Learning perspective and view points

3D box

The nine typical viewpoints

There are nine typical views which will help you many a time. Try to fix these views in your mind by practising as much as you can, first by referring to the model and then gradually on your own.

The 9 typical views of frontal perspective. There are 9 boxes in front of both of these figures. Note that the numbers, from one illustration to the other, are a mirror reflection since the viewpoint represented on the right is that of one or other of the figures facing us on the left. Boxes 4 to 6 straddle the horizon line, so their upper and lower sides will not be visible.

The aspect and number of sides presented by the boxes will of course be the same for the two spectators. Only the floor plan will be seen differently, but this is not what concerns us here. Up to now we have been looking at boxes made of opaque material and with only one, two or three sides visible to us.

But if the boxes were to become transparent, you would be able to see all the other sides and represent them by drawing their edges, even if they are concealed.

You will note that the observations we made in the three preceding pictures remain valid for the sides which were hidden:

  • The vertical lines of the boxes remain vertical in the drawing
  • The horizontal lines perpendicular to the visual ray remain horizontal
  • The horizontal lines parallel to the visual ray all converge on the principal point

If you look at the central box, you see very clearly that the side perpendicular to your visual ray – the front side – is much larger than the rear side. This is an optical phenomenon that one comes across time after time.

This observation seems obvious enough but please remember one very important notion which can be summarised as follows:

The further away an object (or shape), the smaller its size as it appears to us.

Why is this the case?

An illuminated object emits rays in all directions. Each point of the object emits numerous rays, some of which move towards our eyes. Only the rays which reach the crystalline lens are “seen” by our eye. Those that do attain the crystalline lens pass through it and are deflected. The optical properties of the lenses cause all the rays to converge on a single point on the retina. So we can simplify our diagrams by concentrating solely on the ray which passes the focus of the crystalline lens (grey star) and is not deflected. In this way we can determine the place where the image of a point is projected on the retina.

According to this principle, when an object is in front of your eyes, it is “printed” on your retina upside down, like this red triangle.

Each reflected point of an object will follow a trajectory equivalent to the point passing through the focus of the crystalline lens.

The coloured stars dotted around this drawing will follow the same optical principle before appearing on the retina. Thus, as seen by your eye, the red star will be below the blue star and the yellow star above it, whereas in reality it is the other way round.

If several points are situated along the same “path”, they will be situated one behind the other as far as your eye is concerned, and you will see only one of them – the point nearest to you.

The points reflected by the objects constitute in their entirety the “picture” projected on your retina. Look at this illustration. The two grey bars marked respectively by a red star and a green star are two objects of the same size situated at two different distances from an observer. They could just as easily represent two vertical poles as a slanting view of two railway sleepers.

By looking at the trajectories of the luminous rays reaching the retina, we understand very well that the object furthest away is projected in a smaller size on the retina than the nearest object.

The apparently diminishing size of the more distant objects is an additional observation which will help you make a convincing representation of reality.

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