This was the method name used prior to October 2010.
EPSG guidance note #7-2, http://www.epsg.org
2010-11-02
true
false
true
For Projected Coordinate System Makassar / NEIEZ
Parameters:
Ellipsoid Bessel 1841 a = 6377397.155 m 1/f = 299.15281
then e = 0.08169683
Latitude of natural origin = 00°00'00"N = 0.0000000 rad
Longitude of natural origin = 110°00'00"E = 1.91986218 rad
Scale factor at natural origin ko = 0.997
False Eastings FE = 3900000.00 m
False Northings FN = 900000.00 m
Forward calculation for:
Latitude = 3°00'00.00"S = -0.05235988 rad
Longitude = 120°00'00.00"E = 2.09439510 rad
gives
Easting E = 5009726.58 m
Northing N = 569150.82 m
Reverse calculation for same easting and northing first gives :
t = 1.0534121
chi = -0.0520110
Latitude = 3°00'00.000"S
Longitude = 120°00'00.000"E
urn:ogc:def:method:EPSG::9804
Mercator (variant A)
Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for completeness in CRS labelling.
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.
The formulas to derive projected Easting and Northing coordinates are:
E = FE + a*ko(lon - lonO)
N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where symbols are as listed above and logarithms are natural.
The reverse formulas to derive latitude and longitude from E and N values are:
lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi)
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi)
+ (7e^6/120 + 81e^8/1120) sin(6chi) + (4279e^8/161280) sin(8chi)
where chi = pi/2 - 2 arctan t
t = B^((FN-N)/(a*ko))
B = base of the natural logarithm, 2.7182818...
and for the 2 SP Case, ko is calculated as for the forward transformation above.
lon = ((E - FE)/(a*ko)) + lonO