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Thread: Draw a perfect square using two vanishing points

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    Quote Originally Posted by daafone View Post
    Can we please talk only about my question? This thread may be useful in future to others, so why do we have to flame?
    Sure, your question is best answered by practice, study and effort to understand the principles of perspective. A variety of books, that make sense to you, will be the best guide as you practice many of the challenges you will face when trying to learn perspective.

    Because Anid called me out on what I thought was the best advice I could offer.

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    Thanks for taking the time to draw that up, arenhaus. I'm curious about why the rightmost two points on the elevation (thought that was actually a "plan"?) square are directly below the points on the perspective square, while the rightmost point on the elevation square seemingly isn't directly below the corresponding point on the perspective square. Is that a property of perspective, or am I looking at the diagram incorrectly, or is it tiny accumulated errors, or something else?

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    Pretty sure you're right on the money there arenhaus - sort of reverse engineering a bit to get the plan view then moving forward again to establish the perspective. Nice job!

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    Quote Originally Posted by Cider View Post
    Thanks for taking the time to draw that up, arenhaus. I'm curious about why the rightmost two points on the elevation (thought that was actually a "plan"?) square are directly below the points on the perspective square, while the rightmost point on the elevation square seemingly isn't directly below the corresponding point on the perspective square. Is that a property of perspective, or am I looking at the diagram incorrectly, or is it tiny accumulated errors, or something else?
    After puzzling through this a bit, I can elaborate my question. In step #3, I expected you to draw a line between pt A and the rightmost point in the perspective rectangle, and then drop a perpendicular from where that line crosses the HL to find the width of the rectangle in plan. If you feel like wasting more time on this, I'd love to learn more

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    Quote Originally Posted by arenhaus View Post
    I built this demo rather quickly from memory, so double-checks are welcome.
    That's a really helpful Fucking Manual for many to read. Note that it is limited to squares with the frontmost point dead in the center of vision, horizontally. I prefer to start with the stationary point and take it from there.

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    Quote Originally Posted by arenhaus View Post
    It's very much a science, Kev. If you "fake it" and eyeball everything, it does not mean that there is no method to do it precisely.
    Don't misunderstand me. I am a firm believer in the genius of the system you just gave a primer to. (Particularly fascinating is the addition of elevations and floor plans into the mix. It took a lot of brilliance to figure all this stuff out) I encourage every artist to learn it, master it, love it, appreciate it. Etc.

    However, it is a technique. It is not science.

    A linear retreat of perspective is not what actually happens as an object retreats from the eye. The fall off just seems linear from a certain distance. Objects actually retreat from our vision under much more complicated equations, the solutions to which become more or less asymptotic/indistinguishable with linearity beyond some distance only.

    Secondarily, the surface of the earth is curved. The consequences of this are enormous. Anything based on a single horizon line and straight perspective lines beyond a certain point will be incorrect because of the curvature of the plane at a distance, and will be even more curved at the deepest corners of our vision field. Any particular building can be correct in planar perspective in relation to itself (assuming good carpentry.) But using the same parameters to orient another building which is miles from it in the distance will not be a true relationship.

    So, taken together - the falsity of the use of perspective for things in close, and the falsity of the use of perspective for things beyond a certain point... we must appreciate that what we are talking about is a technical procedure which just approximates things (and which is enormously useful in doing so.)

    Let me reemphasize: I did not mean to discourage the understanding of the perspective techniques generally in use by the student artist. It is essential technical information.

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    Quote Originally Posted by kev ferrara View Post
    Secondarily, the surface of the earth is curved. The consequences of this are enormous.
    I beg to disagree here: it is really not noticable in daily life, just as it is not relevant for a carpenter.

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    Quote Originally Posted by Cider View Post
    Thanks for taking the time to draw that up, arenhaus. I'm curious about why the rightmost two points on the elevation (thought that was actually a "plan"?) square are directly below the points on the perspective square, while the rightmost point on the elevation square seemingly isn't directly below the corresponding point on the perspective square. Is that a property of perspective, or am I looking at the diagram incorrectly, or is it tiny accumulated errors, or something else?
    It's just a shortcut to get the scale of the square's elevation plan. Ultimately it does not really matter what scale the plan is, since every square with two sides lying on the same vp1-a and vp2-a lines will share the same diagonal vanishing point, so I just used the perpendicular.

    Of course, you'll want all other measurements to be done with diagonals from there on, or you'll get distortions.

