# Thread: Draw a perfect square using two vanishing points

1. Originally Posted by daafone
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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3. 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?

4. 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!

5. Originally Posted by Cider
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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Originally Posted by arenhaus
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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Originally Posted by arenhaus
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.

kev

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Originally Posted by kev ferrara
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.

9. Originally Posted by Cider
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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11. Originally Posted by kev ferrara
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?

12. 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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14. Originally Posted by kev ferrara
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.

15. Originally Posted by Cider
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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17. Originally Posted by kev ferrara

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.

Originally Posted by s.ketch
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.
Last edited by Velocity Kendall; April 27th, 2012 at 04:46 AM.

18. 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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20. Originally Posted by arenhaus
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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