Lesson 1: Lines, Ellipses and Boxes

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.

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.

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.