| Name | Cassini-Soldner |
| EPSG Code | 9806 |
| GeoTIFF Code | CT_CassiniSoldner (18) |
| OGC WKT Name | Cassini_Soldner |
| Supported By | EPSG, GeoTIFF, OGC WKT |
| Name | EPSG # | GeoTIFF ID | OGC WKT | Units | Notes |
|---|---|---|---|---|---|
| Latitude of natural origin | 1 | NatOriginLat | latitude_of_origin | Angular | |
| Longitude of natural origin | 2 | NatOriginLong | central_meridian | Angular | |
| False Easting | 6 | FalseEasting | false_easting | Linear | |
| False Northing | 7 | FalseNorthing | false_northing | Linear |
+proj=cass +lat_0=Latitude of natural origin
+lon_0=Longitude of natural origin
+x_0=False Easting
+y_0=False Northing
There does not appear to be any scaling support with PROJ.4's Cassini.
The documentation for PROJ.4 just calls the projection Cassini, but does
indicate support for ellipical as well as spherical forms so I presume it
is the same as Cassini-Soldner.
The Cassini-Soldner projection is the ellipsoidal version of the Cassini projection for the sphere. It is not conformal but as it is relatively simple to construct it was extensively used in the last century and is still useful for mapping areas with limited longitudinal extent. It has now largely been replaced by the conformal Transverse Mercator which it resembles. Like this, it has a straight central meridian along which the scale is true, all other meridians and parallels are curved, and the scale distortion increases rapidly with increasing distance from the central meridian.
The formulas to derive projected Easting and Northing coordinates are:
Easting, E = FE + *[A - TA3/6 -(8 - T + 8C)TA5/120]
Northing, N = FN + M - M0 + *tan*[A2/2 + (5 - T + 6C)A4/24]
where A = (* - *0)cos*
T = tan2*
C = e2 cos2*/(1 - e2)
and M, the distance along the meridian from equator to latitude *, is given by
M = a[1 - e2/4 - 3e4/64 - 5e6/256 -....)* - (3e2/8 + 3e4/32 + 45e6/1024 +....)sin2*
+ (15e4/256 + 45e6/1024 +.....)sin4* - (35e6/3072 + ....)sin6* + .....]
with * in radians.
M0 is the value of M calculated for the latitude of the chosen origin. This may not
necessarily be chosen as the equator.
To compute latitude and longitude from Easting and Northing the reverse formulas are:
* = *1 - (*1tan*1/*1)[D2/2 - (1 + 3T1)D4/24]
* = *0 + [D - T1D3/3 + (1 + 3T1)T1D5/15]/cos*1
where *1 is the latitude of the point on the central meridian which has the same Northing
as the point whose coordinates are sought, and is found from:
*1 = *1 + (3e1/2 - 27e13/32 +.....)sin2*1 + (21e12/16 - 55e14/32 + ....)sin4*1
+ (151e13/96 +.....)sin6*1 + (1097e14/512 - ....)sin8*1 + ......
where
e1 = [1- (1 - e2)1/2]/[1 + (1 - e2)1/2]
*1 = M1/[a(1 - e2/4 - 3e4/64 - 5e6/256 - ....)]
M1 = M0 + (N - FN)
T1 = tan2*1
D = (E - FE)/*1","For Projected Coordinate System Trinidad 1903 / Trinidad Grid
Parameters:
Ellipsoid Clarke 1858 a = 20926348 ft = 31706587.88 links
b = 20855233 ft
then 1/f = 294.97870 and e^2 = 0.00676866
Latitude Natural Origin 10o26'30""N = 0.182241463 rad
Longitude Natural Origin 61o20'00""W = -1.07046861 rad
False Eastings FE 430000.00 links
False Northings FN 325000.00 links
Forward calculation for:
Latitude 10o00'00.00"" N = 0.17453293 rad
Longitude 62o00'00.00""W = -1.08210414 rad
A = -0.01145876 C = 0.00662550
T = 0.03109120 M = 5496860.24 nu = 31709831.92 M0 = 5739691.12
Then Easting E = 66644.94 links
Northing N = 82536.22 links
Reverse calculation for same easting and northing first gives :
e1 = 0.00170207 D = -0.01145875
T1 = 0.03109544 M1 = 5497227.34
nu1 = 31709832.34 mu1 = 0.17367306
phi1 = 0.17454458 rho1 = 31501122.40
Then Latitude = 10o00'00.000""N
Longitude = 62o00'00.000""W