Projection Systems

I loved this little book called Drawing Systems by Fred Dubery and John Willats that I found at the Ohlone Library. I decided to share some text and diagrams from the book as they are concise, and effective (not to mention they look super cool). The three woodcuts on the bottom of the post are all by Albrecht Durer. The rest of the text on this post has been appropriated from the original book.

Projection systems

Any projection system depends on the idea of straight projection lines running from points on an object to corresponding points on a flat surface. The type of projection system depends on the relationship of these lines to each other: whether they diverge, converge, or run parallel, and the angle at which they strike the surface.

 

Orthographic projection

In the simplest case, these lines are parallel, and strike the surface at right angles. The setting sun, directly facing a flat wall, will throw shadows on to it which are the same size and shape as the objects they represent; the sun is so far away that its rays are very nearly parallel. These shadows are orthographic projections.

 

 

 

Horizontal oblique projection

Two views of an object, side and front, added together, give a more complete description of the object than either view alone. This extension of orthographic projection appeared first in Egyptian wall painting (fig. 7), and then again, later, in Greek vase paintings after the middle of the fifth century. The method is simple enough with rectilinear objects, like tables and chairs, but with more complex objects, such as four-horse chariots, a compromise must be made where the two views join.

 

Vertical oblique projection

A vertical oblique projection is obtained empirically by adding top and front views together, rather than side and front views as in horizontal oblique. Vertical oblique projections may also be obtained by projecting an image of the object obliquely on to a picture plane (figs 14a and 14b).

Until this century, the use of vertical oblique projection in the West was exceptional, and in China it was rarely used except for the superimposition of mountains one above the other; but in Persian and Indian painting, its use is quite common.

 

Oblique projection

In ordinary oblique projection both the side and top views of the object are tacked on round the edges of the main front view. In order to make these subsidiary views join up, they have to be distorted, so that the edges of the object which run back into the picture or the 'orthogonals' as they are usually called, lie at an angle to the front view. The lengths of these orthogonals may be true lengths, or any proportion of the true length which seems convenient.

 

Foreshortening

Any part of an object which does not lie parallel to the picture plane will appear changed in length when projected. This is true of any projection system, but the extent of the change depends on two quite different factors: the angle between the projection lines and the picture plane (i.e. the type of drawing system used), and the angle between the part of the object concerned and the picture plane. Thus, the side of a chair lying at right angles to the picture plane will disappear altogether in orthographic projection; but can appear as either more than, equal to, or less than its true length in oblique projection or perspective. In addition, if the chair is set obliquely to the picture plane, then all the oblique planes will appear to be diminished. Some very curious effects are produced when both these factors are combined; some of the strangeness of medieval and Persian painting can be accounted for by the attempt to draw objects set obliquely, in oblique projection.

Isometric projection

In an attempt to make the very complex drawings of the industrial revolution more readable, an English contemporary of Monge's, Sir William Farish, introduced a system which he called 'isometric projection' (fig. 35). This combined the use of true dimensions with a more pictorial appearance. At first glance the system seems to be an alternative form of oblique projection, with the top, side and front views drawn as true lengths at equal angles to each other (fig. 36b). Drawings of objects made according to this method had frequently appeared in Roman, Byzantine, Persian and Chinese paintings, and in the eighteenth-century Japanese woodcut the empirical use of isometric projection for whole scenes, as well as for individual objects, is at least as common as the use of oblique projection. 

Perspective

The central problem in perceptual drawing is perspective, and the central problem in perspective is the degree of spectator involvement. 

Euclid's optics deal in general terms with rays of light in space converging to a point at the spectator's eye: constituting the visual pyramid or cone of vision. In perceiving the geometry of natural vision or natural perspective, Euclid c. 300 BC) cleared a path for draughtsmen and perspectivists of the future; for the empirical methods used in Greek and Roman painting; and for the formal scientific methods developed during the Renaissance and after.

Almost the only surviving examples of Roman painting that exist are to be found in Pompeii and Herculaneum. The first century AD wall painting (fig. 38) in the 'House of the Vettil' is a fairly typical example of this period when a rough and ready empirical system was used. It is worth noting, however, that in spite of the fact that the general idea of the convergence of orthogonals to a central point is fairly well understood in this painting, the problem of describing a deep receding ground plan does not occur. The fully articulated ground plan was to play an important part in Renaissance painting when perspective was understood in terms of primary geometry. The understanding that we now enjoy is attributed to the discoveries of two architects, Brunelleschi and Alberti; their system is known as artificial or scientific perspective. 

