# Applying the Bursa-Wolf transformation

I want to transform Gauss-Kruger coordinates into WGS84 coordinates by applying the Bursa-Wolf transformation. I know the Bursa-Wolf parameters for the desired transformation. What confuses me is that the Bursa-Wolf formula expects 3D coordinates (`X`, `Y`, `Z`), whereas my input Gauss-Kruger coordinates are only 2D (`northing`, `easting`), and my output WGS84 coordinates are also only 2D (`latitude`, `longitude`). How do I map my 2D input/output coordinates to the 3D coordinates in the Bursa-Wolf formula?

• I would guess that you need to map Z to zero. Commented May 31, 2017 at 9:55
• @user30184 No, that does not yield meaningful values. Commented May 31, 2017 at 11:42
• Basically, you transform lat/lon of the source CRS to a XYZ-coordinate system centered on the earth center, then apply the shifts and rotations on/around all three axis, finally reproject back to lat/lon of the target CRS. You get slightly different results if you include the height above the geoid in your calculation. Commented May 31, 2017 at 16:06
• @AndreJ Correction, Bursa-Wolf/coordinate frame/position vector Z is from height above ellipsoid unless you also have geoid models or other conversions for the z values. Commented May 31, 2017 at 19:10
• @user30184 you map the ellipsoidal height (h) to zero, then convert the lat-lon-h to XYZ values. Commented May 31, 2017 at 19:12

• `But consider the precision using this transformation is 1 to 8 m depending on area and parameters.` Well, can you propose a better transformation than Bursa-Wolf? `But why the altitude value is the difference to NN ?` What do you mean by that? Commented May 31, 2017 at 15:21