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  1. #1
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    Question How to make a perfect cube in perspective -- does this make sense?

    I found a thread on how to create a perfect cube in perspective here: http://conceptart.org/forums/showthr...ng-perspective
    The solution proposed in the thread assuredly would work, but seemed really complicated. I figured there had to be an easier way, and it occurred to me that by measuring 1/2 the original vertical line, you could find the point at which the diagonals from the top and bottom of line to their opposite corners would intersect.

    This seems to make sense to me, and I can't think of any problems with it, but I wanted to see what other people thought and if anyone could find a hole in my logic. I've included an image to hopefully help clarify the solution:

    Name:  perfect_cube_in_perspective.jpg
Views: 5400
Size:  111.4 KB

    Ps: sorry if this is in the wrong place, I'm fairly new here.

    I'm new here and could always use some advice / criticism. Feel free to take a peak at my sketchbook if you have the time.



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  3. #2
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    How do you determine the angle of the lines you use to locate point C in step 5? Seems to me that depending on the angle of those lines you would get different rectangles and there's no way to determine which angle is the "correct" one that way.

  4. #3
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    The flaw is in placement of C. There is no way to ensure that the distance from it to AB is correct.

    You should simply use the "architect's method" to draw the square base of the cube from its top view. If you search through the forum, you'll find a couple threads dealing with that; or you could get "Perspective Made Easy" by Norling, which also contains an explanation.

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  6. #4
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    A counterexample points out the flaw in your reasoning:

    Name:  persp-prob.jpg
Views: 3102
Size:  30.0 KB

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  8. #5
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    Use this 2pt perspective method:

    Name:  aa11.jpg
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    Last edited by bill618; February 1st, 2013 at 08:28 AM.

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  10. #6
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    You're absolutely right, in retrospect that's very obvious. At least it's still somewhat useful, as it will always be a multiple of a perfect cube.

    I'm new here and could always use some advice / criticism. Feel free to take a peak at my sketchbook if you have the time.


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    Ah, this is a much better approach. Thanks!

    I'm new here and could always use some advice / criticism. Feel free to take a peak at my sketchbook if you have the time.


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    Quote Originally Posted by nickbernstein View Post
    You're absolutely right, in retrospect that's very obvious. At least it's still somewhat useful, as it will always be a multiple of a perfect cube.
    Again, not necessarily (at least not if you mean an integer multiple).

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  13. #9
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    the lines cross at the center of any rectangular face not just squares, as elwell demonstrated
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  14. #10
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    Dont discard the OP's method. If you continue to draw the line cross the mid point of the next vertical line, you will get the relative/realistic equal distance between each line (1,2,3,4,5,6,7)

    Useful for drawing light posts on streets or like a fences where the distance between each poll is equal.

    Here, C is half way point from A to B
    Name:  pers.jpg
Views: 2955
Size:  98.4 KB


    EDIT:
    Or any other things that are same size
    Name:  pers2.jpg
Views: 2917
Size:  113.8 KB
    Last edited by choonhachat; February 4th, 2013 at 12:33 AM.

  15. #11
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    Quote Originally Posted by sytrex View Post
    Dont discard the OP's method.
    The OP is trying to draw a proper cube in 2-pt perspective, not any randomly sized rectanglular block. The OP’s C-point is the center point of any arbitrarily sized rectangle (including a square if you're lucky), as Elwell points out in his example. You're describing an equal spacing technique.

    In order to represent a proper cube (essential for drawing proper squares which are essential for drawing proper ellipses for disk or cylindrical things like wheels, building arches, airplane fuselages, coffee cups, etc.), you need to determine the location of the two vertical edges on either side of vertical line AB of the cube as well as the accurate length of AB. AB (in the OP's example) is a line segment on the picture plane (in 2-pt perspective), so it can be measured 1:1 with the cube reference, as in my example (top and left side reference squares).

    I know this doesn’t explain things in full, but that’s what all of those books and online resources are for, to walk one through the entire process from beginning to end.

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  17. #12
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    Just as a side note, placing VP1 and VP2 is also something not too obvious and should be done thoughtfully.

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    Quote Originally Posted by Erayo View Post
    Just as a side note, placing VP1 and VP2 is also something not too obvious and should be done thoughtfully.
    Their placement is governed by rigid principles of geometry.

