# bounded deviation for straight line motion

I came across the paper(link given below) which discusses about bounded deviation joint path for straight line motion.

Planning and Execution of Straight Line Manipulator Trajectories (RH Taylor) https://pdfs.semanticscholar.org/e01a/58608f4e68f31c7b9e7cdbddceae645727bb.pdf

In this method, the assumption is that the maximum deviation happens at or near the midpoint between the start and end point.

1) Is this assumption true in all cases? 2) Even if the assumption may not be true, will resulting trajectory be a straight line if this method is used for trajectory planning?

I hope someone shed some light on this. Thank you.