[MetaCRS] Re: Equirectangular / Equidistant Cylindrical Parameters

[Melita Kennedy]

On 11/27/08,  Frank Warmerdam <warmerdam at pobox.com> wrote:
> 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)?

Yes, of course. It's very clear when working with conics, but
admittedly is less clear with cylindricals. Many Mercator
implementations set the Y origin to the equator (latitude of origin)
implicitly. The explicit latitude of true scale/standard parallel
doesn't affect the Y coordinate origin at all. 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. Most cylindricals (that
aren't oblique or transverse) just use the equator, but it would be
possible to add a latitude of origin to the math.

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

Personally, I wouldn't assume that a latitude origin is also a
latitude of true scale.

Sincerely,
Melita