3D Intersections Are Maddening

Posted by pladd on March 04, 2016

Thank goodness, I thought to myself. The nightmare was over. I was done with dissections. I had stopped dreaming of lamprey watermelons everywhere, appearing when you least expect them. It would be smooth sailing from here on out, because that is how life works: you finish something hard, and then everything else is easy for the rest of your life.

Yeah, I should have seen that coming. This exercise was no less tedious or difficult than the previous, and I messed it up so hard. Or maybe I did it perfectly. I’m actually not sure anymore.

Anyway, what better way to learn from my (possible) mistakes than to broadcast them to everyone I know, and possibly people that I don’t know?

Background: Why Boxes?

It may be hard to understand why I moved from textures to boxes without a proper introduction. If you want to see the lesson from the source, head to the Draw A Box website (look for “Part 3: Form Intersections” on that page).

Irshad Karim, the creator of Draw A Box, teaches a specific style of drawing called constructional drawing. Constructional drawing stands slightly apart from observational drawing. With observational drawing, you draw what you see without necessarily considering the three-dimensional composition of your subject. You’re attempting to draw what you see exactly as you see it.

Constructional drawing, on the other hand, asks you to find the fundamental underlying shapes that your subject is composed of, and then figure out how those shapes combine in three-dimensional space. Planes. Boxes. Cylinders. Cones. Spheres. By understanding how they relate to each other in three dimensions, you can use fundamental shapes to construct a rough model of your subject, and then build from there, adding layers of progressively finer detail.

The goal of constructional drawing isn’t necessarily to capture something you see. Instead, the goal is to “convey a message through visual means,” as Karim puts it. It doesn’t have to be perfect or entirely true to life: as long as it effectively communicates what you want it to, then you’ve achieved the basic goal.

I’ve greatly simplified both techniques - you can find more complete explanations elsewhere. I only describe the two to give some context: the exercise I’m describing here is all about understanding those basic shapes in three dimensions.

I imagine some of you have already snapped your monitors in half due to boredom. “I ain’t interested in no comparison and contrastation of varying approaches to drawing!” you yell at your monitor, which is lying on the ground questioning its life decisions. “I’m here to see Paul tear down his own works!”

I get you, Angry Strawman. We’re moving on now. Please don’t hurt me, or any other monitors.


The task is straightforward: draw boxes in 3D space. Let them overlap - just draw boxes. Then draw lines to show how the boxes intersect with each other.

Let’s get one thing clear: I can draw boxes. I’m not perfect, but I have drawn some boxes.

I have drawn




None of those exercises required me to draw intersecting boxes, though. If there was ever an overlap, I could just assume that one box comes in front of the other. Easy!

BUT NO MORE. Now I have to figure out where and how these boxes intersect. Which is HARD AS BALLS, which is what everyone said about the exercise, including the instructor.

Kind of stupidly, I assumed that I’d get the hang of it more easily than everyone else had.

Oh Paul. You poor fool.


Ruh roh. That is one confusing as hell drawing. As usual, click here for the ginormous version of this exercise.

Okay, first problem, as noted in the drawing itself: too many damned boxes. “Fill up the page,” the instructions said. “Sounds great!” I replied. “So you mean, like, put a thousand boxes right on top of each other?” “What? Jesus, no, that’s not what I meant at all,” said the instructions.

“‘Kay, got it!” I affirmed. “All of the boxes in the world.”

Second problem, and this one is pretty easy to see after looking closely at some areas: I tried to draw an intersection, failed, realized my failure, and then tried to fix it. I’m not particularly unhappy about this, per se; I wanted to learn! I wanted to get it right and to see what “right” looks like! After all, I’m not trying to make a pretty drawing. I’m trying to crowbar my damn brain into knowing how to draw a bunch of boxes colliding with each other.

But here’s the third problem, and it’s a biggie: I still do not know if I did any of it right.

Part of the way through the exercise, I went to a different page in my sketchbook and drew this:

I had cracked the code. I had it figured the hell out. So I did the rest of the exercise following that rule: find the figure “cutting” the other figure, and follow the planes of the first figure. Perfection!

And then I looked back at the exercise while writing this post, and everything seemed wrong. And I think I’ve realized why: it’s all about perception. It’s the “do you see an old lady or a young lady?” picture problem. When I originally drew the diagram, I meant to show this:

But later, when I looked at it again, I started to see this:

For the life of me, I cannot figure out if one of these is “right” and the other is “wrong.” Maybe they’re both wrong! Or maybe they’re both right, which would mean that perception is relative, perspective is meaningless, and everything is the worst.

Maybe I’ll figure out more as I go along. This is page one of four. Next time, I’ll start using shapes other than boxes: cones, cylinders, spheres, and pyramids. This is going to be interesting. I feel like I’m learning a lot of valuable lessons about—