EPSG guidance note #7-2, http://www.epsg.org
See method codes 1061 and 1062 for this operation in other coordinate domains and method code 9636 for opposite rotation in geographic 2D domain.
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. Transformation of coordinates from one geographic coordinate reference system into another is carried out as a concatenation of the following operations: (geographical to geocentric) + (geocentric to geocentric) + (geocentric to geographic) The Molodensky-Badekas (PV geog2D domain) transformation has 5 steps: (i) geographic 2D coordinates are converted to 3D using EPSG coordinate operation method code 9659; (ii) geographic 3D coordinates are converted to geocentric coordinates using EPSG coordinate operation method code 9602; (iii) the middle step of the concatenated transformation, from geocentric coordinates to geocentric coordinates, uses the Molodensky-Badekas (PV geocentric domain) method, EPSG method code 1061; (iv) the geocentric coordinates are converted to geographic 3D using EPSG coordinate operation method code 9602; (v) finally the geographic 3D coordinates are converted to geographic 2D using EPSG coordinate operation method code 9659.
Input point: Coordinate reference system: La Canoa (geographic 2D) Latitude = 9 deg 35 min 00.386 sec N Longitude = 66 deg 04 min 48.091 sec W This is taken to be geographic 3D with an assumed Ellipsoidal height hs = 201.465 m This transforms to Cartesian geocentric coords: Xs = 2 550 408.965 m Ys = -5 749 912.266 m Zs = 1 054 891.114 m Transformation parameters La Canoa to REGVEN: tX = -270.933 m tY = +115.599 m tZ = -360.226 m rX = 5.266 sec = 0.000025530288 radians rY = 1.238 sec = 0.000006001993 radians rZ = -2.381 sec = -0.000011543414 radians dS = -5.109 ppm Coordinate 1 of evaluation point = 2464351.59 m Coordinate 2 of evaluation point = -5783466.61 m Coordinate 3 of evaluation point = 974809.81 m from which M = 0.999994891 Application of the 10 parameter Molodenski-Badekas Transformation results in REGVEN geocentric coordinates of: Xt = 2 550 138.467 m Yt = -5 749 799.862 m Zt = 1 054 530.826 m This converts into: Latitude = 9 deg 34 min 49.001 sec N Longitude = 66 deg 04 min 54.705 sec W Ellipsoidal height = -18.10 m on the REGVEN geographic 3D coordinate reference system. Because the source coordinate reference system was 2D, the target system ellipsoidal height is ignored and the results treated as a geographic 2D coordinate reference system: Latitude = 9 deg 34 min 49.001 sec N Longitude = 66 deg 04 min 54.705 sec W