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Based on the picture with the green and blue squares in this post, I tried projecting a cube drawn at a generic angle (so it had two sets of receding lines with respect to the observer).

Only, I was not sure how they decided to place the squares, the observer and the image plane in the 'top view' and 'side view', so I tried to remember my high school technical drawing stuff, and came up with this:

enter image description here

The image plane is in green.

Then, applying the method as I understood it from the post picture:

enter image description here

This does not look correct to me.
It's as if a 1.8 m tall man looked at a cube with 1.5 m sides, placed about 2 m away, to his left.
Would he see something like this (while not being on any hallucination-inducing medication?).

What am I missing?

For sure I don't know how one decides where to put the 'image plane'.
Is there a rule for that?


EDIT to explain my (possibly wrong) interpretation of what the 'image plane' is.

enter image description here

I took the 'image plane' to be a simple, actual plane (in green here) placed between the cube and the bounding box of the projection (it's in front of the white axes, sorry I did not make them dotted, too lazy).
I can probably place it closer or farther away from the box, but whatever I do, unless I am told otherwise, I don't see how the distance of my cube from it can ever be very different in the top and side view, if I apply the simple orthogonal projection.
As I mentioned in my comment to @user2098829, I think the observed discrepancy is only due to my imprecision in drawing this stuff by hand in Krita.

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  • Your camera is just very close to the object. Thats what happens even in a 3d application if you make the view very wide.
    – joojaa
    Dec 13, 2023 at 12:21
  • BTW found this YouTube channel youtube.com/@trustyourperspective/videos . I think it's great, clear, straight to the point, practical. I think I understand it all much better after watching these videos. Dec 17, 2023 at 15:22

2 Answers 2

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Under edition. Do not trust my post. I have mixed some concepts...

about 2 m away

Your perspective is correct... except the viewing plane is not at 2m. It is about .5m

enter image description here

If your cube is 1.5m (cian) and I use the same measure to get the distance for the plane, I would need to put the plane where the magenta line is.

But the distance to your green plane is 1/3 of that (lime)


You need to move all the elements of the first orthogonal plane to the right to make space for the magenta viewing plane, and the top view, move it south to make the same space.

enter image description here

Or put the viewing plane on the other side further away.


Your cube is so distorted because you would need an extreme lens to view it let's say an ultra wide angle lens, because is so close to the camera.


What is the image plane?

Have you seen one of these cameras, where the guy hides behind a black cloth, maybe in a cartoon or movie?

enter image description here

What they are doing is seeing a projected image on a frosted glass on the back.

This actually happens on every camera including your phone, but the projection is made inside the camera.

The difference between a perspective drawing vs a camera is that a camera uses the lightrays that converge in the lens (Magenta lines).

enter image description here

But an image plane is something like a photo taken behind a wall made of a stack of pipes.

enter image description here

In this image the stack of pipes (Light purple) only allows parallel rays (Pink) to be projected into our image plane (Purple)

enter image description here

Is there a rule for that?

Depends on the view you need. A photographer puts the camera on what he wants or needs it to be.

But on the new arbitrary location of my camera or stack of pipes, we need to now construct a new set of orthogonal projections to match the parallel pink lines...

enter image description here

And you can see it would be a mess. But can be done.

A rule could be that you define your image plane on the already defined set of parallel lines present in your drawing. They can be near the origin or away from it.

enter image description here

I could put the image plane at any distance (turquoise) because I have space.

On the inside, as the second image on my answer, as we have no space between the axis, which is like a solid wall, we would need to move the object away.

But this "rule" is only to reduce the complexity.

Thank God for 3D applications. There we can have the image plane wherever we want easily...

One additional note. I am calling the "image plane" the one we are using for this kind of perspective drawing. In 3D software, it would be called Orthographic or Orthogonal camera.

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  • Thanks! This confirms that I have no idea what the 'image plane' is, or where I should decide to place it. Now there is also a 'viewing plane', no idea what that is either. Both lines were tagged 'image plane' in the post I referred to, so i assumed they were the same thing and had to be projected exactly as I would project a plane, which i did with my thick green line. When I wrote '2 m away' I meant that the nearest face of the cube is about 2 m away from the eye of the person looking at it, i.e. from the red dot marked as 'O' in my drawings. But OK, at least I know I was not completely off. Dec 13, 2023 at 17:01
  • Let me explain what is the image plane. I am editing the post.
    – Rafael
    Dec 13, 2023 at 19:58
  • I added an extensive part 2.
    – Rafael
    Dec 13, 2023 at 20:55
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The construction you tried is a fundamental one. It projects points (taken from top and side views) to the image plane. It uses no shortcuts like vanishing points nor many others which can be used to draw certain shapes quickly, the method fits anything if the planar parallel projection top and side views are available.

