Regarding your vision...points...line...racet
rack ideas, I believe you may be led astray by the wonders of your intact peripheral vision.
That is, where you talk about viewing the start point and some half-way point down the track and then tracing a straight line from point A to B, in my low-vision condition (which I often consider a special gift), I have become aware that without decent peripheral vision, viewing point A does not mean also viewing point B. Or, viewing the words on the left of a post on screen, does not include also seeing the words at the right end of the same line of text. And, it seems to me that locating point B with the fovea or one's central vision under the reduced, low vision condition is more of a random walk and NOT a straight line trace. Finally, one finds and focuses on the location of point B, but then, point A has usually disappeared.
It may seem like I am lamenting my loss, but I am really trying to point out that what ~people are running is a ~two-layered system where peripheral fields of vision give an overall background view, and within that is nested the roving fovea which seems to perform the line tracing that you describe. I am saying, the straight line trace only occurs given the concurrent background view.
Interestingly, I think, these nested and separate vision systems are very much like attention wandering around in the un-sub-conscious terrain, focusing upon various points of interest. The fovea is like a visual attention.