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Hellraiser 
PH34R M3
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Joined: May 2000
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Posted on: Feb. 13 2002,22:21 |
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Okay, here's the deal. I'm currently enrolled at the Art Institute of Philadelphia, and my perspective drawing professor has told me two things about drawing in perspective that do not make sense from my background in geometry and mathematics. Since linear perspective is essentially a mathematical means of laying 3 dimensions down on 2 dimensional media, it seems reasonable to me that geometry should be applied to it and work properly. Okay, here's some diagrams of what I'm talking about:
This shows a basic perspective grid, with two rectangles drawn on it. The first one, in 1 point perspective on the left, is clearly 2 x 4 units. The second one, according to my professor is 4x6 units. However, they appear very close in size to each other. What's wrong with this picture? According to my professor, in order to draw a 2 point perspective rectangle on a 1-point perspective grid, you draw from a point on the front line on the grid, back to each of your vanishing points, count over the x units to the left, draw to your right vanishing point, and count y units to the right, draw to your left vanishing point. This yields, according to him, a rectangle x units by y units in size. Unfortunately, it looks wrong, and doesn't hold up geometrically: check out this top plan diagram of the two squares:
As you can see, the blue rectangle is not 4x6 units. And according to my professor's method, the purple line and blue line are the same length. Bullshit!!! Apparently no one ever taught him about the pythagorean theorem or even the least bit about geometry. Unfortunately, whenever I try to explain this to him, his answer is, "You're wrong." He cannot tell me why I'm wrong, just refuses to consider the fact that I could be right.
My method involves looking at the floorplan, measuring the angle between purple and blue, using trigonometry to find out the length of the purple if the blue is 6 units, and then drawing from this distance on the front line, repeating process for the second line. This will yield as far as I can tell, a rectangle with the correct proportions.
Which brings us to drawing a circle in perspective.
Below is a diagram that I drew with a circle inside a square in perspective (black) and his idea of a circle inside a square in perspective (red):
According to him, the circle should be tangent to the sides of the square along the major axis of the elipse drawn to represent it, because that's the widest point in the elipse. My contention is that the circle is tangent to the square along the line parallel to the sides of the square that bisects both square and circle. Thus when drawing the elipse to represent the circle, one must make it slightly narrower than the perspective square along its major axis (my black elipse).
To illustrate from top view again, what he is saying, look at this illustration:
This shows my circle, in black, and his circle in red. Which one is in fact a circle within a square? Again, his only reply was, "You're wrong" when I brought this up. When he couldn't answer my reply, he merely said, well its just an illusion of 3-dimensions, thus what you think and I think doesn't matter, it only matters what looks right. When I pointed out that mine looked more correct, he said that was because I had drawn it wrong. What the fuck?!?!?!?!?
With professors like this out there, its no wonder that people are graduating from college without understanding the material they have spent 4 years studying. I'm glad I have a solid background in geometry, because perspective drawing skills are crucial in the animation field, which is what I intend to get into.
Edited by Hellraiser on Jan. 01 1970,01:00
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I wonder if those who are sleeping in the ground are disturbed by the throbbing sound of our One Way Path to Eternity...
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| Post Number: 2
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Rshias
The Insomniac
Group: Members
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Posted on: Feb. 14 2002,02:53 |
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Maybe I missed the gist of this entire thing, but I think you're asking about why the lights (as I take them to be) aren't casting a correct image on the floor? Are the lights supposed to be shining with the same angles? I'm not entirely sure what effect you're trying to demonstrate here.
As for the circles, the logic behind them appears accurate. How the professor got the red ones remains a mystery.
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Sleep is for the weak.
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| Post Number: 3
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Hellraiser
PH34R M3
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Posted on: Feb. 14 2002,03:08 |
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No lights... the light blue lines are simply illustrating where the vanishing points are for the second rectangle. I did them in light blue so they'd be distinct from the grid. The idea is you're looking down at the ground, with a bunch of square tiles. I've layed out two rectangles on the square tiles: the line across the top is the horizon, the two red points are vanishing points for the second rectangle which is in 2 point perspective: i.e. it is not parallel to the plane of vision like the first (red) rectangle. It is cattycorner.
The point was that the professor was trying to tell me that the hypotenuse of a right triangle is the same length as one of the other two sides, and as we all know, the hypotenuse is equal to the square root of the sum of the squares of the other two sides, therefore, it is the same as the other side only when it coincides with said side, which only happens when the rectangle is in 1 point perspective, like the red one.
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I wonder if those who are sleeping in the ground are disturbed by the throbbing sound of our One Way Path to Eternity...
