Three-point perspective question

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    Three-point perspective question

    How does one measure off rows of windows on a building or skyscraper in three-point perspective? It's easy enough using vertical and horizontal scales of equal distance to measure in one and two-point, but that method doesn't seem to work for three-point. All the perspective books I own somehow avoid the issue of measuring in three-point perspective.

    I asked this question in another forum and was told to "eye-ball" it, but I would rather prefer to do it the correct way. So, how's it done?

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    hi balooga,
    if you mean you want to draw exactly windows with measurement 0.8*1.2m like 200 times on a scyscraper in a three-point perspective: i say this is not possible like in a two-point perspective.

    instead of measure the window, you could construct it.
    (check out the attatchement)
    draw the hole bilding. say, its about 100meters high. you want to draw 50 rows of windows.
    to get the middle line of the building, draw on each surface (the irregular quadrilateral) both diagonal lines. connect the cross point with a vanishing point, this cuts the area into two identical parts, each 50meters high (red lines on the left).
    proceed with these parts, draw diagonal lines again and cut the surface again in two parts (red lines on the right)... till you got your 50 rows, each row is now exactly 2meters high.

    oh shit. i hope you understand, geometrical instruction in a different language...

    regards,
    orwell

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    In photoshop you can use this shortcut. remember_orwell, I hope you don't mind that I used your picture.

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    h2rra, i dont mind
    but i think Balooga wants to draw by hand...?
    besides, good trick to doing that by computer.

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    Remember Orwell, thank you for the diagram. That helps a lot.

    h2rra, that's a neat Photoshop trick. It's a cheat, but quick and easy to do -- thanks!

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    If you want to do it manually you can wait for Dobsky's dvd or chew through this text. For me that link is way too complicated...

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    Quote Originally Posted by h2rra View Post
    If you want to do it manually you can wait for Dobsky's dvd or chew through this text. For me that link is way too complicated...
    You ain't kidding! Yikes, that actually made my head hurt!

    Who is Dobsky, and when/where will his dvd be avaiable?

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    Carl Dobsky is a dude in Massive Black. His paintings are insanely awesome. Click http://media.massiveblack.com/ to find dvds.

    h2rra: good link. Kinda complicated though. Working through it now.

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    3-pointer question

    Sorry for reviving this old thread, but I don't wanna clutter the forum by starting another new thread.

    This post is also about 3-point perspective, but of a slightly different nature.

    Pls find below a quick sketch of a typical 3-point setup of a skyscraper.
    The eye level is the horizontal line at the bottom and the sets of vanishing points are indicated by the "Xs":

    Three-point perspective question

    Now, I add another building to the left of this building:

    Three-point perspective question

    Now, you see the problem: the new building (B) LOOKS DISTORTED!

    I thought I understand 3-point perspective pretty well until a friend asked me this question the other day regarding his work, and I was totally thrown off and puzzled myself!

    In 1 point perspective, there can only be 1 vanishing point, right?

    In 2 point, there can be many sets of vanishing points (I'm 100% confident about this) on the same eye level.

    In 3 point perspective, there can be many sets of vanishing points on the same eye level (just like 2 point), but what about that vanishing point at the top ("Zenith")? Can there be multiple vanishing points at the top for 3-point perspective?

    Thanks!
    Xeon

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    If you have distortion, you are drawing outside of the eye's 60 degree cone of vision as represented on your drawing.

    The answer to your question tracks that of the OP in that to avoid the distortion you have to accurately plot your 90 and 60 degree "cones" (represented by circles). And, using this perspective layout, you need to be able to create "measuring points" to allow you to scale/measure exactly how big your windows are (if you want to avoid just doing divisions with diagonals or eyeballing a window and using similar tricks that don't involve using measuring points.

    Measuring points are easy enough to construct in 2 Point. I'm not sure of a source that shows how to construct them in 3 Point. [And, most texts do fluff off any real deep practical instruction on 3 point.]

    I'll see if I can find something. But, me? I've never made it all the way through the "Handprint" discussion either! It's pretty dense!

