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**Molodensky-Badekas (7+3) Transformations **

__Seven+Three Parameter geometric transformation__

**MOLODENSKY-Badekas (7+3) Model**

The transformation is between a non-global local datum and a geocentric global geodetic system. __The rotations are to be considered about the three axes at the "initial" point of the local datum__. The scale factor is also considered with respect to the initial point.

where "i" denotes any point common to the local datum and geodetic system and the (U',V',W') are the coordinates of the "initial" point of the local datum. The three angles correspond to the small rotations taken positive in the counter clock-wise mode, when viewed from the end of the respective axes (at the "initial" point) towards the origin.

Note: When the "initial" point of the local datum (U',V',W') is not provided, assume values of (0,0,0).

**Point of Contact:**Coordinate Systems Analysis Team

phone (314) 676-9124, DSN 846-9124

coordsys@nga.mil

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