[Alpha_Meta]

I've been trying to figure out Loomis's explanation for finding depth in perspective:



and I'm at the point where I'm ready to conclude that he's wrong about "one half the picture area of the ground plane being taken up by a distance equal to twice the height of the viewpoint. I've done an experiment in real life to test this. What I found is that one half the picture area of the ground plane is taken up by only a distance equal to the height of the viewpoint. Not twice the height.

Simple geometry would seem to back up my observations. The human field of vision is roughly 180 degrees - maybe more in some people, less in others. That means if you set 0 degrees straight out, looking at the horizon, you're field of vision will extend down through a 90 degree arc to your feet (which is what I observe. I can't see my feet in sharp detail, but I can see them in peripheral vision).

Half of that 90 degree art is going to be 45 degrees. I measured myself out on the ground, and while standing on one end of the measurement found that the other end lined up roughly with a 45 degree downward angle while I was looking straight ahead. I observed the distance from my feet to 5' 10" out (the height of my viewpoint) to occupy "half the picture area of the ground plane." Twice the length of my viewpoint would have taken up nearly 3/4's the picture area of the ground plane.

Simple geometry would seem to back this up:



Can anyone prove that Loomis is right, or that I'm wrong?

[Lionel]

The mistake you are making is that the human field of vision is only 90 degrees. This only makes it a 45 degree angle arc towards your feet. If you draw your diagram again with half the field of view you will find everything will work out.

If you have a game like quake 3 you can see that the human field of vision is only 90 degrees. You can change the field of view to any angle you like (as long as it is less than 180 degrees iirc). Go to the console and change the value of cg_fov by typing:
\cg_fov 100
for example which will give you field of view of 100. You will find that the one that looks best is 90. Mind people like to play with their fov in quake higher than that so you can see more . Who would have thought that comupter games could be so educational

[Alpha_Meta]

Uhm try stepping away from Quake for a minute in the real world you actually do have a 180 degree field of vision. It isn't acute near the edges but it's there. Hold out your arms and wiggle your fingertips you ought to at least be able to catch the motion.

[AndyT]

I think Quake is right.

Search google for "cone of vision"
_________________
http://www.conceptworld.org

[Alpha_Meta]

[Lionel]

Rofl Well I can assure you that your field of vision is 90 degrees. If you think about it carefully you can clearly see that there is no way your field of view can be 180 degrees after all the bit of your eye that is receiving the light is inside your head. If you did have a 180 degree field of view you would spend a lot of time looking at the inside of your eye.

Rember that the process that 3D games go through to turn 3D models into a flat representation of an image is exactally the same calculation that loomis is doing in his example (which is why I gave it as an example). All the theory of perspective in drawing all comes from the same math that is used in 3D computer games as what you are doing in these games is simulating the way the eye works.

[Impaler]

Close one of your eyes, smarty pants. Your vision will be more like what Loomis is talking about. We have 180 degrees of binocular vision.

Since you can't easily translate binocular vision into 2-D (not without complex vanishing points, etc etc.), Loomis is assuming that you would draw with one eye closed, which is a handy trick that lots of artists use anyways for flattening perspective and framing pictures.
_________________
QED, sort of.

[Tedsuo]

Lionel, if you simply look straight ahead, hold your hand out to the side, and wag it about, you will see that your range of vision extends far beyond 90 degrees. You can do this because your eye has a curved lens.

Edit: Impaler, you would have 180 degrees of monocular vision if your nose didn't get in the way.

Linear perspective like that found in 3d games and Loomis's perspective tutorial is an approximation of the way we see, not an accurate representation. Our vision is quite warped, like a "fish eye" lens, but our brain corrects for this automatically, so it's hard to notice. Also, we only "look at" things with a very small section in the center of our vision, called the fovea. You can notice this as well: stare at something, and try to "look at" other things in your field of vision. You'll notice that everything ouside of that small central circle is blurry and indistinct. Also, it fades to black and white near the edges, but again your brain corrects for this so it's hard to notice.

Anyways, to answer your question Alpha_Meta, linear perspective works because within the narrow range of the fovea, the ammount of warping is minimal. It's not a representation of how we see, it's an approximation of how the very small center chunk of our eye sees. What Loomis is saying is, "according to the math that makes that look right, here's some nifty tricks to help you control the scale of your drawing."

