[OSRS-PROJ] Horrors of --- Krovak projection

[Frank Warmerdam]

Folks,

While I have been happy with the results that the Krovak projection in
PROJ.4 gives (subject to improvement by Gerald), I am having a devil of
a time mapping the coordinate system into a form usable in FME, based on
the libraries from Mentor Software.

In OpenGIS Well Known Text format I have converted the EPSG database dump
of EPSG:2065 to:

PROJCS["S-JTSK (Ferro) / Krovak",
     GEOGCS["S-JTSK (Ferro)",
         DATUM["S_JTSK_Ferro",
             SPHEROID["Bessel 1841",6377397.155,299.1528128,
                 AUTHORITY["EPSG","7004"]],
             AUTHORITY["EPSG","6818"]],
         PRIMEM["Ferro",-17.66666666666667,
             AUTHORITY["EPSG","8909"]],
         UNIT["degree",0.0174532925199433],
         AUTHORITY["EPSG","4818"]],
     PROJECTION["Krovak"],
     PARAMETER["latitude_of_center",49.5],
     PARAMETER["longitude_of_center",42.5],
     PARAMETER["azimuth",30.28813972222222],
     PARAMETER["pseudo_standard_parallel_1",78.5],
     PARAMETER["scale_factor",0.9999],
     PARAMETER["false_easting",0],
     PARAMETER["false_northing",0],
     UNIT["metre",1,
         AUTHORITY["EPSG","9001"]],
     AUTHORITY["EPSG","2065"]]

In PROJ.4 this is:

  +proj=krovak +lat_0=49.5 +lon_0=24.83333333333333
               +alpha=30.28813972222222 +k=0.9999 +x_0=0 +y_0=0
               +ellps=bessel +pm=ferro +units=m +no_defs

However, the FME/Mentor KROVAK coordinate system definition that I think
corresponds looks like this:

   CS_NAME: Krovak S-JTSK
   DESC_NM: Czechoslovakian Grid System (S-JTSK) (precise origin)
   SOURCE: Prof. ing. Bohuslav Veverka, DrSc, GEOSOFT

   PROJ: KROVAK
   EL_NAME: BESSEL

   ORG_LNG: -17.6665931666667
   ORG_LAT: 49.5
   PARM1: 42.5
   PARM2: 59.7575985555556
   PARM3: 78.5
   SCL_RED: 0.9999
   X_OFF: 0
   Y_OFF: 0
   UNIT: METER

The manner in which the projection parameters are described seems to
differ in some fundamental way. The online documentation for this
projection transform type (KROVAK) looks like this:

KROVAK: Oblique Conformal Conic for Czech and Slovak Republics

This an implementation of the Oblique Conformal Conic projection as is used
in the Czech and Slovak republics where the system was devised.

Parameter     Description
Name

PARM1    The longitude, in degrees, of oblique conic pole.
PARM2    The latitude, in degrees, of the oblique conic pole.
PARM3    Oblique Standard Parallel. This is the latitude of the standard par-
          allel of the oblique cone on the Gaussian surface. Note, only a
          single standard parallel is supported, but the effect of two stan-
          dard parallels is achieved through the use of the scale reduction
          factor.
ORG_LNG  Origin longitude for the Oblique Conformal Conic projection.
          For the Krovak system, this is usually the meridian of Ferro:  17
          39 59.735400W. An approximate value of 17 40 00.00W is often
          used.
ORG_LAT  Origin latitude for the Oblique Conformal Conic projection. This
          is usually 49 30 00N for the Krovakl systems.
X_OFF    The false easting to be applied to all X coordinates, selected to
          cause all X coordinates within the coordinate system to be posi-
          tive values of reasonable size.
Y_OFF    The false northing to be applied to all Y coordinates.

My confusion is how the EPSG latitude_of_center, longitude_of_center,
azimuth and pseudo-standard parallel relate to the PARM1, PARM2, PARM3,
ORG_LNG and ORG_LAT parameters.  It would appear there is nothing corresponding
to the azimuth, and instead the location of the "pole" implied by it is
given (as PARM1/PARM2).  Is there an obvious way to compute PARM2, given
the EPSG parameters?

Note, I have not confirmed that the FME Krovak S-JTSK projection gives the
same results as my PROJ.4 formulation.

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


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