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The blue object is a very simple rectangle in two point perspective.enter image description here Next I zoom in on it: enter image description here When I measure the sides, I see is that the back side is shorter than the front side. It is foreshortened. The right side is closer to viewer than the left side. I would think the left side should be shorter because it is farther from the viewer. But it doesn't work. The left side is longer. So the farther side is not foreshortened. Isn't this a contradiction?

Where is my logic wrong?

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  • Simply your intersections dont match your lines.
    – joojaa
    Oct 27, 2021 at 19:01
  • If using something like Illustrator, you need to work in Outline Mode. In Preview Mode the strokes applied to paths obscure the actual path spine. You can't effectively align much manually with any sort of precision in Preview Mode.
    – Scott
    Oct 27, 2021 at 21:52
  • @Scott you can but you have to be comfortable with how smart guides work and keep pressing combos of ctrl+shift
    – joojaa
    Oct 28, 2021 at 5:45
  • Hi Scott, I appreciate the tips on using Illustrator. However, I believe that even if I was more accurate, the observation would still be true. Have you tried it? I believe that the answer from @Wrzlprmft is correct.
    – Chris
    Oct 28, 2021 at 15:54

2 Answers 2

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I don’t see a contradiction. Closer line segments are only larger under the same angle of viewing. In your example, the difference between the viewing angles has a larger effect than the distance. This is roughly because you are closer to the right vanishing point than the left one.

To better see this, let’s take the example to the extreme: Take any non-quadratic rectangle and place it such that your line of sight goes almost along one of the shorter edges. You will see something like this:

rectangle seen as described

Now you go further such that your line of sight is exactly along that edge. Now every point of that edge is closer to your eye than any point of the opposing edge, yet the length of the projection of that edge in your vision is zero, while the opposite edge has a finite (and thus infinitely larger) length.

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  • This is the right answer. My answer is more of a sidenote.
    – Wolff
    Oct 28, 2021 at 5:38
  • @Wrzlpmft Thanks for the answer. I get the concept, however I can't see it in your diagram. I find your diagram hard to understand. Can you add some more details/explanation/guides to your diagram?
    – Chris
    Oct 28, 2021 at 16:33
  • @Chris: See my edit.
    – Wrzlprmft
    Oct 28, 2021 at 20:30
  • @Wrzlprmft Hello, you seem to know a thing or two about perspective drawing. I'm new to it. Could I ask you some questions outside of Stack Exchange? The story is that II hired a professional illustrator to draw some diagrams for an exercise manual. I think he is accustomed to drawing people standing up, but many of my exercises are lying down. He told me he is saving difficulty with the perspective. So, I've been studying perspective myself to understand his difficulty. I have a PhD in physics, so this should not be beyond my capability. Anyway, could I tell you more by email?
    – Chris
    Oct 30, 2021 at 2:24
  • @Chris: I don’t know that much about perspective drawing, let alone of people. I am only good at finding illustrative counterexamples by taking things to the extreme (PhD in physics and such). I would have to invest as much work as you do, probably more so.
    – Wrzlprmft
    Oct 30, 2021 at 7:33
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I just think the difference is very small and your drawing isn't precise enough for you to measure it.

Which application did you draw this in and how do you measure?

It looks like the left vanishing point is a tiny bit lower than the right one. I can see the right one is a few pixels above the horizon.

If I take the closeup and stretch it vertically it's easier to see the details.

Notice how the blue shape is skewed compared to where the red lines actually intersect?

All these little inaccuracies add up.

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