The construction you picked from the linked case looks clean because the image plane is fully in parallel with one cube surface. That generates only one vanishing point to the image of the cube. The linked case as a whole is complex. It's purpose is totally different than to teach the construction you tried. But at least it seems to respect geometry, so it's not a bad idea to try the shown methods.

You have missed one thing - the top and side views should present the same 3D scene. Your image plane is not placed equally far away behind the target. But otherwise it looks right. The distance error is shown in the image at the end of the answer.

Where should the image plane be placed? No limits as long as your workspace is large enough and your projection result is not too small to be drawn accurately.

Some practical things should still be considered for easier work and to avoid bizarre looking extreme perspective:

  1. The image plane is useful to be placed in parallel with one main construction line of the target. You have made it vertical and that's useful if the target has some vertical major lines and in this case it has.

  2. Another good idea is to place image plane to meet the target somewhere, for ex. at some straight corner. This maps just that corner 1:1 to the image which helps to reveal errors.

  3. The image plane should be in top and side views as far away from the observer and as far away from a target point. Your top view image plane is drawn clearly further and this causes some error.

  4. For nice looking perspective it's useful to let the image plane be perpendicular with the sight line which points to about middle of the target. That's not always possible because something important may be hidden or something which is wanted to look rectangular in the image gets skewed. That perpendicular with the mid-target sight line condition happens in cameras.

  5. Most important thing to avoid bizarre perspective is to make the observer distant enough. I mean there's not too large percentage variations between the distances from the observer to the target points. The extreme case is to use parallel sight lines (=infinitely distant observer). The result is no more a perspective image, it's a parallel projection.

You have all ingredients to get a bizarre perspective

  • different image plane distances from corner CG; that's a fatal error
  • the most distant target points are twice as far away from the observer when compared to the closest point

Changing the distance from the observer to the image plane doesn't make the perspective more nor less bizarre. It affects only the drawing scale.

Final note

Get a book of descriptive geometry to find more of the subject. You'll get easily 10000% more than this one elementary construction method.

I guess you have already checked some perspective guides for artists. They do not use this elementary construction as a tool, because its inefficient for complex drawings. Instead they use practical shortcuts which are verified in the descriptive geometry theory. Some of the shortcuts are not exact, they are strongly based on human perception (=eyeballing).

ADD:

enter image description here

The mentioned image plane distance error in the construction is obvious because the magenta squares are equal, but the square fills the gap between the target and the green image plane only in the side wiew. In the top view the green image plane is substantially further.

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  • Excellent, thanks a lot! Indeed, I checked a few videos and websites, but in fact what they call 'simpler' methods to me looked absurdly complicated or insufficient. E.g. yes, I can draw a rectangle in 1- or 2- point perspective using vanishing points, but if I want that rectangle to be a square, how do I determine the appropriate lengths. There are videos on that specific case too (how to draw a square or cube), but even the person describing the method kept saying they were not sure it was a good method(!). How confident can I be about it then? Hand-wavy may not work with geometry, I fear. Dec 13, 2023 at 17:09
  • And that's the reason why I looked for, and tried out, a more 'fundamental' method, as you call it. It is reassuring to see that I did not get it so wrong. But i confess I don't understand this statement " Your image plane is not placed equally far away behind the target.". I thought I had used projection precisely to avoid that, otherwise I could have just placed the horizontal and vertical projections of the image plane a bit floating in mid-air like the post I linked seemed to do. That's what I am still missing. But thanks for your input, I will think about it a bit more and maybe get it. Dec 13, 2023 at 17:12
  • @user6376297 I inserted a proof for the existence of the image plane distance error. Dec 13, 2023 at 18:34
  • Thanks. Would you really say it's 'substantially further' though? In the other post I read smthg like 1.5 m vs 0.5 m, so like 3 times as far (?). Your magenta square is perhaps 0.1-0.15 times its own side farther in the top view vs the side view. And again, from the geometric construction I did, IF it's true that the image plane is indeed just a plane standing between the end of the 'box' and my cube, I don't see how else I could project it or place it. I think the discrepancy you are observing is due to the imprecision of my drawing, which I did by hand in Krita. I'll add smthg to my post. Dec 13, 2023 at 20:39
  • @user6376297 My reference for what I call accurate is the accuracy that can be got in Inkscape or other vector drawing programs. There everything can fit with no visible error even in 5000% zoom in level. Drawing in a raster image program is coarser job. Everything is forced to image pixel boundaries. Get Inkscape. Current version works well and it surely is a big enforcement to your weaponry (after practicing a week to get started). Your choice of the image plane is OK (only drawn inaccurately), but I would place it to touch corner CG or AE. Dec 13, 2023 at 21:11

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