Foreshortening

Foreshortening usually refers to the Perspective of Diminution applied to a single object.  Not all objects present themselves to us in full frontal view or in full profile.  As an object rotates, that part of the object which is further removed from the observer will appear smaller.   Xu Beihong's horse has small hindquarters compared to its chest.  Even more dramatic is the compression in depth. Xu renders the horse about the same measurement from shoulder to rump as across its chest. Even though we know this cannot be true, it appears to agree with what we actually see when we view an object at an angle.  It is important to note that the further the object recedes in depth, the greater this compression will be.

Xu Beihong Running Horse 1942
http://www.chinaonlinemuseum.com/painting-xu-beihong-horse-galloping.php

The battle scene on this Krater shows the Persian soldier pivoting as he falls.  Note that his left foot is rotated toward the observer and is foreshortened convincingly.  We see the Greek soldier's shield in 3/4 view, and it seems properly compressed in depth.  So the Greeks appear to have understood Foreshortening, but not all artists were using it, and surviving examples are sporadic.

Greek Soldier and Persian Archer 430-450 BCE, Antikenmuseum und Sammlung Ludwig, Basel
https://commons.wikimedia.org/wiki/File:Classical_calyx-krater_ARV_extra_-_Persian_archer_-_Greek_soldier_fighting_Persian_archer_%2802%29.jpg

Aside from ceramic decoration, Greek pictorial art is very rare.  In this wall painting from the tomb of Phillip II in Vergina, the horses and chariot seem to run on the diagonal past us. The painter has compressed the chariot wheels, and the background figure is smaller, so clearly there was an understanding that objects diminish in depth as well as in height and breadth.  The horse's shoulder however, is lower than its hindquarters, so the artist's understanding of Foreshortening seems to be intuitive rather than geometric.  That does not however, take anything away from the vitality of the action, and our understanding of the spatial representation is perfectly acceptable.

The same applies to the randomly foreshortened shield in the Roman fresco below. It is not as dynamic as the Vergina fresco, but we still fully understand the relationships between the characters, and the narrative is still perfectly clear to us.

Royal Macedonian Tombs at Vergina, ca. 350 BCE,
https://www.worldhistory.org/article/1490/the-royal-macedonian-tombs-at-vergina/

Hephaestus Offers Thetis the Armor of Achilles Frescoe, 1st Century CE, National Archaeological Museum of Naples
https://www.worldhistory.org/image/12710/hephaestus-offers-thetis-the-armor-of-achilles/

The Roman architect and commentator Vitruvius (De Architectura, Book VII) says the Greek scenic designer Agatharchus was the first person to create painted scenery using a geometric linear perspective, and that he wrote a commentary that must have been a framework for consistent use of both Diminution and Foreshortening.   Unfortunately, neither Agatharchus' backdrops, nor his description have survived. Vitruvius is the best information we have, but he was writing almost 500 years after Agatharchus.  If the Greeks did understand how to do a geometric linear perspective, they were certainly not applying it universally