Ruled Surfaces II

 Alternatively, a line can be given by two points, which yields a slightly different definition: Given two curves ${\bf X}(t)$ and ${\bf Y}(t)$, a ruled surface is the image of the function $$f(s,t) = (1-s) {\bf X}(t) + s{\bf Y}(t).$$ This corresponds to Olivier's process of threading a string through holes in two brass "curves".