# Select transformation method

This second page of the Datum transformation parameters wizard allows you to choose the method you wish to use to calculate the datum transformation parameters between the two sets of control points.

The concept of each calculation method is shortly explained.

Dialog box options:

 Geo-centric datum shift: Calculates the translation vector (dX, dY, dZ, i.e. differences in geocentric coordinates in meters) between: the centroid of all point-coordinates in the first point map, using a local (unknown) datum, and the centroid of all point-coordinates in the second point map, using a global datum (preferably WGS 84), so that the point-coordinates of the first point map can be transformed to the second. Molodensky: Calculates the translation vector (dX, dY, dZ, i.e. differences in geocentric coordinates in meters) between: the centroid of all point-coordinates in the first point map, using a local (unknown) datum, and the centroid of all point-coordinates in the second point map, using a global datum (preferably WGS 84), and inverts the Molodensky transformation equations and avoids the use of geocentric coordinates, so that the point-coordinates of the first point map can be transformed to the second. Bursa Wolf: Calculates translations (dX, dY, dZ, i.e. differences in geocentric coordinates in meters), calculates rotations (Rot X, Rot Y, Rot Z in microradians and in arc seconds), and calculates the scale difference factor (dScale) between: all point-coordinates in the first point map, using a local (unknown) datum, and all point-coordinates in the second point map, using a global datum (preferably WGS 84), using the center of the ellipsoid as the rotation center (pivot), so that the point-coordinates of the first point map can be transformed to the second. Compute scale and rotations first: When you selected the Bursa Wolf or the Molodensky Badekas method: Select this check box to have the scale factor and the rotations calculated first to obtain more accurate scale and rotation parameters (independent of the stochastic errors in the translations). Clear this check box to have the translation vector calculated first. Molodensky Badekas: Calculates translations (dX, dY, dZ, i.e. differences in geocentric coordinates), calculates rotations (Rot X, Rot Y, Rot Z in microradians and in arc seconds), and calculates the scale factor (dScale) between: all point-coordinates in the first point map, using a local (unknown) datum, and all point-coordinates in the second point map, using a global datum (preferably WGS 84), using a user-defined centroid (in X, Y, Z as geocentric coordinates) on the ellipsoid of the first point map as the rotation center (pivot), so that the point-coordinates of the first point map can be transformed to the second. Xo, Yo, Zo: When you selected the Molodensky Badekas method, you must specify a rotation center. As defaults, the centroids of the X, Y, Z geocentric coordinates on the ellipsoid of the first point map are given. If you wish, you can overrule these defaults, and specify your own Xo, Yo, Zo geocentric coordinates (on the ellipsoid of the first point map) as the rotation center.

When you click the Next button, you will go to the Output page where you can inspect, and optionally save, the calculated datum transformation parameters.

The general process of the calculations is presented below. Conversions take place between map coordinates, latlon coordinates on the (local) ellipsoid, and geocentric coordinates.

 x1 , y1 , z1 (map coords on certain ellipsoid with unknown datum) ↓ (inverse projection) j1 , l1 , h1 (latlon coords on certain ellipsoid, with unknown datum) → X1 , Y1 , Z1 (geocentric coords with unknown datum) ↓ ↓ Actual calculationfor Molodensky Actual calculationfor Geo-centric shift, Bursa Wolf and Molodensky Badekas ↑ ↑ j2 , l2 , h2 (latlon coords with WGS84 datum) → X2 , Y2 , Z2 (geocentric coords with WGS 84 datum) ↑ (inverse projection) x2 , y2 , z2 (map coords using WGS 84 datum)

Geocentric coordinates are XYZ coordinates (in meters) where the center of the earth is taken as 0,0,0. Figure 1 below shows the octant of the world where the XYZ-geocentric coordinates are positive.

• The XY plane is the equator plane. The line between the Z-axis and the X-axis is the Greenwich 0° meridian; the line between the Z-axis and the Y-axis is the meridian of 90° East.
• j is the geodetic latitude; l is the geographic longitude.
• The geodetic latitude is larger than the geographic latitude due to the ellipsoidal flattening as the perpendicular onto the ellipsoid does not pass through the center of the ellipsoid.

• The red point is a point in the terrain with a measured height; the green point is a point on the earth surface with ellipsoidal height zero.
• In many texts on GIS and geodesy, this spherical ellipsoidal shape, obtained by turning an ellipse about its shortest axis b, is called a 'spheroid'.

Fig. 1:  Relation between geocentric coordinates (X, Y, Z) and geographic coordinates (j latitude, l longitude).

The formula to perform the Bursa Wolf datum transformation reads: