projected
Research Institute for Geodesy Topography and Cartography (VUGTK); Prague.
2011-05-09
true
false
http://www.opengis.net/def/crs/EPSG/0/5513
S-JTSK / Krovak
Greenwich-based alternative to S-JTSK (Ferro) / Krovak, CRS code 2065.
Czech Republic; Slovakia.
12.09
22.56
47.73
51.06
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/1306
Europe - Czechoslovakia
Large and medium scale topographic mapping, cadastral and engineering survey. Due to distortions in survey network introduced after initial realisation the projection has an inaccuracy of several decimetres.
conversion
Research Institute for Geodesy Topography and Cartography (VUGTK); Prague.
2011-04-16
true
false
49
30
N
24
50
E
30
17
17.303
78
30
N
http://www.opengis.net/def/coordinateOperation/EPSG/0/5509
Krovak (Greenwich)
Longitude is referenced to the Greenwich meridian. See projection code 19952 for original definition referenced to Ferro.
Czech Republic; Slovakia.
12.09
22.56
47.73
51.06
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/1306
Europe - Czechoslovakia
Large and medium scale topographic mapping and engineering survey.
Research Institute for Geodesy Topography and Cartography (VUGTK); Prague.
2010-12-07
true
false
true
For Geographic CRS S-JTSK and Projected CRS S-JTSK (Ferro) / Krovak
Parameters:
Ellipsoid Bessel 1841 a = 6377397.155m 1/f = 299.15281
then e = 0.081696831 e^2 = 0.006674372
Latitude of projection centre = 49°30'00"N = 0.863937979 rad
Longitude of origin = 42°30'00"E of Ferro = 0.741764932 rad
Co-latitude of cone axis = 30°17'17.303" = 0.528627762 rad
Latitude of pseudo standard parallel = 78°30'00"N = 1.370083463 rad
Scale factor on pseudo Standard Parallel (ko) = 0.9999
False Easting = 0.00 m
False Northing = 0.00 m
Calculated projection constants:
A=6380703.611
B=1.000597498
gammao=0.863239103
to=1.003419164
n= 0.979924705
ro=1298039.005
Forward calculation for:
Latitude = 50°12'32.442"N = 0.876312568 rad
Longitude = 16°50'59.179"E of Greenwich
Firstly, because the projection definition includes longitudes referenced to the Ferro meridian, the longitude of the point needs to be transformed to be referenced to the Ferro meridian using the Longitude Rotation method (EPSG method code 9601).
Longitude = 16°50'59.1790"E of Greenwich
Longitude of Ferro = 17°40'00" west of Greenwich
and then
Longitude = 34°30'59.1790"E of Ferro = 0.602425500 rad
Then the forward calculation first gives
U = 0.875596951
V = 0.139422687
T = 1.386275051
D = 0.506554626
theta = 0.496385392
r = 1194731.005
Xp = 1050538.634
Yp = 568990.995
Then Southing (X) = 1050538.63 m
Westing (Y) = 568991.00 m.
Reverse calculation for the same Southing and Westing gives
Xp' = 1050538.634
Yp' = 568990.995
r' = 1194731.005
theta' = 0.496385392
D' = 0.506554626
T' = 1.386275051
U' = 0.875596951
V' = 0.139422687
lat(iteration 1) = 0.876310603
lat(iteration 2) = 0.876312562
lat(iteration 3) = 0.876312568
Latitude = 0.876312568 rad = 50°12'32.442"N.
Longitude of point = 0.602425500 rad = 34°30'59.179"E of Ferro.
Then using the Longitude Rotation method (EPSG method code 9601):
Longitude of Ferro = 17°40'00" west of Greenwich
and
Longitude of point = 34°30'59.179"E of Greenwich.
http://www.opengis.net/def/method/EPSG/0/9819
Krovak
Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.
From the defining parameters the following constants for the projection may be calculated :
A = a(1 - e^2)^0.5 / [1 - e^2 sin^2.(latC)]
B = {1 + [e^2 * cos^4(latC) / (1 - e^2)]}^0.5
gammao = asin[sin(latC) / B]
to = tan(pi/4 + gammao/2).[(1 + e sin(latC)) / (1 - e sin(latC))]^(e.B/2) / [tan(pi/4 + latC/2)]^B
n = sin(latp)
ro = kp.A / tan(latp)
To derive the projected Southing and Westing coordinates of a point with geographical coordinates (lat, lon) the formulas for the Krovak are:
U = 2(atan{to.tan^B(lat/2 + pi/4) / [(1 + e sin(lat)) / (1 - e sin(lat))]^[e.B/2]} - pi/4)
V = B(lonO - lon) where lonO and lon must both be referenced to the same prime meridian.