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    Quote Originally Posted by kev ferrara View Post
    So, taken together - the falsity of the use of perspective for things in close, and the falsity of the use of perspective for things beyond a certain point... we must appreciate that what we are talking about is a technical procedure which just approximates things (and which is enormously useful in doing so.)
    Kind of like Newton's laws of motion are false, because you need Lorentz's model to get it really right... right?

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    As much as a certain evil part of my brain longs to see the extended dust-up that may result from this thread, I say arenhaus has given a rather clean and elegant answer to the OP.

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    Quote Originally Posted by kev ferrara View Post
    A linear retreat of perspective is not what actually happens as an object retreats from the eye. The fall off just seems linear from a certain distance. Objects actually retreat from our vision under much more complicated equations, the solutions to which become more or less asymptotic/indistinguishable with linearity beyond some distance only.

    Secondarily, the surface of the earth is curved. The consequences of this are enormous. Anything based on a single horizon line and straight perspective lines beyond a certain point will be incorrect because of the curvature of the plane at a distance, and will be even more curved at the deepest corners of our vision field. Any particular building can be correct in planar perspective in relation to itself (assuming good carpentry.) But using the same parameters to orient another building which is miles from it in the distance will not be a true relationship.
    It's like in calculus when you zoom in on a circle or a curve enough, it appears as a straight line. Though beyond a certain frame of reference, it's certainly not.

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    Quote Originally Posted by Cider View Post
    Thanks for taking the time to draw that up, arenhaus. I'm curious about why the rightmost two points on the elevation (thought that was actually a "plan"?) square are directly below the points on the perspective square, while the rightmost point on the elevation square seemingly isn't directly below the corresponding point on the perspective square. Is that a property of perspective, or am I looking at the diagram incorrectly, or is it tiny accumulated errors, or something else?
    I have simply taken a shortcut, for clarity. Since we are dealing with a perfectly aligned square here, it does not matter what the scale of the elevation plan is; all squares aligned to anchor point a like that will have the same diagonal and the same diagonal vanishing point vpd. So I had just used a quick and lazy way and plotted a perpendicular to get a referent.

    Now, if the square was not aligned to a, that would not work. This is a modified architect's method aimed at plotting a perfectly aligned square, remember? The full architect's method would have a at the viewer's position and two additional horizontal lines for the picture plane bottom, one in the elevation plan and one in the perspective plot. You'd use them to measure horizontal positions of each point, and diagonals to measure relative proportions. But in that version of the method, the elevation plan is much larger than the resulting perspective plot, and typically requires two separate pages.

    This simplified version is still very useful for plotting any square with sides parallel to the sides of the perfectly aligned one. You can use this perfectly aligned square's diagonal VP and the existing vp1 and vp2 to plot any number of squares not aligned to a, as long as their sides are parallel.

    So often it's worth finding a vpd for a rectangle perfectly aligned to a, and then just use the three VPs to plot the real unaligned rectangle - instead of bothering with the full-blown architect's method.

    After puzzling through this a bit, I can elaborate my question. In step #3, I expected you to draw a line between pt A and the rightmost point in the perspective rectangle, and then drop a perpendicular from where that line crosses the HL to find the width of the rectangle in plan. If you feel like wasting more time on this, I'd love to learn more
    Technically, yes, I would. But in this case I only needed to calculate the vpd, and so didn't bother to keep the scale right. The diagonal is the same for any size of a square perfectly aligned to a, remember, and in this particular case I don't need to care about distortions anywhere else.

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    Quote Originally Posted by kev ferrara View Post

    A linear retreat of perspective is not what actually happens as an object retreats from the eye. The fall off just seems linear from a certain distance. Objects actually retreat from our vision under much more complicated equations, the solutions to which become more or less asymptotic/indistinguishable with linearity beyond some distance only.

    Secondarily, the surface of the earth is curved. The consequences of this are enormous. Anything based on a single horizon line and straight perspective lines beyond a certain point will be incorrect because of the curvature of the plane at a distance, and will be even more curved at the deepest corners of our vision field. Any particular building can be correct in planar perspective in relation to itself (assuming good carpentry.) But using the same parameters to orient another building which is miles from it in the distance will not be a true relationship.
    kev
    I think the thing that really messes people in contructing perspective is all the straight lines.
    when you look around at things its all bending out at you.
    if you dont belive me sit in your chair and make a mosaic of shots of your surroundings. the walls will all bow outward along apparent curves as they come close and recede fom you.
    brainy just builds it all into a picture we understand.
    sure there are vanishing points, but theyre in every direction, and most objects higgledypiggldy.
    Buildings stand at funny angles on steep hillsides or along river banks.
    that and most vanishing points are usually way the fuck off the canvas your drawing on..



    those simple perspective excercises cant handle that so drawing anything that isnt boxy and perfectly alignedwith its surroundings is a nightmare.

