How to calculate position in MPR?

I am implementing MPR (multiplanar reformation) in my project. I have finish all the calculation except the position. For example, the RadiAnt display position as:

I understand the charact of R/L/A/P/S/I as:

R: right
L: left
A: Anterior
P: Posterior
S: Superior
I: Inferiro

Also, dicom has a tag: ‘Patient Position’ to record the position in scanning.

My question is: how to calculate the position in MPR (R/L/A/P/S/I)?

Let’s say, the Image Orientation (0020|0037) is: x=[cos(80°) sin(80°) 0], y=[cos(10°) sin(10°) 0], z=[0, 0, 1], and the Patient Position (0018|5100) is HFS.

  1. Is it means that the RL direction is x=[cos(80°) sin(80°) 0], AP direction is y=[cos(10°) sin(10°) 0], and SI direction is z=[0, 0, 1]?

  2. How to obtain the position when rotate the MPR direction? For example the following picture, how to obtain the SR/IL?


    In my understanding, I need to use calculate the intersection angle between the red line with RL/AP/SI, and find the direction with the minimum intersection angle. Is that correct?

Any suggestion is appreciated~~~