Hi AlexC.,
You're very welcome.
I'm not clear which one is plane 2. (The spy cameras are un-usual observer)

So let me answer both. In the small image on the left is a demo about even it is perfectly aligned still doesn't "know" its position in space, (or more precisely the distance to the camera/projector). The rays from the projector get bigger as they project further away while spreading. Perhaps it becomes clearly when animated and viewed in the top editor view.
I intended to emphasize the importance of the set survey, including details such as camera placement, height, distance from the walls, and other relevant measurements. When this is clear, it becomes clear that all depend on each other.
The one on the right shows that only with a perfect angle to the camera, an undistorted image is re-created. If the plane aligns with the wall (or the windows), then the orientation is correct and the window is presented as it is in reality, a rectangle. (Note we identify a trapezoid shape in a photo as rectangular perhaps, it is typically distorted.)
Both examples, distance and orientation, provide the foundation for effective camera projection.
The windows are all rectangles in the 3D real world. When the image was taken, the "drawing of the windows was no longer rectangular, baked in 2D as a Trapezoid. With camera mapping, we "re-dimensionize" the shape again to a rectangle. If that is clear, the base of the Camera project is well grounded as a mental model in someone. That is what I tried to do here, which helps (hopefully to feel easy with this. In the late '90s, a good friend in Berlin introduced me to Camera mapping. It took me a while to understand what he did. That was pre-YouTube, and Handbooks were shipped across the Atlantic with a 6-week delivery time. Hence, the long time it took me to translate that inside of me.
Nearly three decades later, I hope to retain this memory as vividly as I felt back then, to clear all obstacles for others regarding this powerful technique.
The relevance is not outdated; for instance, if the concept is understood, the idea of LED studios (the next level) is just a step away. I found it quite useful since.
Let me know if that answered your question.
Cheers