Why are lines closer to the vanishing point appear to be longer on paper?

1:13 PM, Wednesday February 9th 2022

Hi drawabox community!

I've completed lesson 1 and I'm doing the 250 box challenges. When planning lines for a box I'll double check if the line is correct by measuring the angles and lengths and I discover that sometimes lines closer to the vanishing point appear to be longer on paper!

From lesson 1 - vanishing point we know that for a set of parallel and equal-length lines, the ones closer to the vanishing point should appear shorter.

However consider this image, specifically the blue line A and the green line B. We see that line B is cloer to the bottom vanishing point, but it is obviously longer than line A. As I'm drawing a box line A and line B should have the same length in a 3D space. Why is this the case? Am I misunderstanding something?

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5:44 PM, Wednesday February 9th 2022
edited at 6:07 PM, Feb 9th 2022

Hi TSReaper, that's an interesting observation.

It appears that you have placed your top left vanishing point too closely to the box. I drew my own 3-point box as you showed, but placed the vanishing points farther out, and the parallel lines further away (from the viewer) no longer appeared to be longer than the closer (middle) one; while you have followed the basic rules of 3-point perspective, it appears there is some skewing that has taken place due to your vanishing point being placed too closely to the box. Remember that 3-point perspective is only a simplification of reality and not reality itself, and certain measures must be taken (e.g. like placing the vanishing points at realistic positions/distances) to get a realistic result.

You'll notice that the parallel lines receding towards your other two vanishing points (which are placed further away from the box) do not have the same issue. Your two top vanishing points are too close together. Try moving that top left vanishing point farther away (from the box, or from the top right vanishing point if you're trying to keep it on a horizon line) and you should find that the problem is resolved.

Regarding your sentence,

As I'm drawing a box line A and line B should have the same length in a 3D space.

while Lines A and B may be the same length physically (i.e. in reality), do keep in mind that as soon as you apply any amount of foreshortening to a box (i.e. draw it in 3D with perspective applied rather than keeping it isometric), Lines A and B will no longer be the same length visually unless they are an equal distance from the vanishing point (in 3-point) or you're using 1 or 2-point perspective where vertical and/or horizontal lines are locked to a certain orientation.

You also said:

we know that for a set of parallel and equal-length lines, the ones closer to the vanishing point should appear shorter.

I'd just like to mention that when trying to learn to think in 3D space (as DAB aims to teach you), rather than thinking of which line is closer to the vanishing point, it may be more helpful to think of which line is farther from the viewer, since things farther in the distance appear smaller, even if that distance is not too far away. Thinking mainly in terms of vanishing points may be helpful to complete the challenge/exercises, but thinking in terms of "depth of space" is really the desired goal for artists in my opinion; so for now the vanishing points are like training wheels to help you grow, but eventually (hopefully) the way you think will develop beyond having to rely on them too strictly.

edited at 6:07 PM, Feb 9th 2022
4:20 AM, Thursday February 10th 2022

Thanks for the detailed explanation and the following tips. Very helpful!

5:37 PM, Thursday February 10th 2022

You're welcome, TSReaper. I'm glad I could help.

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