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    Quote Originally Posted by h2rra View Post
    If you want to do it manually you can wait for Dobsky's dvd or chew through this text. For me that link is way too complicated...
    You may want to try John Raynes' 'The complete guide to perspective', which gives a more accessible presentation of measure points.

    Last edited by eezacque; September 2nd, 2010 at 11:11 PM. Reason: Oops, didn't notice this thread is really old...
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    Quote Originally Posted by Xeon_OND View Post
    In 3 point perspective, there can be many sets of vanishing points on the same eye level (just like 2 point), but what about that vanishing point at the top ("Zenith")? Can there be multiple vanishing points at the top for 3-point perspective?
    There is one vanishing point for every direction: this principle is the same in 1, 2 and 3 point perspective. So, to answer your last question: no, there is exactly one vanishing point for the vertical.

    However, this does not mean you can freely choose your vanishing points somewhere on the horizon line: vanishing points need to be constructed, and generally, the vanishing points in 2 and 3 point perspective correspond to directions that make right angles.

    Assuming that your sky scrapers are blocks, with all corners having perfectly right angles, the vanishing points of sky scraper B must be either on the left or on the right of the corresponding vanishing points of A, because the orientation of B is rotated with respect to A. For your B, the vanishing points are 'outside' the vanishing points of A, which means that its corners are not right.

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    Quote Originally Posted by Xeon_OND View Post
    Sorry for reviving this old thread, but I don't wanna clutter the forum by starting another new thread.

    This post is also about 3-point perspective, but of a slightly different nature.

    Pls find below a quick sketch of a typical 3-point setup of a skyscraper.
    The eye level is the horizontal line at the bottom and the sets of vanishing points are indicated by the "Xs":

    Three-point perspective question

    Now, I add another building to the left of this building:

    Three-point perspective question

    Now, you see the problem: the new building (B) LOOKS DISTORTED!

    Xeon
    Parallel lines have the same vanishing point.

    In a normal city block, buildings are lined up so that they are square to one another, meaning that various lines for two buildings would have the same vanishing point. Your buildings likely look somewhat distorted because you have given them different vanishing points, thereby implying that their walls/roofs are not parallel to one another.

    I suspect that the vertical axis might also have different vanishing points, but you could only really test this by finding/making a bunch of regular shapes which are not parallel vertically. So... not buildings, since those kinda tend to have vertical walls.

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    Wow, thanks guys! This shit is more complicated than I thought!

    For now, I'll just take it as the fact that Building B is caused by distortion, because in a real life situation, I don't think it's too possible to see 3-point perspective in action and yet, at the same time, take in a wide field of vision (for e.g: standing 600 feet away from the Empire State Building, looking at it and still be able to see clearly other tall buildings).

    I'll try to ask my teacher on this and see what he says.

    Quote Originally Posted by Kamber Parrk View Post
    I'll see if I can find something. But, me? I've never made it all the way through the "Handprint" discussion either! It's pretty dense!
    Same here. I like perspective and all, but that damned "Handprint" perspective website is so technical as fuck and I clicked the "Back" button after 5 mins. If it was published into a book, I may read the whole thing, cos' paper is more comfortable than the LCD screen.

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    Three-point perspective question

    Now, you see the problem: the new building (B) LOOKS DISTORTED!

    Everything that's in your image should be within an equilateral triangle with each vertice as a VP. If you enlarged your first set up to encompass both buildings there wouldn't be the distortion you have here. Just keep each VP at sixty degrees from the other two.

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    Quote Originally Posted by Xeon_OND View Post
    Sorry for reviving this old thread, but I don't wanna clutter the forum by starting another new thread.

    This post is also about 3-point perspective, but of a slightly different nature.

    Pls find below a quick sketch of a typical 3-point setup of a skyscraper.
    The eye level is the horizontal line at the bottom and the sets of vanishing points are indicated by the "Xs":

    Three-point perspective question

    Now, I add another building to the left of this building:

    Three-point perspective question

    Now, you see the problem: the new building (B) LOOKS DISTORTED!

