Hello folks, I'm cross-posting from sci.mat, sorry.
I have the following problem, but not the solution, that's why I'm writing to you.
The context is a 3D world where I need to find out the distance between a torus and a line. Indeed, what I realy need is the collision point of a Torus centered in C=<p,q> (the torus can only move along the Z axis) with a line that lies below the torus itself (I'm sure that the line is below and the torus is going to collide). I also have two point: A=<Ax,Ay,Az> and B=<Bx,By,Bz>, that describe the segment of line where the torus will collide.
I've tried some ways: parametrizing a point on the segment and then looking for the minimum distance between that point with the torus, playing with points projections on the segment, but not one give me the solution.
I'm asking you if you know a theorical aproach that can describe the answer. Even the torus-line distance could be a shot!