'Best method'

The bones of Alberti's 'best method' are contained in the diagrams, figs 40a and 40b. In fig. 40a, the picture plane is placed vertically, with the base line joined to the near side of a horizontal chequered floor. Another plane containing V (vanishing point) and SP (spectator point) is set at right angles to the picture plane though 00. The array of projection lines from the chequered floor passes through the picture plane, forms on it an image of the floor in perspective, and ends at the spectator point. The orthogonals of this image must necessarily meet at the vanishing point.

In fig. 40b the plane containing the spectator point, SP, has been folded back about the axis 00 on to the picture plane: this point is now called DP (distance point). The lines representing the visual rays must inevitably fall across the diagonals of the squares, showing that the distance from the vanishing point to the spectator point is the same as the distance from the vanishing point to the distance point. Thus the triangle SP - V - DP (figs 40a and 40b) is a right-angled isosceles triangle, so that two of the angles are 45°. This brings us back to Brunelleschi's painting of the Baptistry; the two receding planes of the octagonal Baptistry at 45° to the picture plane (fig. 39b) are converging to points on the horizon. These points are therefore the distance points, and accordingly indicate the distance of the spectator from the central vanishing point. It can now be seen that Brunelleschi invented the distance point method and that Alberti supplied the scientific proof. Alberti must in addition be given credit for comparing the picture plane with a window frame.

Leonardo's contribution to the techniques of artificial perspective concerns using perspective backwards, that is elucidating information about the position of objects in space by using linear measurements taken from paintings and drawings. He wrote: 'If you draw the plan of a square (in perspective) and tell me the length of the near side, and if you mark within it a point at random, I shall be able to tell you how far is your sight from that square and what is the position of the selected point.' Leonardo then goes on to explain the procedure; an adaptation of the method is as follows. (In Leonardo's description

of the procedure, the central vanishing point V and the side view of the picture plane VG are not in coincidence. The result however is precisely the same.) Take a square ABCD (in perspective) (fig. 41). Produce AD and BC to intersect at V. The point V is the central vanishing point (on the horizon or eye level). Produce the diagonal AC to meet the eye level; this gives the distance point DP. Mark off a number of equal divisions along AG passing through B. Join these points to DP and V. The intersections on VG will give the horizontal co-ordinates and the intersections along AB will give the orthogonal co-ordinates.

'Scale your drawing' Leonardo says, 'and you will see the position of your point marked at random in the square.'

  

Method of drawing a portrait

In fig. 42 the artist is seen drawing a seated man on a pane of glass, keeping his eye in one place by looking through a sight vane. 'Such is good for all those wishing to make a portrait but who cannot trust their skill', recommends Dürer.

The artist simply traces the contours that appear on the glass, with a paint brush. The drawing that results is transferred to a panel ready for painting. 

There is a drawing of a similar machine in one of Leonardo's notebooks; probably Dürer learnt of the device when he met Leonardo in Venice.

By using a window with a view, closing one eye and keeping the head still, it is possible for anybody to demonstrate the principle of the machine. A chinagraph pencil or white paint may be used for tracing the outlines.

A man drawing a recumbent woman

Again the spectator keeps his eye in one place by using the sight vane. The frame (picture plane) is here covered with a network of lines; squared up like a map. The spectator's drawing paper is also squared up, not necessarily to the same scale. As the contours are observed in relation to squares within the frame, these contours can then be drawn on to the corresponding squares on the paper. By using this method, Dürer shows the man overcoming the difficulties involved in a close-up foreshortened view, also that this is a good method for reducing or enlarging a drawing proportionally.

A man drawing a vase

In 'method of drawing a portrait', the spectator is restricted to the size that he can make his drawing by the length of his arm plus the brush. When light rays converge to the spectator's eye, the size of the image formed by the intersection of these rays on the glass or picture plane is the size that can be seen, so the drawing is sight size. Sight size can be infinitely variable and depends on the distance between the spectator, the picture plane and the object. 'A man drawing a vase' method extends the possibilities of size and spectator distance from the picture plane, by substituting a ball and socket joint attached to the wall for the visual cone. The use of a rigid bar with a plain sight at the operator's end and the ball and socket at the other end simulates a single ray of light. The operator aims at the vase, tracing the contours on to the glass, moving his head with the contour because the bar is rigid. The machine is nicer in theory than in practice, although perhaps a skilled operator could produce good results.

A man drawing a lute

This method also provides for those who require long-distance projection; it also removes the tiresome business of looking through a sighting device. It does however require two operators, one for calculating, and one for drawing. A simple pulley is attached to the wall, a piece of string passes through the pulley with a weight at one end and a pointer at the other end. The pulley is substituting for the spectator's eye, the apex of the cone of vision. The string from the pulley to the pointer represents a single ray of light and passes through the picture plane. As the man with the pointer fixes different reference points on the lute, his assistant measures off the vertical and horizontal co-ordinates and plots each new point on the drawing. When there are enough points, he joins the relevant ones, and completes the drawing.