Hi,

I think I am still confused. How is then possible to express the major and minor axis in terms of these two angles?

I thought that the centre of the ellipse correpsonds to the 3d point, found in the first column of the 3x3 orthogonal matrix.

I know that the 2nd column represents the major axis. If we have an arbitrary orientation of this ellipse, then the second column should be translated as a separate point in 3d space.

By using the cartesian to spherical coordinate transformation:

For example the second column given in the matrix below

:[-0.51746 0.024186 0.85537

-0.84703 0.1275 -0.51602

-0.12154 -0.99154 -0.045487]

is expressed in Cartesian coordinates. Can we not express this in spherical coordinates? Am I wrong?

Thanks

Regards

Alex