The Theory and Practice of Perspective Part 27

CXLVII

THE PERSPECTIVE OF CAST SHADOWS

There is a pretty story of two lovers which is sometimes told as the origin of art; at all events, I may tell it here as the origin of sciagraphy. A young shepherd was in love with the daughter of a potter, but it so happened that they had to part, and were pa.s.sing their last evening together, when the girl, seeing the shadow of her lover's profile cast from a lamp on to some wet plaster or on the wall, took a metal point, perhaps some sort of iron needle, and traced the outline of the face she loved on to the plaster, following carefully the outline of the features, being naturally anxious to make it as like as possible.

The old potter, the father of the girl, was so struck with it that he began to ornament his wares by similar devices, which gave them increased value by the novelty and beauty thus imparted to them.

Here then we have a very good ill.u.s.tration of our present subject and its three elements. First, the light shining on the wall; second, the wall or the plane of projection, or plane of shade; and third, the intervening object, which receives as much light on itself as it deprives the wall of. So that the dark portion thus caused on the plane of shade is the cast shadow of the intervening object.

We have to consider two sorts of shadows: those cast by a luminary a long way off, such as the sun; and those cast by artificial light, such as a lamp or candle, which is more or less close to the object. In the first case there is no perceptible divergence of rays, and the outlines of the sides of the shadows of regular objects, as cubes, posts, &c., will be parallel. In the second case, the rays diverge according to the nearness of the light, and consequently the lines of the shadows, instead of being parallel, are spread out.

CXLVIII

THE TWO KINDS OF SHADOWS

In Figs. 261 and 262 is seen the shadow cast by the sun by parallel rays.

Fig. 263 shows the shadows cast by a candle or lamp, where the rays diverge from the point of light to meet corresponding diverging lines which start from the foot of the luminary on the ground.

[Ill.u.s.tration: Fig. 261.]

[Ill.u.s.tration: Fig. 262.]

The simple principle of cast shadows is that the rays coming from the point of light or luminary pa.s.s over the top of the intervening object which casts the shadow on to the plane of shade to meet the horizontal trace of those rays on that plane, or the lines of light proceed from the point of light, and the lines of the shadow are drawn from the foot or trace of the point of light.

[Ill.u.s.tration: Fig. 263.]

[Ill.u.s.tration: Fig. 264.]

Fig. 264 shows this in profile. Here the sun is on the same plane as the picture, and the shadow is cast sideways.

Fig. 265 shows the same thing, but the sun being behind the object, casts its shadow forwards. Although the lines of light are parallel, they are subject to the laws of perspective, and are therefore drawn from their respective vanishing points.

[Ill.u.s.tration: Fig. 265.]

CXLIX

SHADOWS CAST BY THE SUN

Owing to the great distance of the sun, we have to consider the rays of light proceeding from it as parallel, and therefore subject to the same laws as other parallel lines in perspective, as already noted. And for the same reason we have to place the foot of the luminary on the horizon. It is important to remember this, as these two things make the difference between shadows cast by the sun and those cast by artificial light.

The sun has three princ.i.p.al positions in relation to the picture. In the first case it is supposed to be in the same plane either to the right or to the left, and in that case the shadows will be parallel with the base of the picture. In the second position it is on the other side of it, or facing the spectator, when the shadows of objects will be thrown forwards or towards him. In the third, the sun is in front of the picture, and behind the spectator, so that the shadows are thrown in the opposite direction, or towards the horizon, the objects themselves being in full light.

CL

THE SUN IN THE SAME PLANE AS THE PICTURE

Besides being in the same plane, the sun in this figure is at an angle of 45 to the horizon, consequently the shadows will be the same length as the figures that cast them are high. Note that the shadow of step No. 1 is cast upon step No. 2, and that of No. 2 on No. 3, the top of each of these becoming a plane of shade.

[Ill.u.s.tration: Fig. 266.]

[Ill.u.s.tration: Fig. 267.]

[Ill.u.s.tration: Fig. 268.]

When the shadow of an object such as _A_, Fig. 268, which would fall upon the plane, is interrupted by another object _B_, then the outline of the shadow is still drawn on the plane, but being interrupted by the surface _B_ at _C_, the shadow runs up that plane till it meets the rays 1, 2, which define the shadow on plane _B_. This is an important point, but is quite explained by the figure.

Although we have said that the rays pa.s.s over the top of the object casting the shadow, in the case of an archway or similar figure they pa.s.s underneath it; but the same principle holds good, that is, we draw lines from the guiding points in the arch, 1, 2, 3, &c., at the same angle of 45 to meet the traces of those rays on the plane of shade, and so get the shadow of the archway, as here shown.

[Ill.u.s.tration: Fig. 269.]

CLI

THE SUN BEHIND THE PICTURE

We have seen that when the sun's alt.i.tude is at an angle of 45 the shadows on the horizontal plane are the same length as the height of the objects that cast them. Here (Fig. 270), the sun still being at 45 alt.i.tude, although behind the picture, and consequently throwing the shadow of _B_ forwards, that shadow must be the same length as the height of cube _B_, which will be seen is the case, for the shadow _C_ is a square in perspective.

[Ill.u.s.tration: Fig. 270.]

To find the angle of alt.i.tude and the angle of the sun to the picture, we must first find the distance of the spectator from the foot of the luminary.

[Ill.u.s.tration: Fig. 271.]

From point of sight _S_ (Fig. 270) drop perpendicular to _T_, the station-point. From _T_ draw _TF_ at 45 to meet horizon at _F_. With radius _FT_ make _FO_ equal to it. Then _O_ is the position of the spectator. From _F_ raise vertical _FL_, and from _O_ draw a line at 45 to meet _FL_ at _L_, which is the luminary at an alt.i.tude of 45, and at an angle of 45 to the picture.

Fig. 272 is similar to the foregoing, only the angles of alt.i.tude and of the sun to the picture are altered.

_Note._--The sun being at 50 to the picture instead of 45, is nearer the point of sight; at 90 it would be exactly opposite the spectator, and so on. Again, the elevation being less (40 instead of 45) the shadow is longer. Owing to the changed position of the sun two sides of the cube throw a shadow. Note also that the outlines of the shadow, 1 2, 2 3, are drawn to the same vanishing points as the cube itself.

It will not be necessary to mark the angles each time we make a drawing, as it must be seen we can place the luminary in any position that suits our convenience.

[Ill.u.s.tration: Fig. 272.]