You are reading something into what I said that I wasn't saying. Yes, I think that one simple step is better than several more complicated steps. But as Einstein said, make things as simple as possible but not simpler. Obviously there are many cases where you really need multiple steps. In those cases trying to cram everything into one step is as bad as trying to cram too much into one line of code. You will get no disagreement on that from me!

Still, and I am speaking here as someone who has taught linear algebra at the university level, the solution that I presented is the textbook solution to this type of problem. The only concepts that you need are that you can put a coordinate system on your subspace starting with a finite set of points (you need one more than the dimension of the space), and then use that coordinate system to write down the affine transformation if you know where those points go.

I won't put any more effort into trying to convince you of the merits of the textbook solution. This is a programming forum, not a mathematics class. Nor does it seem productive to continue to respond if you read this post as saying something else that I didn't say. So unless someone has a genuine question, I am leaving this conversation.