That can not be solved with CGA since CGA starts with a given shape. Shape-Shape interactions cannot be done with CGA.
Either, you'd have to use Python or preprocess the data in ArcGIS / FME.
Note that points have no orientation and that CE creates little rectangular shapes, which are oriented in XZ ( XY in GIS terminology ) coordinates - means along the world axes. So I'd recommend you work with all the rotation values preprocessed.
Let me know if you're an ArcGIS user or not. If not, I could help with Python.