I'm sorry for confusing you, but math-wise, that approach should be pretty okay, I think! Maybe if you could put your confusion into specific questions, I could help you?

Honestly, it's actually not that hard. If you understand the graphics and the general concept, you can pretty much take the rest for granted, as thats just "putting it in math-speak" and then getting the proper conditions for "t". I know that it looks confusing, but isn't it at least worth a try? You just need to convert the last line into script (by which I mean: replace "|v_b|" with "vec_length(v_b)", and "x²" with "x*x"), but then, you should have a working piece of code!

It's not a guarantee, mind you, but I still don't see a rpoblem with the math, and I do think that its worth a try. We can try simplyfing it when we find that it works generally.