    Straight line perspective constructions are quite good for architecture, tiled floors, toasters and streets.

    For mountains and coral and building sites theyre really not that helpful at all
    Youre pretty set if you just remember stuff close to you looks bigger than stuff thats far away.





    Quote Originally Posted by s.ketch View Post
    It's like in calculus when you zoom in on a circle or a curve enough, it appears as a straight line. Though beyond a certain frame of reference, it's certainly not.
    interesting that. but corners you can zoom on forever. like theyre different elementary particles of shapes.

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    Not only is the real world not built on infinite straight lines, your vision isn't a straight line, either... It's a combination of input from two eyes at different positions, and includes a chunk of information from peripheral vision, all mixed together and edited into a presentable form by your brain...

    So perspective only gives an approximation of what we actually see, or think we see. It's good for getting you 90% of the way there, but to make a picture "look right", you generally need to do a little eyeballing and adjusting after you've done the technical part of the perspective.

    This is why un-adjusted 3D scenes often look weirdly distorted in places (especially near the edges...) They rely on formulaic perspective, and aren't tweaked by a human to "look right" to a human viewer.

    Oh, and if you wear glasses, everything is curved...

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    Quote Originally Posted by arenhaus View Post
    I have simply taken a shortcut, for clarity...This simplified version is still very useful for plotting any square with sides parallel to the sides of the perfectly aligned one. You can use this perfectly aligned square's diagonal VP and the existing vp1 and vp2 to plot any number of squares not aligned to a, as long as their sides are parallel.
    Awesome discussion--thank you! This really helped me understand the theory behind the method you demonstrated.

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    arenhaus: looks fine, you rock!

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    Quote Originally Posted by Velocity Kendall View Post
    Straight line perspective constructions are quite good for architecture, tiled floors, toasters and streets.

    For mountains and coral and building sites theyre really not that helpful at all
    Youre pretty set if you just remember stuff close to you looks bigger than stuff thats far away.
    I understand where you're coming from, but I fear this could be misleading. The heart of perspective is the stationary viewpoint, not vanishing points and station points. One consequence of the stationary viewpoint is diminishing, but another is orientation. By this I mean the orientation of an object in space in relation to the viewpoint, which more or less boils down to "is it facing me or not?". It's absolutely critical for drawing the figure and even landscapes.

    A lot of people just assume that perspective is only for buildings and toasters as you say, but they fail to realize that anything in a picture is really subject to perspective (presuming you are working representationally)- including things like heads, arms, clouds, etc.

    I understand that you're referring to more formal linear perspective construction and I completely agree that this begins to break down at a certain level for all but the stoutest perspective fetishists. However I think it's important to make the distinction as perspective is really at the heart of all representational drawing, and a lot of people learn the very basics of how to draw a cube in one or two point perspective and never go further.

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    Quote Originally Posted by arenhaus View Post
    Kind of like Newton's laws of motion are false, because you need Lorentz's model to get it really right... right?
    Well, it took the smartest people in the world 200 years to figure out that Newton's laws were distorting our understanding of the fundamental forces and preventing a proper conceptualization of Gravity. It takes the average artist about 3 hours to notice that something is screwy about artistic perspective.

    At least Icarus tried!


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    Quote Originally Posted by dose View Post
    perspective is really at the heart of all representational drawing.
    <contravening argument that derails thread>

    At least Icarus tried!


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    perspective is really at the heart of all representational drawing
    Please, please qualify this so that beginners will not go out and start perspectivising the whole world.

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    Please please... I'm really tired about all this posts, I did a question and
    arenhaus replied with a wonderful explanation and Anid Maro tried to reply. Can you please post only about his reply. Other ways to do what I asked for are appreciated too.

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    Quote Originally Posted by daafone View Post
    Please please... I'm really tired about all this posts, I did a question and
    arenhaus replied with a wonderful explanation and Anid Maro tried to reply. Can you please post only about his reply. Other ways to do what I asked for are appreciated too.
    Sadly these threads are not owned by anyone. Trying to stop the flow is like the little Dutch boy trying to plug the dike with his fingers and toes. Actually some pretty good discussions have come from the chaos. You got some good answers to your inquiry now you might just have to let nature takes its course and stand back. I think it's happened to everyone who has ever posted here.

