I'm working on a sun tracking project using mirrors to direct the sun into a skylight, but have struck a 3d geometry issue. You can check the project out if your interested here: http://arduinobeam.blogspot.com/
I didn't see this issue coming and still struggle a bit to visualise it but a 3d model helps.
See image below..
Because of the way the primary mirror is offset to prevent shadow being cast onto it from the secondary mirror, it turns out a few complications occur. The adjustment of the primary (elevation) mirror angle effects the azimuth alignment because the reflection plane is not vertical (as it would be if both mirrors were in line). To solve this I need to be able to calculate the two angles marked with ? from the elevation angle E and the mirror offset (currently 18.4deg). I know that the angles A are equal (this is the path of a ray in the plane of reflection).
I have had a go at this, but so far am struggling with the derivation. I assumed that the solid lines were of known length (1 for convenience) but this may not be necessary. If anyone feels inspired please give it a crack and let me know how you get on!