There are at least two ways to tackle drawing in perspective; the “architects approach” and the “artists approach”. The architect takes his floor plan and elevations of a building, makes a series of projection drawings and produces an impression of a structure which may not even exist yet. The artist sketches the scene before him and uses the principles of perspective to avoid inconsistencies and to produce a realistic impression. I will assume that you are an artist rather than an architect, but it is worth noting that text books usually deal with either one approach or the other, not both. Some of them do not make this clear on their cover, but a quick glance at the diagrams and illustrations will usually settle the question.
Most books on perspective start with single point perspective and then build up to two and three points. For variety I will work the other way round.
Imagine a view of a large cube. Edges of the cube which are parallel in reality will all converge at one point in the drawing, if the drawn edges are extended. This point is called a vanishing point. See figure 1. Since a cube has three sets of parallel edges, there are three vanishing points. This is sometimes called Aerial Perspective. A more complex drawing could easily have many more vanishing points, one for each set of parallel lines. If the cube is viewed from a slightly different angle, there would still be three vanishing points but they will have changed position.
Why do parallel lines converge at vanishing points? The fact that they do can be proved by taking a cross section through the artist, his drawing and the object drawn, or a bird’s eye view of them. It would take too long to explain here and you should consult a good book on perspective if you are interested or sceptical. Too much importance is often placed on the vanishing points. As an object turns, so the vanishing points move in a precise mathematical relationship, but before long these points are well outside the drawing board. If a precise movement is required, there are much easier ways of plotting it, as I will explain later. The vanishing points are a consequence of drawing in perspective but are only of limited use in the initial stages of plotting the drawing. Leave the mathematics of perspective to the computers.
If we are looking straight on at a set of edges, then for all practical purposes their vanishing point is irrelevant. It is at infinity and we can show them all as parallel in the drawing itself. By looking straight on I mean that the parallel set of edges are also parallel to the picture surface (the sheet of glass).
For example the uprights of a building when viewing it at eyelevel. See figure 2. This is sometimes called Oblique Perspective. As we have eliminated one vanishing point, it is easier to draw, but aerial perspective generally gives a more dramatic effect.
If there are two sets of lines square on to the viewer and the drawing, then the vanishing points for both sets become irrelevant. Both sets can be drawn parallel. This is single point perspective. Because single point perspective is easier to draw, the rules are sometimes bent slightly so that it can be used even where one or more sets of lines are not quite square on.
Figure 3A shows the cube in single point perspective. The hidden edges are shown by dotted lines. Figure 3B still uses single point perspective, but manages to show us not only the front but also the side. Surely, if we can see the side, we cannot be square on to the front? But this drawing is sufficient for some purposes. It gives the eye the information it needs to build up a picture in the brain, even though it is not a perfect representation. Figure 3C manages to include the top as well.
Although single point perspective is sometimes enough, oblique or aerial perspective should be used whenever possible. In the same way it is possible to use oblique perspective in the drawing of a building even when the artist intends to show a view other than at eye level, for example, looking up to the roof. (Remember the glass is supposed to tilt as he lifts his gaze and the uprights are no longer square on). Again the drawing may be sufficient, but a rule of perspective has been broken and the result is a loss of realism.
“The angle of view of the human eye is 60 degrees”. This bold statement needs some explanation. As I said earlier, the human eye is not a camera. We see in detail and full colour in the centre and in black and white in less detail towards the edge. Our nose gets in the way, we have two eyes, our eyes swivel, most of us have defective vision. Nevertheless, when we consider placing an image on a flat surface in front of us and viewing it with one eye, the amount we are able to see in sufficient detail for perspective to matter is an angle of about 60 degrees.
When an architect plans a drawing he considers the angle of view very carefully, but an artist rarely gives it any thought at all. If he can see the whole of what he wants to draw without turning his head, then the drawing will automatically stay within the 60 degree rule. The animator however is normally drawing from his imagination and memory, he must be careful with the angle of vision. In drawing it is possible to take in an angle of view up to 90 degrees without any apparent breach of the rules of perspective, but beyond 90 degrees these rules become difficult or impossible to apply. The view then is not human but “fish eye”. Does it matter? Yes, if you want to create an illusion of reality.