The Perspective: (3) CUBES AND VANISHING POINTS

In this third part of our perspective guide, we continue with the core building blocks of classical perspective. We explain why cubes are so important and learn how to draw them with 0, 1, 2, and 3 vanishing points.

Why do we always talk about cubes?

First of all, we talk about “cubes”, but it’s a bit of an abuse of language. In reality, these are rectangular parallelepipeds (also called right prisms).

All classical perspective is based on the fact that a right angle belonging to a horizontal plane (in real life) is represented on a drawing or photo by a larger angle — except if this right angle is placed exactly on the observer’s retina, in which case it remains a right angle on the drawing! Everything else follows from this principle.

It may seem trivial at first, but we must not forget that this is a peculiarity of human vision. Many animals do not see in 3 dimensions, and many also distort perspective (if we consider human perspective as the reference).

The “cubes” — having only right angles — are therefore the only geometric objects directly (or easily) usable in perspective. The other geometric objects usable must be constructed from cubes as we will see.

Drawing a cube in perspective with… 0 vanishing points

How? 0 vanishing points? But that contradicts everything we’ve said so far!

Yes… and no 😊

Yes, because parallel horizontals must converge to a common vanishing point in classical perspective. But no, because there are many other types of perspective besides classical perspective. Perspectives without vanishing points are very common and widely used, especially in architecture and engineering (for example cavalier perspective), but also in art.

Many video games use isometric perspective or axonometric perspective.

We can see that edges parallel in real life remain parallel on the drawing.

Here are some examples of views without vanishing points:

There is a true art to “perspective” without vanishing points.

Drawing a cube in perspective with… 1 vanishing point

We return to classical perspective 😊. What is needed to see a cube with a single vanishing point perspective?

It is necessary (and sufficient) that the front face is parallel to the observer’s retina.

In this case, the front face (square) appears… square on the drawing (… and the bottom face is parallel to the ground… if the observer looks straight ahead).

All verticals remain vertical on the drawing and horizontals (parallel to the horizon line) remain horizontal on the drawing.

Only the edges perpendicular to the retina will converge toward the vanishing point.

This vanishing point is special. It is placed exactly at the center of vision. It therefore moves depending on where we look.

Plunge and counter-plunge

Any object whose top we see is viewed in plunge (when you dive, you see the surface of the water…).

Any object whose bottom we see is viewed in counter-plunge.

Objects where we see neither the top nor the bottom are viewed “normally”, i.e. they straddle the horizon line 😊

For those who wonder, it is not humanly possible to see both the top and the bottom of a cube at the same time (with only one eye, I remind you).

If the observer looks straight ahead, all cubes are seen in a “neutral” way. On the other hand, if the observer lowers or raises their gaze, all cubes will be seen in plunge or counter-plunge.

Drawing a cube in perspective with… 2 vanishing points

To go from 1-point to 2-point perspective, simply rotate the cube while keeping the bottom face (and therefore also the top face) parallel to the theoretical ground.

Verticals remain vertical on the drawing, but the other edges converge to a vanishing point on the right or left (depending on their position on the cube).

In the scene below:
• The pink cube is in 1-point perspective,
• The house and the blue cube are in 2-point perspective and share the same pair of vanishing points,
• The ochre cube is also in 2-point perspective but is not parallel to any other cube or to the house.

Drawing a cube in perspective with… 3 vanishing points

If we now look upward, the cube will be seen in counter-plunge and the verticals will no longer be vertical on the drawing. They will converge toward a third vanishing point located vertically above the central vanishing point.

It is obviously the opposite if we look downward. We will have a plunge view and the 3rd vanishing point will also be vertically below the central vanishing point.

We can note that the “verticals” become more and more inclined because the 3rd vanishing point gets closer to the horizon line until the gaze forms a 45° angle with the horizon.

The 3rd vanishing point is located above the horizon line if the observer looks upward and below if he looks downward.

Next in the series: Circles & ellipses + false horizon line + practical exercises.