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Lesson 1: Lines, Ellipses and Boxes
Boxes
Regarding perspective
Before we get into this, I want to make one thing very clear: the lesson content on this page is a LOT to take in. The video may help you understand better, but it's not all going to sink in all at once. Watch the video, then read through the written material, then even if you're unsure of things, move onto the exercises. As you work at it and employ the concepts described, it will gradually start to make more sense over time.
Finally, having sloughed through lines and ellipses, we've reached the namesake of this website  boxes. I chose that as our name not because it is all I wish to teach you, but because it is representative of so much more.
A box consists of three sets of parallel lines. If you're familiar with three dimensional geometry, each set defines an axis  either x, y or z  and in doing so, it establishes the foundation of what we understand to be 3D space.
Any object can be simplified into the box that encompasses it. Any form can be represented and constructed within  you guessed it  a box. And any box can be subdivided, carved, and built upon to create any complex object.
But if we want to learn how to draw a box, first we need to learn something about perspective.
Vanishing points and parallel lines
If you've heard anything about perspective in the past, you've probably heard about the concept of a 'vanishing point'. It is a representation of the most fundamental rule of perspective  as an object moves farther and farther away from you, it's going to appear smaller and smaller to you.
Eventually it'll get so small that it collapses to a single point, after which it effectively vanishes due to being so infinitesimally tiny. A vanishing point.
Instead of an object, we can also think of this as applying to a distance, represented by a single line. As this line moves further and further away, its length (the distance between the end points of the line) would shrink until it too collapsed to a vanishing point.
Finally, if you think of this distance as being the distance between any two parallel lines (which remains consistent in 3D space by nature of them being parallel), when drawn in 2D any lines that are parallel to one another will ultimately converge towards  you guessed it  a vanishing point.
This brings us to the rule that exists at the core of understanding perspective: any set of lines that are parallel to one another in 3D space will, as they grow farther and farther away from the viewer, ultimately converge to a single, shared point.
1, 2 and 3 point perspective
Again  if you know anything about perspective already, you'll probably have heard about 1, 2 and 3 (vanishing) point perspective systems. While we will deal with these each in small amounts at first, I want to make one thing clear:
These 1, 2 and 3 point perspective systems do not exist. It's a simplification of the concept intended to help beginners learn, but one that I find to be extremely limiting. When I was first learning perspective, it was something that confused me for years, and I've seen the same in many of my own students.
VPs in a scene
A scene will be governed by any number of vanishing points. It simply depends on how many sets of parallel lines you have. If you throw a box into your empty scene, that gives you three sets of parallel lines. If you duplicate this box and move it slightly to the side  so it's still sitting parallel to the original, you still only have three sets of parallel lines between them, and therefore 3 vanishing points.
If however you take that second box and rotate it on one of its axes, two of its sets of lines will no longer be parallel to the corresponding ones in the other box, and you'll end up with 5 sets  therefore, 5 vanishing points.
If you think about drawing a scene in your kitchen in perspective, you're going to have all kinds of objects laying around  a fridge, a microwave, a cutting block, an oven, etc. And while you may be super neat and obsessive about keeping everything perfectly aligned to a grid, you're not perfect  some of those things are going to be off at some kind of an angle. In fact, if everything were perfectly aligned, it'd feel... off. Too sterile. Not to mention the fact that not everything is just a simple box.
There are so many different sets of parallel lines in a scene, and a vanishing point for all of them.
VPs at infinity
Now, 3 point perspective would be fine if all we had was a single perfect box in a scene, alone. But what about 1 and 2 point perspective? Those are also used to draw similar setups (a perfect cube alone in a scene), but we know that our box is made up of 3 sets of parallel lines  so how can we have fewer than 3 vanishing points?
There are ways, based on how we look at a given object, that we can eliminate some of its vanishing points. Or, perhaps a better way to put it is, those vanishing points are placed so far outside of our canvas or page that the convergence of all the parallel lines leading to it is negligible. It's effectively at infinity, and while in theory if we can look infinitely far away from where we're actually drawing, we'd be able to see those lines converge.
Two point perspective generally involves the vanishing point for your vertical lines, which usually sits very high up, generally off the page or canvas, being moved so high up that the convergences become pointless. Anywhere within the frame of your composition, any lines going up to that vanishing point will effectively run straight up and down, perpendicular to the horizon. We can achieve this effect only when we are not looking at the box from too high or too low of an angle.
One point perspective goes one step further. In two point, the vertical vanishing point is at infinity, leaving the remaining two vanishing points on the horizon line. To move into one point perspective, we move one of those vanishing points so far off to the side that it too goes to infinity. Your one remaining vanishing point in this scenario is going to be sitting somewhere visible within your composition (rather than being off the page/frame), otherwise things are going to look really weird and distorted. This means that the viewer is going to be looking down the barrel of your box, or at least close to it.
1, 2, 3 point perspective simplified
Now, all of this is probably really confusing and is going to take a while to sink in. Don't worry about that, you'll start to grasp it gradually. What you can keep in mind for now, in terms of when to use 1, 2 or 3 vanishing points for a box are these much simpler rules of thumb:

