Strictly speaking, isn't a line (what you're looking for) no a parabola (how you describe pads)?
Parabolas come in the form Ax^2+Bx+C=0, whereas lines com in the form Bx+C. Although both still polynomials, they have different ways of computation, right? You couldn't solve a Bx+C through the quadratic formula because you would be dividing by 0 (math's way of saying you made a big no no). And even then, how would you arbitrarily find it? Because like a line has a parabola's equation with A 0, your specific line sets B=0, or just C. I don't know about the quake engine, because I haven't programmed for it or anything, but when would it ever be useful to make that? I'm assuming they define a couple of entities:
Climbable
Surface
Air
This game engine seems mildly based on physics. The general consensus is that you fall towards the x-y plane, if the z-axis is your height. Therefore, it is probably easy to define movement in "air" to be "AHHH I AM FALLING". I don't think they built this with space in mind, though I could be wrong. If you played the original quake, feel free to prove me wrong.