    I thought I understand 3-point perspective pretty well until a friend asked me this question the other day regarding his work, and I was totally thrown off and puzzled myself!

    In 1 point perspective, there can only be 1 vanishing point, right?

    In 2 point, there can be many sets of vanishing points (I'm 100% confident about this) on the same eye level.

    In 3 point perspective, there can be many sets of vanishing points on the same eye level (just like 2 point), but what about that vanishing point at the top ("Zenith")? Can there be multiple vanishing points at the top for 3-point perspective?

    Thanks!
    Xeon

    I'm going to just ramble on my own terms for a bit to make the explanation easier to give and hope it makes sense to you in some way. Feel free to ask questions.

    If you have two objects with parallel lines, their parallel lines converge on the same point. So if tower A was square with tower B and they were using the vanishing points of tower A, you would not be able to see any walls on tower B except for the closest wall since all walls would converge towards the vanishing point right under it.

    A change in vanishing points describes a change in angle.


    If you were to hold a cube in front of your face. .. lets say a giant foam block so you could hold it and it would be large enough to easily see the edges begin to converge. As you rotate it, one side would seem to get thinner, and the other would get more square. This could be seen as an effect of the vanishing points moving. (If you can, actually do this. If not, visualise with me.)

    (just imagine 2pp for now.) On one side, the vanishing point is getting closer and closer to the center of the object, so it gets thinner and thinner. When the vanishing point eventually is right behind that side's edge, you won't see that side anymore. We will call this the thin side because it is getting smaller.

    The other visible side is also getting wider and more square looking. It's vanishing point is getting farther and farther away from the cube. We'll call this the fat side because it's getting larger.

    Eventually, all of the cube's side edges will be invisible to you, hidden behind that front face. Behind what we called the fat side. Once the vanishing point of the thin side is perfectly centered on the horizon behind the cube, you have 1pp. What happened to the fat side's vanishing point? It traveled so far away from the cube, it is now an infinite distance away. It's lines will never converge and so appear parallel. You see a square instead of a trapezoid. Rotate it just a little farther and the vanishing point for the fat side will reappear on the opposite side of the cube, while the thin side's vp will keep going in the direction it has been going. And you will start to see a new side emerge.

    The problem with tower A and tower B is that they do not obey this rule. Tower B does not have the same vanishing points as A, so it cannot be square with it in angle. It also does not have one vanishing point moving closer to it as the other gets farther away. Both vanishing points are getting farther away. It gives the impression that the angle between it's sides is becoming more obtuse. This is the problem. Building edges are not normally obtuse angles.

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    Here's a diagram that uses measuring points in 3-point.

    I don't pretend to understand this. But, it's from an old technical drawing book I got from the library.

    Over the next day or so, I'm going to read the text and see if I can get my mind around an answer for both Xeon and the (ancient) OP.

    Uh, I ain't promisin' nuthin'!

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    Although the construction of measuring point is good to study, it is irrelevant for the question of the original poster.

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    What is line OG for?

    Three-point perspective question

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    Quote Originally Posted by Robotus View Post
    What is line OG for?
    The line OG acts as a ruler to measure verticals with respect to the measure point M1 for height

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    Quote Originally Posted by Robotus View Post
    The problem with tower A and tower B is that they do not obey this rule. Tower B does not have the same vanishing points as A, so it cannot be square with it in angle. It also does not have one vanishing point moving closer to it as the other gets farther away. Both vanishing points are getting farther away. It gives the impression that the angle between it's sides is becoming more obtuse. This is the problem. Building edges are not normally obtuse angles.
    Thanks Robotus! I can fully understand everything you said, except the above paragraph.

    What I'm thinking is: couldn't we just add another point up there in the air for Building B, so that it would have its own set of 3 vanishing points? I think that will solve the problem.

    In a 2-point scene with several cubes rotated at various angles, each of these cubes would have their own set of vanishing points on the eye level. If we could apply this to a 3-point scene, then....