Make sense?

-T

[Lionel]

Tedsuo that is a much better explanation then me . I was tring to give an extreme example of why you filed of view was not near 180 degrees after all you can't see you chin .

Determing your field of view experimentally is quite hard. At the periferals of your vision the bits of your eye that receive the light are predominatly rods (I bet I get rods and cones the right way round ). This means at your visions periferals you can only see in black and white. Also rods are more sensitive to light than cones (which detect color) which is why at night you can often see better in your periferal vision at night. The way the brain seems to be wired up is that it is very good at detecting movement in you visions periferals but you don't see obects. This means that when you move a hand in your visions periferals you will see the movement but not really see the object. Also the brain warps and process the image we receive what we actually see probably bears very little resemblance to what information is received by our eyes.

I had a very interesting course at Uni about how the brain actuall processes the information you get from your eyes. They really don't know that much but there are all sorts of interesting things like edges being amplified so you see the eges of things more clearly and also how you don't seem to see true color but you see a color as an absolute value but you see more as a relationship to the colors around it. You can see all this for yourself but looking at thouse silly eye puzzle things. If people are interested I might be able to dig a few up.

Our vision is not just fish eyed but there are big gaps in it like where your optic nerve enters the eye. The brain componsates for all of this and the final effect seems to be the same as having a field of view of 90. You can check this out in a computer game like quake trying different fields of view and seeing if they look funny or not. Like Tedsuo said the reason for this is that there is a very sensitive middle bit of the eye that is the bit our eye actaully sees object with and it is this that determins our filed of view.

I should have written all this to start of with. ahh well

[Alpha_Meta]

Lionel - Here's a diagram of the eye:



As you can see the part in the red square, the part that first picks up the light, sticks out from the eyeball itself. I think you can probably see how it can pick up light from 180 degrees, but look at the retina (inside the blue line) too. It clearly encompasses more than a 90 degree hemisphere, even a little more than 180. I think that's because it actually has a 180 degree field of vision.

Impaler - I've seen 120 degrees of binocular vision quoted on eye anatomy sites. I'm not sure why it isn't higher, although I'm guessing it's because the bridge of the nose prevents a large area of each eyes field of vision from overlapping.

Tedsuo's right about having 180 degrees of monocular vision, except that he should probably say part of it is taken up by seeing your nose. I'm nitpicking though. The point is, the 180 degree field of vision is still there whether you close one eye or not.

Tedsuo -

[Tedsuo]

You can't see your chin because your lips get in the way. Which you can see, if they're big enough. But yeah, most of what you said is right on. However:

[Lionel]

Right you have you yourself in a complete muddle. The first think you need to think of is what am I trying to achive. The answer to this is you want to be able to draw 3D objects like sphere on a piece of paper so that they apear to be 3 dimensional. Forget completly about eyes for the moment. Now if you look at the loomis diagram what he is saying is when you are drawing a 3D object onto a piece of paper you are projecting that object onto the piece of paper with a field of view of 90 degrees. Why 90 degrees well experimentally that is what seems to work best.

Given that your field of view is 90 degrees loomis makes that correct assumsion that one half the picture are on the ground plane is taken up by a distance equal to twice the height of the viewport. Now I have just tried this and it seems right to me.

But if you are still not convinced then go into a computer game and try out some field of view values other than 90 degrees and it will quickly become apparent that 90 is about the right value.

The problem you are having is why your field of view is 90 degrees and the answer to that is it is very hard to explain as we don't know how the brain processes the data from the eyes but a lot of it has to do with the size of the fovea which is the sensitive bit of the eye where all the cones are. Rember that you can detect light on parts of your eye that are not the fovea
so you will be able to see things not in your fovea but your brain seems flattens the image so you get the impression of image with about a 90 fov which iirc is about what the fovea detects.

[Alpha_Meta]

Lionel -

[Alpha_Meta]

Hmm - come to think of it Loomis's second illustration is right for one point perspective. My guy's pretty clearly in 3 point perspective since he's tapering off at the bottom. Interesting.

Now I wonder why Loomis's halfway point doesn't line up with a 22.5 degree angle?



I think I'm going to leave my previous post up there if no one minds. I may want to refer back to it later.

