座標轉換 - 三參數法與七參數法

座標轉換通常使用兩種方法. 第一種是平移, 第二種是平移加旋轉. 平移法要使用到三個參數, 通稱三參數法(3 parameter formula). 平移旋轉法要使用到七個參數, 通稱七參數法(7 parameter formula). 底下為兩種參數法的解釋說明:

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.

全文參照: http://www.environment.sa.gov.au/mapland/sicom/sicom/tp_scs.html

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