    Quote Originally Posted by Kamber Parrk View Post
    Here's a diagram that uses measuring points in 3-point.
    When I saw that diagram, my first reaction was:

    Three-point perspective question
    YEE-YEE AH-AH EEE-EEE-AH-AH EEE-ARGH!!!!!!!!!

    LOL I'll take some time to understand it. Thanks Kamber!

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    Quote Originally Posted by Xeon_OND View Post
    What I'm thinking is: couldn't we just add another point up there in the air for Building B, so that it would have its own set of 3 vanishing points? I think that will solve the problem.

    In a 2-point scene with several cubes rotated at various angles, each of these cubes would have their own set of vanishing points on the eye level. If we could apply this to a 3-point scene, then....
    When you have various vanishing points for various cubes, what you really have is various vanishing points for various angles to the camera. Straight up is always straight up and so it always takes one vanishing point.

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    Hey Xeon,
    The reason that building B looks distorted is because you are not applying the rules of perspective between parallel objects correctly. Parallel planes share vanishing points but here you made 2 new vanishing points for building B when you shouldn't have. Only when objects are twisted or tilted in relation to each other is when you need to add new vanishing points. I don't want to compound the question by adding "how to" in regards to twisted or tilted objects so for now here is your original art with the vanishing points fixed.

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    Thanks, Robotus and Jason!

    Quote Originally Posted by Jason Ross View Post
    Hey Xeon,
    The reason that building B looks distorted is because you are not applying the rules of perspective between parallel objects correctly. Parallel planes share vanishing points but here you made 2 new vanishing points for building B when you shouldn't have. Only when objects are twisted or tilted in relation to each other is when you need to add new vanishing points. I don't want to compound the question by adding "how to" in regards to twisted or tilted objects so for now here is your original art with the vanishing points fixed.
    Oh yes, I can understand that. I guess my question is how to rotate Building B in 3-point perspective (so that it's base is not parallel with Building A) and still have it come out looking correct.

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    Xeon_OND,
    I believe that this is what you are referring to. The top image is the "method" of finding the vanishing points for a 90 degree or 45 degree view angle (which is what you have already). The bottom is when another building (purple building) is introduced but is rotated on its base "X" amount. You'll see that the more you rotate the wider the vanishing points get.

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    (so that it's base is not parallel with Building A)
    I think he's talking about making a leaning tower now.

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    Quote Originally Posted by Jason Ross View Post
    Xeon_OND,
    I believe that this is what you are referring to. The top image is the "method" of finding the vanishing points for a 90 degree or 45 degree view angle (which is what you have already). The bottom is when another building (purple building) is introduced but is rotated on its base "X" amount. You'll see that the more you rotate the wider the vanishing points get.
    Ah, I guess that's it! I understand now!

    Quote Originally Posted by Robotus View Post
    I think he's talking about making a leaning tower now.
    LOL, let's not talk about inclined planes in 3-point perspective for now. I might go mad.

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    Quote Originally Posted by eezacque@xs4all.nl View Post
    Although the construction of measuring point is good to study, it is irrelevant for the question of the original poster.
    I respectfully disagree! The OP wanted to know how to place windows exactly in 3 Point and was having trouble figuring out how to make measuring lines work in 3 Point.

    Being that nothing, but maybe a point, touches the Picture Plane in 3 Point, you need to be able to construct that 3rd vertical measuring line to place things exactly.

    I'm still trying to reverse engineer the diagram, but the text was next to useless-- just labelling, no procedure on construction.

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    Quote Originally Posted by Robotus View Post
    I think he's talking about making a leaning tower now.
    As I was failing at figuring out my diagram this afternoon, my thoughts turned to those tower images:

    Thought: There's probably a very narrow range of vantage points from where you can look UP at a tower and still see the base.

    I was thinking the same thing. Some of the views may well be those of leaning towers. (But, don't ask me to prove it!)

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    Note: 'Remember Orwell's' picture violates the "90 Degree Rule." The bottom of his tower comes to a big sharp < 90 degree point.

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