[Lionel]

You are you trying to relate the top three diagrams and the bottom diagrams but they quite clearly show different things. The top digrams show what happens if somebody is looking straightahead of them. The second diagram is quite clearly an ilistration of how the base line scales when using one point perspective. In no way is it meant to be an ilistration of what the human eye can see. After all if the lower diagram was the same as the bottom one they would have the same scale and you would only be able to see from 8 ft onwards.

[Alpha_Meta]

O.K. I think I see what's going on here now. The half way line in the 2nd illustration is at 26.4 degrees instead of 22.5 degrees because of the distortion of 1 point perspective. In reality "what the man sees" would probably look more like this:



But without perspective on the vertical acccess "what the man sees" gets flattened into that plane.

Loomis's third and fourth illustrations make sense if they're drawn inside the 90 degree picture plane he favors. So, in the last illustration, where it says 0 on the base line, it's really 8 feet away, where it says 16 it's really 24 feet away, etc. That was not at all clear.

Now, on to 2 point perspective.

[Lionel]

Hmmmm I was a bit ill yesterday and lookiing at the one point perspective diagram I think loomis has got the scale along the base line wrong. Sorry about my last answer being misleading that but was having bad day yesterday and wasn't really thinking straight. There is no reason that one point perspective should distort things and infact the reason it works is because our field of view is 90 degrees. If you ignore loomis' scale on the base line and start it off at 8 feet with 16 feet at the mid point then the digram should be right. I am a bit busy atm but if I get some time i will draw up a correct diagram. Incidentally the digram does ilistrat the point he was trying to make which is that the mid point line (The Line AB) is at 16 feet which is twice the height of the baseline. It was just the rest of the diagram which is a bit off (Just shows none of us are perfect).

[Capt. Fred]

I was just browsing and saw this thread and I'm not really part of the loomis 'debate'.

To find out about field of vision i tested it out: Staring straight a head I can see my fingers wiggling at the ends of my outstretched arms, but with my arms vertically above my head, i cannot, and neither can I with arms below. Standing infront of the mirror (so I'm looking eye-level straight a head) with one arm jutting out from eye height and my tongue out like a baboon, and with rulers and straight edges jutting out from my temple, I seemed to find that I can see my tongue when it's within an angle about 40-50 degrees below horizontal. And I can see my fingers above me when they make about the same angle above horizontal.

With this 90 vs 180 degree vision disagreement, is it not possible that horizontally we can see 180 (which I know is true of myself) and vertically we can see only 90?

From my own (absurd) observations I feel this true, and it wouldn't seem unreasonable given the 'eye-shape' which is wide enough to leave the whites visible at the sides and squat enough to cover the top and bottom parts of the lens.

And infact, sitting here, I just realised eyelids and eye shape do have major affect on field of vision: With arm vertically above head fingers wiggling, looking straight ahead and with eyes wide wide open I see no movement; lowering my arm until I do and keeping it there, I find that relaxing my eyes (eyelids) means that I can no-longer perceive that movement, opening wide again i see the movement again.
So I think it's 180 horizontal, 90 (for relaxed eye) vertically.

I haven't actually read every post so this could well be a redundant post, but it was fun in front the mirror trying to figure it out! lol see ya guys

[Alpha_Meta]

Lionel - I'm down with something today too. I don't have enough energy to see if what you said is right or not but it sounds sorta like what I wrote last time.

One point perspective is distorted because it doesn't have perspective on the vertical axis.

Capt. Fred - I can see past a negative 45 degree angle vertically, no problem. My brow ridge limits my upper field of vision but I don't doubt that the eye could see more if my face weren't in the way. I think Loomis's 90 degree vertical field of vision is only what he considers useful to an artist, and what 1 point perspective can work within without too much distortion.

When I feel better I'll post some stuff on 2 point perspective when I feel up to it. One thing I noticed, looking at the next page in Successful Drawing where Loomis explains 2 point perspective, is that there doesn't seem to be any way to guage depth. Depth is determined by the two vanishing points, and his only advice on placing them is to set them far apart. I don't like the sound of that at all.

[aphelionart]

hey alpha... if you can figure out how to judge vanishing points, i'd love to hear it! that's the part i got caught up in too and it seems like loomis just left it up to intuition.

-matt