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 similarity transformation in algebraic form is:¶¶XT = XT0  + XS * M * cos q  + YS * M * sin q¶YT = YT0  – XS * M * sin q  + YS * M * cos q¶¶where:¶XT0 , YT0    =   the coordinates of the origin point of the source coordinate reference system expressed in the target coordinate reference system;¶M                 =  the length of one unit in the source coordinate reference system expressed in units of the target coordinate reference system;¶q                  = the angle about which the axes of the source coordinate reference system need to be rotated to coincide with the axes of the target coordinate reference system, counter-clockwise being positive. Alternatively, the bearing of the source coordinate reference system Y-axis measured relative to target coordinate reference system north.¶¶The similarity transformation can also be described as a special case of the parametric affine transformation where coefficients A1 = B2  and  A2 =  - B1.¶¶Reversibility¶The reverse formula for the Similarity Transformation is:¶¶XS = [(XT  – XTO) * cos q   –  (YT – YTO) * sin q ] / [M ]¶YS = [(XT   – XTO) * sin q   +  (YT – YTO) * cos q] / [M ]