QUICK CONTENTS:

1. What’s a Cube?

2. Cubes in Perspective

3. Viewing Angles

4. Contour Lines

5. Drawing Through

6. Exercises

Things in our world tend to be very cube-like. Our buildings are approximately cubes, our vehicles are approximately cubes, and the list goes on and on. Fortunately, the cube is the easiest basic shape to draw in perspective!

## What’s a Cube?

Technically, a cube is a three-dimensional square, but I will use it as a term for boxes of any size, just as I used *rectangle* for all shapes with four corners. A cube is what happens when you add depth to a rectangle, and essentially extend it in the z-direction. Cubes can be found nearly everywhere, and are often a good way to establish the overall form of objects before adding in the details.

## Cubes in Perspective

Because a cube is just a set of rectangles, we can use foreshortened rectangles to make it look nice in perspective. Because we can never see more than three sides of a cube – if you disagree, check for yourself – we only need (at most) three *vanishing points*. I already told you that parallel lines angle towards each other in perspective, and the reason for this is that parallel lines converge or intersect at those so-called vanishing points. They are nothing more than imaginary points somewhere in the distance where two parallel lines would eventually meet. You often don’t even need to know their exact position, as an approximation is enough to create accurate cubes.

So, when drawing a cube, simply establish the vanishing points and draw lines from them, and you’re done!

As you can see in the image, if you choose your vanishing points too close to your object, you get a very distorted perspective, which often isn’t realistic at all. Something you perhaps also noticed, is that the three vanishing points always form a nice triangle. After you’ve chosen two vanishing points (which shouldn’t be too close to each other), the third one should be at an equal distance from both points.

If you’re wondering *why* parallel lines converge, think about looking down from a very high spot, such as a mountain. Below you can see the houses and maybe even people, but they are nothing more than dots to your eyes. Because they are so far away, their shapes converge towards a single point (from your point of view). More will be explained in the chapter on perspective.

## Viewing Angles

You probably noticed that I said you needed *at most* three vanishing points. You can remove one vanishing point, which means that parallel lines in that direction simply stay parallel. In this case, you’ll only see two sides of the cube. In fact, sometimes a cube even requires only a single vanishing point. To understand when or why this is the case, I need to talk about viewing angles.

There are three dimensions in which you can rotate, which I’ll call *x*, *y* and *z*. You may also call them *width*, *height*, and *depth* if you like. Not only can we rotate other objects in these directions, we can also tilt our own head and by doing so change the *viewing angle* at which we see the world.

Essentially, when one of our viewing angles aligns with one of the cube’s angles, we have only one or two vanishing points. When all viewing angles are aligned, there are no vanishing points; the cube has become a flat rectangle to our eyes. When none of our viewing angles are aligned, we get the three vanishing points again.

## Contour Lines

Because I already took the time to explain to you how to divide rectangles, drawing contour lines on cubes is easypeasy. Cubes have only flat sides, which means you can simply draw the individual contour lines for each rectangle shape, and you should be good.

If you’re wondering – “*what are those contour lines good for?”* – just think about how often shapes in the real world are cubes with holes in them or certain parts extruded. If you want to accurately morph your cube into the actual shape you were looking for, you need the contour lines to show you how the surface wraps in perspective.

## Drawing Through

One last tip I have for you is applicable to all (basic) shapes really, and especially useful if you need to draw the interior of an object (like, for example, what’s inside a box) or a transparent object. The technique is called **drawing through**, and it means that you draw the lines at the other side of the shape, even though you’re not actually going to see them all. This helps build an understanding of how an object is build, and makes it even easier for you to add details.

## Exercises

These exercises will generally take a bit longer than the previous ones, but I still suggest you practice drawing your cubes every day.

### Simple Cubes

Place four dots on the paper, making sure that two of them are on the same horizontal line, and the other two on the same vertical line. Connect them with lines to get a hugely distorted rectangle, which represents the top of the cube. Now draw the rest of the cube.

This is kind of the reversed way of drawing a cube. First, you draw the division lines, and then you use them to create your foreshortened rectangles.

### Advanced Cubes

Place one, two or three random vanishing points on the paper. Now draw the cube that results from them.

### Connecting Cubes

Draw a random cube. Now divide all the sides, and connect a smaller cube to one of the subdivisions. This one takes some practice, but is extremely useful. Once you get better, start adding more and more cubes, and maybe even some variations.

*a point in 3D space that parallel lines are angled towards. 0*?