Rather than simply recapping Homer's plot, Kubrick runs variations on the main themes, testing man at different stages to similar events, like testing metals to the fatigue point. There are resonances with Plato's cave. Film audiences in the dark watch a distorted shadow play on the wall. Modern man walls out the unknown even as he explores it. No one in the film looks out the window to see where they're going except pilot functionaries.
Most vehicles have tiny or nonexistent windows.
When Floyd uses the picturephone he completely ignores the rolling earth beyond. Even Discovery's pods are myopically designed, one of the few clearly nonfunctional elements. Poole and Bowman plot against the cyclops inside a pod which is a cave within a cave. The pods are also like the cyclop's flock of sheep, which Odysseus' crew tied themselves to whle escaping the cave. Contrasting Homeric cyclops behavior, HAL doesn't want to eat them, but spit them out.