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| Post Number: 4
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editor
forum whore
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Posted on: Feb. 14 2002,04:08 |
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Well, wouldn't it be fun to show this to your old Trig/Geometry proffs and let them duke it out with this prick? I'd like a full report on the fireworks! heheheh
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| Post Number: 5
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PTL
I Ish A Duckie!
Group: Members
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Joined: Feb. 2002
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Posted on: Feb. 14 2002,04:30 |
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Honeys, I sure wish I could see the images you're questioning. I sorry 
BTW...I miss talking to you. My work sucks. 
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[quote][I][B]Wolfguard:[/I][/B]
The women like me cause im hung like a baby.
8lbs 22 inches...[/quote]
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| Post Number: 6
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ASCIIMan
-- Insert Witty Title Here --
Group: Members
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Posted on: Feb. 14 2002,04:31 |
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Just remember... One step on the way to his becoming an art professor was probably failing all of his math classes.
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| Post Number: 7
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veistran
We don't listen to people that don't like us.
Group: Members
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Posted on: Feb. 14 2002,04:56 |
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| Quote (ASCIIMan @ 13 Feb. 2002,02:31) | | Just remember... One step on the way to his becoming an art professor was probably failing all of his math classes. |
He probably also failed history, and just about everything else... "Momma sez that Alligators is 'ornry cuz of all them teeth they have." 
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V|-
"Headed down the hard way
Concrete battleground
Urban monkey warfare
Sabotage underground camouflage"
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| Post Number: 8
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Wiley
©0®ÞØ®4+3 whØ®3
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Posted on: Feb. 14 2002,05:47 |
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mmm ...two point perspective ...brings back a lot of memories. (I studied art in school before I became a geek) I think the issue here is that you are trying to use math to mimic perception of the natural world. This will always come and bite you in the artistic ass in the end. I was always taught to use geometry as a guide and then fuzz the edges a bit depending on elements you want to add or imply in your image. Take railroad tracks for instance, geometrically speaking they should vanish to a single point on the horizon. If you drew this picture it would look like a poor attempt to draw railroad tracks going into the horizon, it would never look real because it's not the type of thing you see in the real world. You got to make the tracks come together just short of the horizon with a tiny bit (really tiny and a bit blurry at the point of intersection) of a line going straight up to greet the horizon. This would account for the fact that you have two eyeballs and can't accurately calculate where on the horizon the two points would meet ...each eye has a slightly different point of reference. It would also add a slight valley to your image ..because it's never perfectly flat to the horizon. You could also have the tracks meet the horizon just before they make contact or without making a sharp point to add a bit of a hill or downward slope to your picture. The same with buildings, you have to exaggerate the perspective a bit to make it look more [i]real[/]. This is where talent surpasses mathematics in the art world and why computers cannot generate believable images ...they don't understand imperfections. Remember, humans are used to looking at the world from about 6 feet (5 feet for Nikita) above the plane that you are trying to use as a reference point ...and from two different angles at once. Take a good perspective drawing and overlay your geometric grid on it, does it line up perfectly?
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There's a sucker born every minute ...but swallowers are hard to find.
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| Post Number: 9
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Hellraiser
PH34R M3
Group: Members
Posts: 977
Joined: May 2000
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Posted on: Feb. 14 2002,12:05 |
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I can show you a few good perspective drawings using linear perspective, and every time they use a perspective grid similar to the one I've shown, only slightly more accurate. The point is not so much about rigidly following mathematical rules as exposing two erronious ideas about perspective drawing that my professor is trying to teach us. Regardless of how close to reality the final output is, his methods look worse and make less sense than the methods I use and will continue to use in perspective drawing.
With a computer, it is possible to render images that proportionally are just as close to reality as images shot through a good professional camera, because the way light travels through the lens can be mimicked exactly by mathematical means. However, the real reason a cgi image doesn't look real is because we have no way yet to make it detailed enough. The human eye can distinguish details down to 1/100th the width of a human hair, and to make scenes this detailed by computer would require astronomical polygon counts and massive textures. It is relatively easy, through modelling, atmospheric effects, and texturing, even lighting, to mimic imperfections in an image, so that is really not the issue.
Obviously it is impossible to mimic exactly what the eye sees on a 2-d plane, however one can give a very believable substitute using proper perspective drawing. When I've finished the one I'm working on, perhaps I'll scan it and show you all. But regardless of how much you want to fudge the end result to make it aesthetically pleasing, its not gonna look like it should if you use shody methodology to come up with your reference points, and the like.
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I wonder if those who are sleeping in the ground are disturbed by the throbbing sound of our One Way Path to Eternity...
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