### 座標轉換 - 三參數法與七參數法

Common Transformation Models

If the XYZ coordinate axes of two datums are known to be parallel and identically scaled, a three parameter transformation can be derived to represent their relationship (see Diagram 13 and Insert 5).

If the coordinate axes are not parallel and identically scaled, a seven parameter transformation can be derived (see Diagram 14 and Insert 6).

Diagram 13
3-Parameter Transformation

Insert 5
Three-Parameter Transformation Formulae

X1 = X2 + DX Y1 = Y2 + DY Z1 = Z2 + DZ

where

 X1, Y1, Z1 = Cartesian Coordinates of Datum 1 X2, Y2, Z2 = Cartesian Coordinates of Datum 2 DX, DY, DZ = The difference between the centres of the two spheroids

Diagram 14
7-Parameter Transformation

Insert 6
Seven Parameter Transformation Formulae

(Bursa-Wolf Model)

where

 X1, Y1, Z1 = Cartesian Coordinates of Datum 1 X2, Y2, Z2 = Cartesian Coordinates of Datum 2 DX, DY, DZ = The difference between the centres of the two spheroids RX, RY, RZ = The rotations around the three coordinate axes SC = The scale difference between the coordinate systems

Rotations are positive anticlockwise about the axes of Datum 2 coordinate system when viewing the origin from the positive axes.