I googled asymptote and got almost 3 million hits?
In a proper strike, the final 'line' can't be hit without activation so it can't be said that the line is ever reached.
Googling asymptote or activation could never help with this-- it is not conventional usage.
There are lots of ways to think about what a strike is and why it works I guess.
When I strike a bag, the target is most certainly reached. And according to the bag's motion, it looks like it has been activated. Pretty simple, but I'm a simplistic kind of guy I guess. I could talk about striking in more complex terms but I'm not sure if it means much to anyone.
Daniel, my answer-- I did TKD before, and I looked at it from a syllabus point of view. In TKD we worked with strikes from just over leg's distance away to just under arm's length away. Nothing closer. Aikido had stand-up grappling. Seemed like I would be a very incomplete martial artist if I couldn't at least do that.
Also the idea of not being prosecuted for self-defense seemed nice.