Something important to understand about what you're thinking of, the most common formula for two-dimensional ancient Egyptian funereal art, is that it was to a great extent a tool to give a component of the soul called the "ka" somewhere to live after death. This is what the mummification process was for as well, but since immortality was an important matter, they wanted as many backups as possible.
We think of representational art today as primary illustrative, so this is perhaps a bit alien to us, but because of these religious views, the ancient Egyptian formula for two-dimensional depiction was designed on a sort of functional/conceptual basis, rather than an optical one. The deceased would want the best two-dimensional facsimile of a complete human body that was available, and that didn't necessarily mean photorealism (or, at least, photorealism doesn't seem to be the solution they went with).
In a two-dimensional image, they therefore felt the need to show the most accurate possible view of each individual part of the body. Thus, we have front-on eyes, torsos and hands, and side-view legs, feet, and faces. If you look at the statues of the period, you'll see that they were pretty spot-on in terms of proportion, because there's no translation really necessary if you're already working in three dimensions and their artists genuinely were quite skilled.
Gardner's Art Through the Ages is where I'm getting this. I wish I could provide a source you could look into that's more totally devoted to the topic, but just being a college student who learned this in class last month, I can't.
The Fayum mummy portraits - so-called because these were paintings done on wooden boards that were attached to mummies - are a good example of naturalist paintings of people from the ancient world.
Coincidentally, these portraits are also ancient and Egyptian, though by "Egyptian art" I'm assuming that you were probably referring to Old through New Kingdom Egypt. These portraits date to when Egypt was a part of the Roman Empire.
hi! not discouraging expert on Ancient Egyptian art from providing more detail specifically on that culture, but fyi, you'll find lots of related discussion - including several references to Egyptian art - in this section of the FAQ