Finite geometry is easily illustrated:

Click to enlarge.

I don't see the lines receding infinitely, linearly, and continuously into the distance. Do you?

The Ancient Greek model taught in schools is a H-Y-P-O-T-H-E-S-I-S.

The concept of finite perspective lines also has consequences related to the rotation of receding overhead objects.

An object suspended one foot above your head, that recedes into the distance, will rotate to perspective quickly. An object suspended 10 feet above your head that recedes into the distance will rotate to perspective a little slower, and slower still as the object increases its height.

The perspective model of the Ancient Greeks predicts that the perspective lines recede infinitely without connecting, and therefore the object will never reach a point where it stops turning.

If the Ancient Greeks are wrong, and a finite geometry model is correct, then the usual point of infinity is actually at a finite distance and an object will stop turning at a finite distance away.

The particular makeup of finite perspective geometry might subject to a number of properties; perhaps that there is a difference between overhead and horizontal positions/motions -- but that is speculation until additional empirical data can be generated on this subject.

At the moment, much of the true nature of perspective seems to still be a question mark -- hence the multiple non-euclidean geometries that are in competition to each other, none necessarily demonstrated to be wrong to the world, as there is no good evidence for what happens at real world limits.

Rowbotham did demonstrate in his chapter

Why a Ship's Hull Disappears Before The Mast Head that perspective seems to operate on multiple motions on the horizontal, in contradiction to how traditional perspective theory is taught, showing that the postulates of Euclid are not necessarily true and, if the experiments are to be believed, demonstratively false.