T = asin[cos(alphaC).sin(U) + sin(alphaC).cos(U). cos(V)]
D = asin[cos(U).sin(V)/cos(T)]
theta = n.D
r = ro.tan^n(pi/4 + latp/2) / tan^n(T/2 + pi/4)
Xp = r.cos(theta)
Yp = r.sin(theta)
Then
Southing (X) = Xp + FN
Westing (Y) = Yp + FE
The reverse formulas to derive the latitude and longitude of a point from its Southing and Westing values are:
Xp' = Southing ? FN
Yp' = Westing ? FE
r' = [(Yp')^2 + (Xp')^2]^(1/2)
theta' = atan[Yp'/Xp']
D' = theta' / sin(latp)
T' = 2{atan[((ro / r')^(1/n)).tan(pi/4 + latp/2)] - pi/4}
U' = asin[cos(alphaC).sin(T') - sin(alphaC).cos(T').cos(D')]
V' = asin(cos(T').sin(D') / cos(U'))
Then latitude lat is found by iteration using U' as the value for lat(j-1) in the first iteration:
lat(j) = 2*(atan{to^(-1/B) tan^(1/B).(U'/2 + pi/4).[(1 + e sin(lat(j-1)) / (1 - e sin(lat(j-1))]^(e/2)} - pi/4)
Then
lon = lonO - V' / B where lon is referenced to the same prime meridian as lonO.
49.5
EPSG guidance note number 7.
1999-09-09
false
For an oblique projection, this is the latitude of the point at which the azimuth of the central line is defined.
http://www.opengis.net/def/parameter/EPSG/0/8811
Latitude of projection centre
24.833333333333
EPSG guidance note number 7.
2003-09-22
false
For polar aspect azimuthal projections, the meridian along which the northing axis increments and also across which parallels of latitude increment towards the north pole.
http://www.opengis.net/def/parameter/EPSG/0/8833
Longitude of origin
30.288139722222
OGP
2010-12-06
true
false
The rotation applied to spherical coordinates for the oblique projection, measured on the conformal sphere in the plane of the meridian of origin.
http://www.opengis.net/def/parameter/EPSG/0/1036
Co-latitude of cone axis
78.5
EPSG guidance note number 7
2000-03-07
false
Latitude of the parallel on which the conic or cylindrical projection is based. This latitude is not geographic, but is defined on the conformal sphere AFTER its rotation to obtain the oblique aspect of the projection.
http://www.opengis.net/def/parameter/EPSG/0/8818
Latitude of pseudo standard parallel
0.9999
EPSG guidance note number 7.
2000-03-07
false
The factor by which the map grid is reduced or enlarged during the projection process, defined by its value at the pseudo-standard parallel.
http://www.opengis.net/def/parameter/EPSG/0/8819
Scale factor on pseudo standard parallel
0
This alias applies only in the case of projection methods which have an axis positive west, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8806
False easting
0
This alias applies only in the case of projection methods which have an axis positive south, e.g. Transverse Mercator (South Orientated).
EPSG guidance note number 7.
2002-07-31
false
Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.
http://www.opengis.net/def/parameter/EPSG/0/8807
False northing
geographic 2D
Research Institute for Geodesy Topography and Cartography (VUGTK); Prague.
2010-11-02
true
false
http://www.opengis.net/def/crs/EPSG/0/4156
S-JTSK
S-JTSK is the Uniform Trigonometric Cadastral Network. It is a modification of the Austrian MGI geogCRS, code 4312. In Czech Republic technically improved by S-JTSK/05 (Ferro) (CRS code 5229) in 2009 but this remains the legal system.
Czech Republic; Slovakia.
12.09
22.56
47.73
51.06
OGP
2014-05-01
false
false
http://www.opengis.net/def/area/EPSG/0/1306
Europe - Czechoslovakia
Geodetic survey.
ellipsoidal
OGP
2008-06-23
false
http://www.opengis.net/def/cs/EPSG/0/6422
Ellipsoidal 2D CS. Axes: latitude, longitude. Orientations: north, east. UoM: degree
Coordinates referenced to this CS are in degrees. Any degree representation (e.g. DMSH, decimal, etc.) may be used but that used must be declared for the user by the supplier of data. Used in geographic 2D coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/106
Lat
north
http://www.opengis.net/def/axis/EPSG/0/107
Long
east
geodetic
Research Institute for Geodesy Topography and Cartography (VUGTK); Prague.
2010-11-02
true
false
http://www.opengis.net/def/datum/EPSG/0/6156
System Jednotne Trigonometricke Site Katastralni
S-JTSK = System of the Unified Trigonometrical Cadastral Network.
Geodetic survey, cadastre, topographic mapping, engineering survey.
Modification of Austrian MGI datum, code 6312.
Cartesian
OGP
2001-04-29
false
http://www.opengis.net/def/cs/EPSG/0/6501
Cartesian 2D CS. Axes: southing, westing (X,Y). Orientations: south, west. UoM: m.
Used in projected and engineering coordinate reference systems.
http://www.opengis.net/def/axis/EPSG/0/119
X
south
http://www.opengis.net/def/axis/EPSG/0/118
Y
west