how to compute the components of fields on the sloped plane

I have compute all the components of electromagnetic fields on the normal plane (Ex, Ey, Ez, Hx,Hy,Hz). Thn I project all fields to another plane with the theta angle with the normal plane as the input fields. Since the wave-vector is titled to the defined plane, I need to know the components that really works in finite-difference method. I am bad at solid geometry, so I have difficulty (e.g. ）. Could you please lend me a hand?

[darova]

Do you have any data? Code?

Do you know how the result should look like?

[Jiali]

I don't know how to write the code since I don't have a clear idea. Finally I find a licenced software can achieve it for me.