[OSRS-PROJ] Test runs on Polish grid system

Gerald I. Evenden gerald.evenden at verizon.net
Wed Apr 7 20:48:19 EDT 2004

```Test run for Polish Grid region Strefar-I 1965 and the city of Lublin
with the three stereographic projections A) original GCTP clone
from Snyder, B) alternative with complete Gauss conversion and
C) Roussehli' polynomial.

Note: my non-French ability interprets Roussehli to claim
3 decimeter accuracy which explains the noise in the least
significant figures of the h-k calculations.  I will be checking
my interpretation by hitting on a local friend who can read
scientific French.  ;-)

See further comments in the second test run with k_0=1. which
explains my lies of a few days ago.

#Stereographic
#	Azi, Sph&Ell
#	lat_ts=
# +proj=stere +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=0.9998
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569422.55
Northing (y):  4705679.74
Meridian scale (h) : 0.99992871  ( -0.007129 % error )
Parallel scale (k) : 0.99992871  ( -0.007129 % error )
Areal scale (s):     0.99985743  ( -0.01426 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'8.409" [ 1.13566911 ]
Max-min (Tissot axis a-b) scale error: 0.99993 0.99993

#Oblique Stereographic Alternative
#	Azimuthal, Sph&Ell
# +proj=sterea +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=0.9998
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569418.92
Northing (y):  4705681.24
Meridian scale (h) : 0.99989334  ( -0.01067 % error )
Parallel scale (k) : 0.99989334  ( -0.01067 % error )
Areal scale (s):     0.99978670  ( -0.02133 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'19.367" [ 1.13871319 ]
Max-min (Tissot axis a-b) scale error: 0.99989 0.99989

#Roussilhe Stereographic
#	Azi., Ellps.
# +proj=rouss +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=0.9998
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569439.41
Northing (y):  4705694.98
Meridian scale (h) : 1.00009338  ( 0.009338 % error )
Parallel scale (k) : 1.00009335  ( 0.009335 % error )
Areal scale (s):     1.00018674  ( 0.01867 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'19.369" [ 1.13871366 ]
Max-min (Tissot axis a-b) scale error: 1.00009 1.00009

Second test with k_0=1.  I statement of a few days ago said the
the error figure for method b was better than method A.  This was
determined when I did not specify k_0 so default was 1.  In the
above run where the Polish factor of .9998 was used, the scale
error was better for method A.  Go figure.

The following is with k_0=1 where you can see that method A has
the poorest showing for scale error.

#Stereographic
#	Azi, Sph&Ell
#	lat_ts=
# +proj=stere +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=1.
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569443.04
Northing (y):  4705693.48
Meridian scale (h) : 1.00012874  ( 0.01287 % error )
Parallel scale (k) : 1.00012874  ( 0.01287 % error )
Areal scale (s):     1.00025749  ( 0.02575 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'8.409" [ 1.13566911 ]
Max-min (Tissot axis a-b) scale error: 1.00013 1.00013

#Oblique Stereographic Alternative
#	Azimuthal, Sph&Ell
# +proj=sterea +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=1.
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569439.41
Northing (y):  4705694.98
Meridian scale (h) : 1.00009336  ( 0.009336 % error )
Parallel scale (k) : 1.00009336  ( 0.009336 % error )
Areal scale (s):     1.00018673  ( 0.01867 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'19.367" [ 1.13871319 ]
Max-min (Tissot axis a-b) scale error: 1.00009 1.00009

#Roussilhe Stereographic
#	Azi., Ellps.
# +proj=rouss +a=6378245 +rf=298.3 +lat_0=50d37'30 +lon_0=21d5
+x_0=5467000
# +y_0=4637000 +k_0=1.
#Final Earth figure: ellipsoid
#  Major axis (a): 6378245.000
#  1/flattening: 298.300000
#  squared eccentricity: 0.006693421623
Lublin
Longitude: 22d33'E [ 22.55 ]
Latitude:  51d14'N [ 51.233333333 ]
Easting (x):   5569439.41
Northing (y):  4705694.98
Meridian scale (h) : 1.00009338  ( 0.009338 % error )
Parallel scale (k) : 1.00009335  ( 0.009335 % error )
Areal scale (s):     1.00018674  ( 0.01867 % error )
Angular distortion (w): 0.000
Meridian/Parallel angle: 90.00000
Convergence : 1d8'19.369" [ 1.13871366 ]
Max-min (Tissot axis a-b) scale error: 1.00009 1.00009

--
Gerald I. Evenden <gerald.evenden at verizon.net>

----------------------------------------
PROJ.4 Discussion List
See http://www.remotesensing.org/proj for subscription, unsubscription
and other information.

```