# 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. May 31 '17 at 9:55
• @user30184 No, that does not yield meaningful values. May 31 '17 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. May 31 '17 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. May 31 '17 at 19:10
• @user30184 you map the ellipsoidal height (h) to zero, then convert the lat-lon-h to XYZ values. May 31 '17 at 19:12

You can't use the Helmert-transformation (with Bursa-Wolf parameter) with geographic coordinates. First transform the geographic coordinates into geocentric coordinates. see

That's 3D coordinates, so you can easily integrate the altitude value.

But consider the precision using this transformation is 1 to 8 m depending on area and parameters.

But why the altitude value is the difference to NN ?

• `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? May 31 '17 at 15:21
• The better way is, for example is ntv2, but you need gridshift grid file for that and it could be slow. Bursa-Wolf Parameter are available, the precision is ok for map visualisation. For small areas the precision is better then 1m. May 31 '17 at 18:37
• Sorry MAMSL/AMSL is the right acronym. NN is a old acronym for standard zero. If you are not changing the Elevation model why calculating a new altitude value. If you change the Elevation model, there are special transformations for vertical value systems. May 31 '17 at 19:02