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    Or you could refer to that tutorial that never gets mentioned anymore that Carl Dobsky did.


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  20. #15
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    What exactly is meant by 'perfect cube'? Google's not my friend for this apparently. For months after my perspective class finished I believed it meant a cube where all the dimensions were equal (apologizes for lack of proper terminology). That is, a perfect Platonic equally propotioned cube.

    If it isn't that, then I don't know what it is.
    Last edited by Cortes; February 14th, 2013 at 12:51 PM.
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    Quote Originally Posted by Cortes View Post
    What exactly is meant by 'perfect square'? Google's not my friend for this apparently. For months after my perspective class finished I believed it meant a square where all the dimensions were equal (apologizes for lack of proper terminology). That is, a perfect Platonic equally propotioned cube.

    If it isn't that, then I don't know what it is.
    You want me to explain the difference between a cube and a square?
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    I don't think you understood my question, sorry. By 'perfect square', I meant cube. My apologies. I guess that a perfect square is just one plane of the whole cube though, like the first side that you plot from the VP's as in here: http://thevfxartist.blogspot.com/201...utorial-1.html. I suppose my question could be shortened to, what is meant by 'perfect'?
    Last edited by Cortes; February 14th, 2013 at 12:59 PM.
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  23. #18
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    A perfect square, cube, chick with boobs and everything, is well-defined in mathematics, and perspective theory teaches you how to project these on a 2 dimensional plane. If you want to know how a perfect chick with boobs and everything looks, study mathematics, if you want to know how to project these, study perspective.
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    Well, I am going to throw my hat in the ring here...

    Knowing how to do this in 2pt perspective is very useful for keeping things in scale, when translating a diagram, or just trying to come up with units across the image that look correct; thus, I made a tutorial video on how to make a perfect cube in 2pt perspective, that only assumes very basic knowledge, and hopefully should help.

    http://www.youtube.com/watch?v=OB3UEpxFlj8

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    https://i.imgur.com/npYGPDJ.png

    Perfect square in 2pp and 1pp. Probably not the most convenient method for 2pp cube? Maybe someone would find it useful how to draw a perfect cube in 1pp, though.


    How to choose the viewpoint:
    Name:  perspcub.GIF
Views: 716
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    (from http://www.math.utah.edu/~treiberg/P...t/Perspect.htm)
    Last edited by onemax; June 26th, 2015 at 01:41 PM.

  26. #21
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    Quote Originally Posted by maxpancho View Post
    https://i.imgur.com/npYGPDJ.png
    Perfect square in 2pp and 1pp. Probably not the most convenient method for 2pp cube? Maybe someone would find it useful how to draw a perfect cube in 1pp, though.
    I suggest you construct your main vanishing point(s) from the stationary point, using appropriate angles, as well as the diagonal vanishing point(s), at the angle inbetween, and take it from there.
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    This isn't necessary. Correct DVP will follow from this method.

    And actually, in general, DVP in the middle (to find a perfect square) of two VPs assumes that the viewer is in front of this DVP. Practically, this means that if one of your VP's is on the picture plane (paper) and the other one is somewhere very far off the paper, then if you draw your 2pp square with the diagonal vanishing to this DVP, then it will only look right if it's within the 60° viewing cone from the point in the middle of the two VPs (so obviously the cone might easily be off the paper, since one of your VPs is on the paper, and the other one is very far off the paper). That's if we are talking about perfect squares though? I don't think there's a way to find cube's height from it, but maybe I forgot or I don't know it.

    So actually, the method above can also help you find the perfect square for any configuration of VPs (not just for 60° cone in the middle of two VPs) and the correct DVP for it, if you just use the top or bottom face of the perfect cube (well, obv). DVP in the middle of two VPs is the more practical for finding a perfect square the more evenly these VPs are spaced from the paper (happens pretty often I think, but not always), and is more of a shortcut.


    PS But actually, the method in the video from thepace is a bit easier I think (don't need space above), for 2pp cubes, than the one in my post.

    For 1pp cube within a 2pp scene, the method I've outlined could be useful, though.
    Last edited by onemax; June 24th, 2015 at 03:37 PM.

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