only the latitude of origin, does it make sense to assume
this is also the latitude of true scale (stdparallel1)?


Objective
---------

I would like to hammer down what parameters this projection method can
have, and I'd like to hammer down geotiff, and OGC/OGR WKT definitions.
If convenient, I'd like these to match the ESRI PE definition.

I've burned quite a few hours reading various materials on this simpliest
of projection methods and I'm quite frustrated.  I'm holding off on publishing
GDAL/OGR 1.6 Release Candidate 1 in the hopes of settling this before setting
the release in stone.  I'm looking for advice, and pointers on assumptions
of mine that are wrong.

Best regards,
-- 
---------------------------------------+--------------------------------------
I set the clouds in motion - turn up   | Frank Warmerdam, warmerdam at pobox.com
light and sound - activate the windows | http://pobox.com/~warmerdam
and watch the world go round - Rush    | Geospatial Programmer for Rent