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    Quote Originally Posted by daafone View Post
    Please please... I'm really tired about all this posts, I did a question and
    arenhaus replied with a wonderful explanation and Anid Maro tried to reply. Can you please post only about his reply. Other ways to do what I asked for are appreciated too.
    Hey look! Another great reason to buy a book intead of asking the universe for help!

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    Quote Originally Posted by kev ferrara View Post
    <contravening argument that derails thread>
    Seriously? I've never known CA to be a place that is strict about staying on topic. This isn't RP. And anyway, I actually think I'm saying something similar to what you were saying- although maybe I wasn't particularly clear.

    Quote Originally Posted by bcarman View Post
    Please, please qualify this so that beginners will not go out and start perspectivising the whole world.
    Actually my intention was to do exactly that. I apologize if I wasn't clear- I was writing in a hurry.

    My point is that perspective is very important, but figuring out a zillion vanishing points is not the part that's the most important. Perspective is understanding that if your eye position doesn't move, it has consequences about how you see things: if a box is facing you and placed at the center of your vision, you only see its front; move it a foot straight down and then you see its front and its top. A common beginner problem is to draw every part of the figure as if it was being viewed straight on at the center of vision, right down to the feet. All the vanishing points and whatnot are one technical solution to that problem, but it's not necessary to get really hung up on that particular part of it, unless you enjoy competing with computers.

    Another consequence of the fixed eye position is diminishing/foreshortening, but it's not the only one, and certainly not the only that's important. Saying that the main part of perspective is just things getting smaller as they get further away is like saying all you really need to worry about with color is getting the hue right. It's omitting a critical part of the concept.

    I'm not recommending people get hung up with vanishing points and crazy perspective projections. But on the other hand, I feel that some people just learn to construct a building in one and two point perspective and think they understand the whole thing, but their drawings are full of basic errors from not understanding how things generally sit in space in relation to the viewer.

    Quote Originally Posted by daafone View Post
    Can you please post only about his reply. Other ways to do what I asked for are appreciated too.
    I apologize if you feel I'm derailing your thread. I'm posting because I feel it's relevant to the broader discussion of perspective that was taking place in this thread; if it's distracting to you then I apologize. My hope is that it's at least beneficial to others if that's the case. And unfortunately, that seems to be the way of things at this site.

    (d'oh!, Bill beat me to it while I was typing my tl;dr)

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    Quote Originally Posted by JeffX99 View Post
    Hey look! Another great reason to buy a book intead of asking the universe for help!
    What's your problem? Why don't you go to read your f***ing books instead of replying to this topic in order to humiliate me?
    You have a better knowledge? Ok! You don't want to share it because you studied a lot? Stop replying, who cares about you? Nobody.

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    Dude...chill. Not trying to humiliate you at all...and my apologies that you interpreted it as such. Just a bit of humorous ribbing, but I know that doesn't always translate well.

    I would like to make the comment that I've sincerely offered you the best advice I can...and even explained the why behind it...yet no response. Oh well...good luck in life...hopefully someone will always be handy to answer your questions for you so you don't have to work too hard figuring anything out.

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    As I already replied I studied perspective and I didn't found anything about this. And I think you didn't find it too (or maybe you just ignored the question in your life)

    Dude, I have a philosophy, we live to learn, so as I can reply to a question, if I don't find a reply myself, I can try to ask someone else. Knowledge have to be shared. Don't think I found a question and I didn't try to reply myself. You don't know anything about me.

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    Fair enough. Arenhaus laid it out for you very well, and I backed him up on it. If you want a pretty good book recommendation Loomis's "Succesful Drawing" has an excellent chapter on perspective. But as I said, not every book works well for every type of person, the way they think and the problems they encounter, which is why I've continued to say "find one that makes sense to you".

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    Elwell is offline Sticks Like Grim Death Level 17 Gladiator: Spartacus' Dimachaeri
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    Quote Originally Posted by daafone View Post
    What's your problem? Why don't you go to read your f***ing books instead of replying to this topic in order to humiliate me?
    "Nobody can make you feel inferior without your permission."
    –Eleanor Roosevelt


    Tristan Elwell
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    Well, "do ____ in order to humiliate me" is not "you're humiliating me"

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