PSTEROSL projection south-oriented variant broken

[pnalos]

The PSTEROSL projection incorrectly computes the scale value for the south-oriented variant. See patch attached to MetaCRS post sent July 19, 2013. The PSTEROSL projection in CS-MAP is not documented. Details follow.

The PSTERO projection is documented as follows:

• org_lng - The longitude, in degrees, of the origin of the projection.

• org_lat - The latitude, in degrees, of the origin of the projection. Must be either 90 degrees north (i.e. positive), or 90 degrees south (negative).

• Scale - The scale of the coordinate system. This one factor must include the conversion from meters to coordinate system units, the scale reduction factor, and the mapping scale that is to be applied.

• scl_red - The scale reduction factor, independent of all other scaling, is obtained from this element and is necessary for correct computation of the grid scale factor in some cases.

• x_off - The false easting to be applied to all X coordinates, usually selected to cause all X coordinates within the coordinate system to be positive values of reasonable size. This is the X coordinate of the coordinate system origin.

• y_off - The false northing to be applied to all Y coordinates. This is the Y coordinate of the coordinate system origin.

• quad - An integer that indicates the cartesian quadrant of the coordinate system, 1 thru 4. A negative value indicates that the axes are to be swapped after the coordinates have been placed in the indicated quadrant.

(I believe the "Scale" element above is incorrect and should be removed. The "conversion from meters to coordinate system units" part is covered by the "UNIT" entry, and the "scale reduction factor" part is covered by the "SCL_RED" entry.)

As example definition is:

CS_NAME: WGS84.UPSNorth

GROUP: POLAR

DESC_NM: WGS 84 / UPS North

SOURCE: EPSG, V6.3, 32661 [Large and medium scale topographic mappi]

EPSG: 32661 SRID: 32661

DT_NAME: WGS84

PROJ: PSTERO UNIT: Meter

SCL_RED: 0.994 ORG_LNG: 0 00 00.0000E ORG_LAT: 90 00 00.0000N

X_OFF: 2,000,000.000 Y_OFF: 2,000,000.000

QUAD: 1

EPSG_QD: -1

ZERO_X: 0.0001 ZERO_Y: 0.0001

MAP_SCL: 1.0

The PSTEROSL projection is not documented, but substitutes PARAM1 (meaning standard parallel) for SCL_RED. The relationship between these two parameters is documented here (​http://earth-info.nga.mil/GandG/coordsys/Polar_Stereo_phi1_from_k0_memo.pdf). I believe CS-MAP implements exactly this algorithm to do the conversion.

There are no non-deprecated coordinate systems using the PSTEROSL projection shipping with CS-MAP now. FME, which uses CS-MAP internally, ships with this one:

CS_NAME: WGS84.ArcticPStero_FME

GROUP: POLAR DESC_NM: Arctic Polar Stereographic SOURCE: EPSG 3995 DT_NAME: WGS84 PROJ: PSTEROSL UNIT: Meter ORG_LAT: 90 ORG_LNG: 0 X_OFF: 0 Y_OFF: 0 PARM1: 71

(We would welcome its inclusion in CS-MAP proper, ideally without our _FME suffix, but I'm providing it here only for context.)

One of our users asks for the equivalent south-oriented coordinate system, i.e. EPSG 3031 instead of 3995. Changing ORG_LAT to -90 and PARM1 to -71 in the above definition produces the incorrect results. This is because the conversion from PARM1 to SCL_RED is hard-coded for the north-oriented variant.

A reasonable workaround is to compute the SCL_RED factor manually and use a PSTERO definition instead:

CS_NAME: WGS84.AArcticPStero_FME DESC_NM: Antarctic Polar Stereographic DT_NAME: WGS84 PROJ: PSTERO ORG_LAT: -90 ORG_LNG: 0 SCL_RED: 0.97276901289181761 UNIT: Meter

(I've omitted some less-critical elements here: GROUP, SOURCE, etc.)

Would it be possible to apply our patch to resolve this issue?