Aribtrary Projection Mapping

We have just tried matching the projector for projection mapping and it is rather tricky. We got a close result but not a perfect match. The plan is to use rather complex curvilinear geometry and so it would be best to avoid point tweaking.

If someone could take me through the practical steps of matching it would be super (I have seen this: how to project on 3d geometry)..)

For examples, I am not sure how to measure some of the projector parameters. See below, in red. Any advice?

For example, here is my lens. Is the “Image Width on Lens” something I can measure on the outside (“a” in the photo)? Is this also true for “Lens Radius” (“b” in the photo)?

Do you typically use devices for measurement? Lasers for distance, gyroscopes for angels? Or tape measure is enough?

We used LookAt to measure the center of the projected image and calculated orientation this way. Is this a good way to go?

Thank you for the practical tips.