Closest point of line segment without endpoints I know of a formula to determine shortest line segment between two given line segments, but that works only when endpoints are included.  I'd like to know if there is a solution when endpoints are not included or if I'm mixing disciplines incorrectly.
Example : Line segment $A$ is from $(1, 1)$ to $(1, 4)$ and line segment $B$ is from $(0, 0)$ to $(0, 2)$, so shortest segment between them would be $(0, 1)$ to $(1, 1)$.  But of line segment $A$ did not include those end points, how would that work since $(1, 1)$ is not part of line segment $A$?

In this case. there is no shortest segment.  If you make the segment from $(0,1)$ to $(1,1+ \epsilon)$, a shorter one is from $(0,1)$ to $(1,1+ \epsilon /2)$
