Hello Mark0,

I've got a few questions about the confidence ellipses I get in JAG3D. When adjusting 2D network I get a (major semi axis) and c (minor semi axis) with gamma as a rotation angle of the confidence ellipse.

Yes, that is right.

But once I take the same project (and add a height data) and do 3D network adjustment I get the same results when it comes to the coordinates, but I also get b (middle semi axis) and two more rotation angles that I didn't have in 2D network. Now when I look at the numbers I see that b and c are very close in values that I had as a and c before. What is the meaning of major semi axis in this case then?
And none of the rotation angles are close or similar to one I had before in 2D network adjustment. So how would I draw one for example in CAD software when having 3 rotation angles? What do they represent?

Each dispersion matrix (covariance matrix) is diagonalizable using, for instance, the eigendecomposition. Appliying the eigendecomposition results in a diagonal matrix, which contains the so-called eigenvalues, and an orthogonal matrix, which contains the corresponding eigenvectors. In case of a spatial network, a 3x3 sub-matrix of the total dispersion matrix refers to each estimated point. Decomposing a 3x3 dispersion yields three eigenvalues and three eigenvectors forming a 3x3 orthogonal matrix. The eigenvalues relate to the semi-axis of the confidence region, which is represented by an ellipsoid in case of a spatial network. (In a horizontal network, the confidence region forms an ellipse. In case of a levelling network, the confidence region is just an interval.) The eigenvectors are the direction vectors of these semi-axes. The eigenvectors forms a 3x3 orthogonal matrix. If the determinate of this orthogonal matrix is +1, it is also a rotation matrix. In case of a horizontal network, a single Euler angle represents the rotation. However, in case of a spatial network, three Euler-angles are required to describe a full rotation sequence. For more details, please take a look to the documentation.

All the best
Micha