I have a camera and a table and I want to align the camera to co-exist in the same coordinate system as the table. Here is an image of the setting.
What type of mathematical transformations I need to apply?
Here is what I think I need to apply: 1. Translation to the Z-axis. 2. Rotation to the Y-axis with a negative angle. 3. Rotation to the X-axis with a positive angle.
Do I need to rotate the Z-axis as well? The camera sees points on the table and I want to rotate my points around the Y-axis only. However, is this even correct if my coordinate systems are not aligned for all axis.
Sorry if it is not very clear. English is not my first language.
The problem is similar to transformation of the virtual world onto the rectangular screen of the virtual camera of 3D computer graphics, see e.g. here.
The transformations here are affine 3D transformations, which can be expressed nicely as $4 \times 4$ matrices using homogeneous coordinates.
So I would suggest to pick up some good book on 3D computer graphics, e.g. Foley-Van Dam.