EPSG Dataset :: v12.003

Molodensky-Badekas (CF geog2D domain)

Coordinate Operation Method Details [VALID]

Name:

Molodensky-Badekas (CF geog2D domain)

Code:

9636

Operation is Reversible:

Yes

Formula:

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 (CF 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 (geocentric domain) method, EPSG method code 1034;

(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.

Example:

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

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
X-axis translation	8605	Yes	The difference between the X values of a point in the target and source coordinate reference systems.
Y-axis translation	8606	Yes	The difference between the Y values of a point in the target and source coordinate reference systems.
Z-axis translation	8607	Yes	The difference between the Z values of a point in the target and source coordinate reference systems.
X-axis rotation	8608	Yes	The angular difference between the Y and Z axes directions of target and source coordinate reference systems. This is a rotation about the X axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Y-axis rotation	8609	Yes	The angular difference between the X and Z axes directions of target and source coordinate reference systems. This is a rotation about theY axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Z-axis rotation	8610	Yes	The angular difference between the X and Y axes directions of target and source coordinate reference systems. This is a rotation about the Z axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Scale difference	8611	Yes	Scale factor for source CRS axes minus one, where the scale factor is a multiplication factor to be applied to coordinates in the source CRS to obtain the correct scale in the target CRS. dS = (M – 1). If a distance of 100 km in the source CRS translates into a distance of 100.001 km in the target CRS, the scale difference is 1 ppm (the ratio being 1.000001). When the scale difference dS is expressed in parts per million (ppm), M = (1 + dS10-6). When the scale difference dS is expressed in parts per billion (ppb), M = (1 + dS10-9).
Ordinate 1 of evaluation point	8617	No	The value of the first ordinate value of the evaluation point.
Ordinate 2 of evaluation point	8618	No	The value of the second ordinate of the evaluation point.
Ordinate 3 of evaluation point	8667	No	The value of the third ordinate of the evaluation point.

Meta Data

Remarks:

See method codes 1034 and 1039 for this operation in other coordinate domains and method code 1063 for the opposite rotation convention in geographic 2D domain.

Information Source:

EPSG guidance note #7-2, http://www.epsg.org

Data Source:

EPSG

Revision Date:

February 21, 2019

Change ID:

[2002.51] [2004.47] [2009.083] [2013.021] [2014.039] [2014.065] [2017.018] [2018.001] [2019.006]

Alias:

Alias	Naming System	Remarks
Molodenski-Badekas transformation	EPSG alias	This alias is ambiguous as it gives no indication of the source and target CRS domain nor of the rotation convention used.
Molodensky-Badekas (geog2D domain)	EPSG alias
Molodensky-Badekas 10-parameter transformation	EPSG alias	This alias is ambiguous as it gives no indication of the source and target CRS domain nor of the rotation convention used.

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.