Lesson 1: Lines, Ellipses and Boxes

This is going to be the first major exposure to something I do sometimes with my lesson's exercises: assigning tasks that are not necessarily going to be within your current ability to complete. To put it simply: these are probably going to be too hard for you. But that doesn't matter - you should still do them.

All I ask is that you complete the exercise - not perfectly, not even well. Just finish it to the best of your current ability. I ask for nothing more than that.

To start the exercise, using a ruler we draw a horizontal and vertical axis in the middle of our page.

The horizontal line should be familiar. It will serve as our horizon line, along which vanishing points move when the a box at its center is rotated along its vertical axis.

The vertical line serves the same kind of purpose, except for the vertical vanishing point, as a box at the center gets tilted up or down.

Next, draw a square centered on the middle of the two axes, once again using your ruler. This will represent the front face of the box in the middle of our set, and we'll be using this box (which will be finished up a few steps later) as a source of information to help us construct the boxes we'll construct around it.

One problem we encountered a lot in the past was that students often found it difficult to judge just how much they should rotate each box as they radiate out from the center. This step serves to help address this problem.

Place another square (again, with your ruler) - smaller than the central one - beyond the end of each axis.

These squares are just going to be left as squares - unlike the central one, which we'll develop into a complete 3D form next, those squares are only meant to serve as reminders as to the fact that we're rotating our boxes across a full 180 degree arc. By being able to see these representations of the side planes of fully rotated boxes that would be in those positions - but if we worried about also constructing them as full boxes, we'd be making the exercise more complex, rather than helping the student to achieve the core goal more effectively.

Put your ruler aside, as we won't be needing it for the remainder of this exercise.

Using the ghosting method, draw the rest of the central box by placing a smaller square inside the outer one. Its size beyond being smaller doesn't really matter, but you can't go wrong with making it half as big.

Then connect the corners of the larger square to those on the smaller square with diagonal lines to complete the box.

So far the instructions for this exercise have been pretty straight forward, just drawing squares, lines, and a box in a fairly familiar configuration. Now, things will get a little more interesting.

Pick a side of the central box, and on that side, draw a single plane. You're essentially going to take the central box's side plane and copy it, moving it slightly away. You can keep your lines all parallel to the original (so this plane's top edge would for example run parallel to the corresponding top edge on the central box's side).

While this slight bit of space between the plane and the original box would technically result in convergence rather than lines that are parallel on the page, we're taking advantage of the fact that the distance is so small, and that the convergence would be so minor, that it's not really going to be noticeable at all.

In other words, it's close enough to correct, and we're taking advantage of that fact.

In essence what we have to do here is take each corner of our plane and think about what is going to happen to it as it is rotated and pushed over to the side, to find the opposite plane of the box.

We know the following:

• The lines representing the top/bottom edges of the box's front face will be shorter than those same lines on the central box, given that our box is going to be slanting away from the viewer.

• Because we're transitioning from those top/bottom lines converging to an infinite vanishing point to a concrete vanishing point (meaning those top/bottom lines will start converging), this means that as we transpose our corners from one side to the other, they're also going to move closer to the horizontal axis.

Keeping these in mind, in my example I took each corner and moved it over by a distance less than the length of the original box's top/bottom edges, and moved them closer to the horizon line by a small amount.

With these front corners positioned, we need only place the back two, but for these we can think of them in relation both to the back-left corners, as well as in relation to the front-right ones we just placed. While it can be a little challenging at first to balance all of these different relationships at the same time, having more points of reference does help us make better estimations.

Using the same considerations as above, and keeping these points of reference in mind, place the remaining back corners. With all of your corners placed, using the ghosting method, connect your corners to one another to build out the rest of the box.

Do the same thing all over again, but this time for a box above or below the central one. If for whatever reason you have trouble translating the instructions thus far (which were largely related to adding a box to the right side), here's a trick! You can just... rotate the page. And all of a sudden, you're drawing the same box all over again!

Magic!

While the video at the top of this page gets into tackling the corner boxes a little more, at the end of the day it's still largely applying the same concepts, the same considerations, and relying on the available points (and lines!) of reference.

So, construct the rest of the boxes, so you've got two on either side of the central box on each major axis, then filling in the quadrants that remain. Anything that directly neighbours a box you've already constructed, be sure to take advantage of it by keeping your gaps tight and consistent.

You'll also note that in the example from the previous step, I added tight, consistent hatching on select planes of my boxes. This is one useful way to help clear up confusion over the many lines at play.

Another tool we can use to achieve that is line weight, which helps to clarify when an edge should be interpreted as being physically in front of another. As explained in this video, though line weight can be used in a wide variety of ways in general, for your work in this course we want you to limit it to only the localized areas where overlaps between lines occur, to help clarify them.

Keeping your gaps narrow and consistent is critical to being able to use neighbouring forms as effectively as possible to infer information about space.

Drawing through boxes helps us to understand how those forms sit in 3D space, and how they relate to other forms that are present. That understanding of space is something that develops slowly, and we can work on it by exploring it in this manner.

If you do this exercise without drawing through your forms, you're going to end up missing on a great deal. It may look a lot cleaner, but it'll be worth a lot less in terms of what you get out of it.