If your view is aligned mostly to a box's face, use 1 point perspective.

If your view is aligned mostly to a box's edge, use 2 point perspective.

If your view is aligned mostly to a box's corner, use 3 point perspective.
This actually works pretty well, until you're able to grasp the more complex reasons behind it all. When you're looking directly at a face of a box, one set of its parallel lines are going to be receding to a vanishing point in the frame, somewhere pretty close to the face you're aligned to. When you're looking directly at an edge, you've got two sets of parallel lines going off to either side of it. When you're looking at a corner, all three sets of parallel lines are coming off of that single point towards their own vanishing points.
While the focus on boxes does sometimes make it seem that Drawabox is primarily a perspective course, it's not. We merely get into the concepts of perspective that are necessary to explore 3D space in a more organic fashion, and right from the beginning once we lay down that basic foundation, we immediately start pulling away from critical tools (like vanishing points) so students learn how to draw without needing to refer to the vanishing points that might sit way off their page.
There are however a ton of useful perspective techniques and tools to be learned beyond what we cover here. If you're interested, you can check out this course from our sponsor, New Masters Academy:

This is one of the most comprehensive breakdowns of perspective you can find. Many courses don't go much farther than looking at 1/2/3 point perspective, but one of the things I love about Erik's course is that he dedicates an entire lesson to the idea that scenes and objects are not restricted to a maximum of 3 vanishing points  a concept that is often overlooked, or left to the student to figure out on their own.
That said, there's a lot of value in exploring a looser, more freeform approach to traditional perspective challenges:

This course focuses on the essential principles of perspective without getting lost in the technical stuff  it's great for going out and drawing scenes and buildings from observation, and a great way to learn to have fun and relax with your art.
Sign up to New Masters Academy with the coupon code DRAWABOX22 — you'll get a full 35% off your first billing cycle.
Homework and exercises
Every Drawabox lesson consists of lecture content and exercises that are assigned as homework. It's best to complete this homework before moving onto the next section. As this lesson consists of three sections (lines, ellipses, boxes), it is best that you only submit your work for review when you've completed all three.
The homework assignment for this section is as follows:

1 filled page of the Plotted Perspective exercise

2 filled pages of the Rough Perspective exercise

1 filled page of the Rotated Boxes exercise

2 filled pages of the Organic Perspective exercise
All the assigned work for this section should be done in ink, using fineliners/felt tip pens as described here. In a pinch, I will accept work done in ballpoint, but only if the situation is dire. This is an exception only for this lesson as students get started.
Ellipse Master Template
This recommendation is really just for those of you who've reached lesson 6 and onwards.
I haven't found the actual brand you buy to matter much, so you may want to shop around. This one is a "master" template, which will give you a broad range of ellipse degrees and sizes (this one ranges between 0.25 inches and 1.5 inches), and is a good place to start. You may end up finding that this range limits the kinds of ellipses you draw, forcing you to work within those bounds, but it may still be worth it as full sets of ellipse guides can run you quite a bit more, simply due to the sizes and degrees that need to be covered.
No matter which brand of ellipse guide you decide to pick up, make sure they have little markings for the minor axes.