25. Deformations due to Displacement of the Viewpoint. When a perspective is looked at from a point other than its viewpoint, the different parts of the image are no longer seen at the same angles as the corresponding parts of the subject. The representation in this case is falsified, and one no longer appears to see the object but only a more or less distorted form of it.
If we suppose at first that the eye with which the perspective is observed remains at a distance from it equal to the principal distance, but without being placed at the viewpoint, th€ object undergoes a torsion. For example, if the eye is in a position higher than the viewpoint, all the horizontals of the sub ject appear to slope down from the observer to the horizon their vanishing O points become in fact lower than the eye, and the apparent slope of each horizontal will be that of a straight line joining the eye to the corresponding vanishing point.
Next, suppose that the eye, while remaining at a distance from the pro jection plane equal to the principal distance, is displaced laterally. To make this clear, suppose it is placed opposite the vanishing point F (Fig. 4). This point, being now substituted for the principal point, would be on a perspective examined under correct con ditions, the vanishing point of the straight lines of the subject perpendicular to the projection plane. Under the actual conditions of examin ation one is thus led to consider the facade of the shed as perpendicular to the plane of pro jection, which is not the case.
Every combination of the two displacements of the eye, the effects of which we have just considered separately, will result in a double torsion of the object. Notably, the straight lines, which in the object were perpendicular to the plane of projection, will appear always pointing towards the eye, whatever may be its position relative to the projection plane.
Now suppose that the eye, whilst being kept on the perpendicular from the projection plane to the principal point, is displaced along the length of this line. The object will appear drawn out in depth or compressed, according as the distance of observation is greater or less than the principal distance, the deformation being in every case proportional to the ratio of these two distances. Imagine two objects at A and B in the horizontal plane (Fig. 5). In the perspective traced from the viewpoint 0 on the projection plane T, the images of these two points are at a and b. If, instead
of observing this perspective from its viewpoint, the eye is moved to 0'. at double the dis tance, obviously the objects cannot be considered as hanging freely in the air, but must be resting on the plane shown. One is, therefore, compelled to assign to these points the positions A' and 13', the object thus being drawn out in the ratio of I to 2. If the distance AB is more or less fixed (the case of a man lying down to whom cannot reasonably be attributed double the normal stature), the details of the object situated at A', which we intuitively consider as being at A", will be on an exaggerated scale for the position that we attribute to them in the object. The front planes are expanded relatively to the back planes.
Obviously, these deformations may occur in addition to those due to the displacement of the observer upwards or across.' 26. Normal Distance of Vision and Angle of Visual Field. A normal-sighted person generally chooses a distance of io or 12 in as the distance from his eyes at which to examine such objects as printed matter, etc. This distance is usually known as the normal distance of vision. The smallest distance of distinct vision at which things can be seen without any abnormal effort is rarely less than 6 or 8 in. ; a normal eye can often see distinctly an object only from 4 to 6 in. away, but in such cases fatigue sets in so rapidly that this can only be done for a few seconds.
In order that the eye may perceive simul taneously all the objects represented in a picture, the latter must not be too extended. The eye places itself at distances from the picture ranging between the length of the diagonal of the picture and three times this length, the extreme angle between the rays used varying between 53° and 27. In order that a perspective may be examined with avoidance of the distortions described in § 25, it must be looked at from its viewpoint. The principal distance should then be at least equal to io in. (or, as an extreme, 8 in.), unless the picture is examined by means of a magnifying glass, which allows it to be brought nearer to the eye ; 2 moreover, it is essential that the included angle (angle between extreme rays converging to the viewpoint) does not appreciably exceed 50°.