monocular, binocular, and trinocular vision for vertebrates with regular complex eyes. Not going over simple or compound vision.
here is a video that breaks down how monocular and binocular visions fields work:
and here is an image showing how the location of the eyes can change the way the vision field works:
(image description: two diagrams showing the visions fields for a cat and a horse. the cat has a wide triangle of binocular vision where both of its eyes can overlap their view, while the horse has much wider ranges for each eye but a very small overlap between the two eyes. end description.)
Having one eye like a cyclops or being a two eyed creature missing one eye for some reason would only produce a monocular vision field, which lacks a lot of depth perception. monocular vision can only see things from one angle at a time, so it's harder to compare how far away things are, or how big around something might be. it's not impossible to perceive depth with only one eye though! if you test it yourself by closing one eye, you'll notice how much smaller your field of view is without the extra peripheral, but you probably won't have too much trouble judging the distance and location of things in your immediate area, though it might be harder in an unfamiliar location. The farther away something is, the more difficult it will be for monocular vision to judge that distance.
a lot of herbivores rely on monocular vision. they have two eyes, but only a small overlapping area between their vision fields, so for the most part they have two separate monocular vision fields. they prioritize being able to see as wide a field as possible and reacting to unusual shapes and movements.
many predatory animals rely on having more effective binocular vision, having better depth perception with a narrower field of view. it's a more precise way to see, very good for detecting and keeping track of motion, judging distances, etc. you can see objects from two angles at once, giving a better sense of how big they are and where exactly they're located.
so how would trinocular vision work? would it have any extra advantages? Well, it's hard to say if it would be an advantage or not, since different methods of vision serve different purposes. but adding a third eye to something like a cat would certainly alter its vision field, and it might be more useful for such a predatory creature. it would, at the very least, provide one more angle of view. seeing things from one slightly higher angle than the two other eyes. not drastically different, just a slight change. it's hard to draw fully 3d vision fields in a way that fully illustrates how they overlap on every angle, but i have done my best to show the trinocular vision field here.
(image description: a simple sketch of a cat with a third eye on its forehead. in front of each eye is a colored field like a slice out of a circle, showing where each eye's vision overlaps with the others. it does not look much different from the binocular vision field, having a wide range of overlap in front of the face. end description.)
I wasn't sure how wide to go with the center eye's vision. how much would the placement restrict its peripheral? does it have an equally wide, more narrow, or more wide field of vision compared to the other eyes? those are all questions I think you'd have to answer for yourself if you're creating a trinocular creature. the wider the field of vision is for the third eye, the more it overlaps with the other eyes. this would make the binocular vision fields much wider on each side, essentially giving the creature more precise side vision and then creating a triple layer of vision in the middle. whether this is more helpful or more confusing is up to you I guess! like having two regular screens on each side of your head and then a 3d screen in the very front. I imagine the third eye might have a broader range of peripheral vision above the head.
I'm sure someone who studies vision more professionally than me could say a lot more and go into some real detail about the matter! this is all I can manage. maybe it will spark more ideas for someone else!
