I have two different 3D coordinate spaces where I am using affine transformations to convert points between one coordinate space to the other. My problem is that these points also include tilt and azimuth as well. How can I transform these tilt and azimuth values? Can I make use of the 4×4 affine transformation that I have for converting the $x,y,z$ points?
So to begin, I have 8 points in coordinate space one, with the corresponding 8 points in coordinate space two. What I calculate is the Affine transformation matrix that can transform points in coordinate space 1 to coordinate space 2, like this Affine Transformation Matrix: $$\begin{bmatrix}{X_p\\Y_p\\Z_p\\1}\end{bmatrix}=\begin{bmatrix}M_{11}&M_{12}&M_{13}&M_{14}\\M_{21}&M_{22}&M_{23}&M_{24}\\M_{31}&M_{32}&M_{33}&M_{34}\\0&0&0&1\end{bmatrix}\begin{bmatrix}X\\Y\\Z\\1\end{bmatrix}$$ Where $X_p,Y_p,Z_p$ is projected points and $X,Y,Z$ are original points. Last row of the transformation matrix can actually be ignored cause we know $w$ is always equal to 1. $M_{11}$ through $M_{34}$ are the coefficients for the transformation matrix.
So all I have to do to transform a point in coordinate system 1 is multiply by transformation matrix. But I also have tilt and azimuth, how can I convert these values? Can I use my transformation matrix or do I need to handle tilt and azimuth separately?