GH/C# - Present WorldXY Coordinates and Directions in CPlane ditto

OK, so if I rotate a whole bunch of geometry working in WorldXY coordinates and directions but when done rotating, I want to present the resulting coordinates and directions also in a local construction Plane coordinates & directions, how do I in simplest manner transmogrify all the numbers I have as viewed from the local CPlane instead?

In short: I would like to present all numbers in both World and CPlane terms, performing all transforms in World (I only want the numbers, never mind the annotation in the example below)

Fig 1. Example: An angle defined in World with would have different numbers when viewed from the perspective of the rotated CPlane, aso.

[Edited]
// Rolf