Have you ever tried to explain 1, 2, 3, 4 or 5-point perspective to someone?

Well, I’m going to attempt something like that next Tuesday evening in the Figure Drawing session I moderate. I want it to make sense, be helpful and do away with a mystery or two. This blog post will hopefully help me identify the crux of the matter and help me keep it either very simple on Tuesday or give me the knowledge I need if someone has a really tricky question. The quintessence of this post is that parallel lines must converge.

When you start learning perspective you hear a lot about vanishing points and the horizon line. I’ve always been troubled with that one horizon line which is always mentioned, and now I’m pretty sure, every set of parallel planes has its own horizon line. The one you always hear of is the one defined by the flat surface you are standing on when looking at your subject, or the flat plain you want your constructed object to stand on. I’ll come to the vanishing points in a second.

Then you have all those different types of perspective (1, 2, 3, 4, 5), which can be a bit overwhelming.

So here goes: Perspective is just a constructional help for us artists to emulate on a flat piece of paper the data our spherical(!) eyes collect when observing the real world. If you get the construction lines correct, the eye cannot tell the difference between our flat piece of paper and what I’m calling “the real world”. Great, right?

Now, the whole thing is just a mathematical problem which has been solved masterfully by many scientifically interested artist/researchers, e.g. in the renaissance by a few well-known characters.

For 1, 2, 3 and 4-point perspective, I’m going to put the main rule in a succinct sentence of my own and then try to make sense of it:

“Parallel lines always converge at the same point on their horizon line.”

Before I go into explaining that, let me mention that 1, 2, 3, and probably even 4-point perspective are only approximations of the real mathematical solution and therefore only work in a limited cone of sight. That means, if we were looking at the subject of interest through a cone (just a rolled up newspaper will do), then this approximation only works well for an opening angle of 60 degrees. That’s really ok, if you’re far enough from your model and are not tempted to draw all types of other stuff going on around you. (Ok, glad I’ve got that one out of the way for now … notice I haven’t even started talking about 5 point perspective yet.)

OK, so the sentence above contains the following words:

- parallel
- line
- converge
- point
- horizon line

Let’s start with “line”, sounds simple. A line is constructed from two points. E.g. the two corners of a square, or any adjacent corners of a cube. So let’s imagine a cube around the torso and let’s look at the two top-most, frontal (anterior) points (the head of the humerus bone). By connecting those two points we construct a line along the top of the torso (thorax and abdomen). There are more such lines on the torso, we’ll probably get to one or two of them in a second.

OK, next word: “parallel”. Two lines are parallel to each other if they lie on the same plain and(!) the distance between both lines does not change. So, let’s look at our constructed cube around the torso again. Every line you construct on the front of the cube (across the thorax or abdomen area) sits on the same plain. But not every line there is parallel to the one we identified first (the connection between the two humerus protuberances). That line defines the edge of the very plain we’re looking at (or is at least very close to it). Another line, parallel to this first one could for example be a line that connects the two nipples. There you have it, we now have two parallel lines (you can probably find many more). On to the next point.

Before we get to “point” though, let’s talk about “converge”. The trouble is actually that we can only draw those two lines parallel on our sheet of paper if we are looking at our model straight in the face. If by fortune we have a seat slightly off-centre to the model, then we can use our newly budding perspective skills and draw those parallel lines converging to some point on or even off the paper. Now, let’s not get carried away and start bending those lines, they stay as straight as they ever were, we are still approximating the torso as a cube. (By converging, we mean that the lines are getting closer to each other as they extend across our sheet of paper.) The end of the lines which lie on the part of the cube which is to be seen closest to us must be further apart than the opposite ends. This is an important point, and you should always notice whether the lines in real life are approaching you or receding from you.

When the (possibly imaginary) extension of the two lines eventually meet (either on or off the paper), then we have a “point”. Now this point will be shared by every single line which is parallel to the first two. This is the vanishing point.

Wow, let’s relax, we have now learnt 1-point perspective. But 1-point perspective can be used multiple times in one drawing. If you keep on finding new sets of parallel lines on the same plain, ones which actually cross other parallel lines on that plane (e.g. imagine a chessboard), then you will eventually end up with so many vanishing points that you will see a line: the “horizon line”. (If you select a plain which is parallel to the ground you are sitting on, then the horizon line is at the level of your own eye.)

The “horizon line” is where every line on a plain parallel to this “horizon” will end. Take a moment to imagine a few parallel plains, we have been looking at parallel lines up until now. The front and back of the torso cube are parallel planes, so they will share the same “horizon”. And the top and bottom of the torso cube are also parallel plains and therefore also share a “horizon”, even if it is not the same horizon as the other two plains.

And there you have 2-point perspective, it just creeped up on you without us noticing. When people talk of 2-point perspective, they are simplifying the above, but thereby hiding information. A cube can be cut into horizontal slices and therefore every line joining two new corners are not only on a side plain but also on a plain parallel to the ground. You end up with 2 vanishing points on one horizon line. Voila: 2-point perspective.

Similar simplification will give you a perspective model which is described as 3-point perspective. If you are close to your model and are peaking up at her, this model will help you abstract and construct one vanishing point far above the model. In reality, based on my sentence above, all we have here is a side plain with an orientation which leads to a new horizon line which is oblique to the vertical.

4-point perspective is also a simplified perspective model to help you construct lines which are converging to a vanishing point below the model. But now we know for sure, all we have here is a new plain with another horizon line, negatively oblique to the line we found earlier while looking up at the model.

All of this is, as mentioned before, only an approximation and if you really want to realistically construct the world our eyes report to our brain you need to fall back on 5-point perspective. The construction lines here are curves, and believe me, if you risk going down that path, you will start seeing curves and will begin drawing curves too. As soon as you want to step out of the “60 degrees cone of vision”-prison, this is one way you can go (it is not the only one, you can stretch the “rules” or just disregard them. There are more ways to represent real life than the way the construction of our eyes believe to be correct).

I know, I should and could add drawings to this post, but believe me, there are so many drawings out there on this topic. Don’t go and look. Try and construct it yourself (perhaps take a peek at 5-point perspective, as I only scratched that topic).

If you got this far, you can add n-point perspective to your CV.