In presenting this plane under the same obliquity to an observer whose eye, placed at 0, would be forced to look in the direction of the principal point F, especially in the absence of external marks which would indicate to him the obliquity of the plane on which was the perspective, he might have the illusion of the object represented. But an observer who did not know, examining such a perspective under the same conditions as he would regard a normal one, would be led to conclude that the solid object represented was not a parallelepiped, but a truncated pyramid. Re might not unnaturally conclude that the solid figure was represented as in the act of falling.' A vertical plane of projection is the essential condition for the reproduction of vertical lines as verticals in the perspective.
Experience shows that once the perspective has been drawn under these conditions, the projection image can be then shown obliquely without its being displeasing (the case of pictures hung rather high in such a way that their view point is at the height of the observer's eyes when standing), though from the moment when we realized this obliquity we should not consider as admissible the representation of an object on an inclined surface, even if this was viewed under its normal inclination.
32. Panoramic Perspective. In cylindrical per spective, known as panorama, the viewpoint is we are not envisaging here the case of views inten tionally taken looking downwards or upwards for documentary purposes or in order to achieve some special effect.
situated on the axis of the cylinder of revolu tion (vertical cylinder), which constitutes the projection surface. In this system of per spective, verticals are represented by verticals, the horizon line by a meridian circle, and all other straight lines by ellipses. When the pro jection surface is maintained in its cylindrical form and looked at from the viewpoint, what is seen is identical with the subject, but if the projection surface is now unrolled and becomes a plane, all the straight lines of the subject, with the exception of the verticals and the horizon line, are represented by curves. Thus \ # b r ---- • it is, for example, that the straight line ABC (Fig. 9) is represented in the panoramic per spective, after this has been flattened out to a plane, by the curve abc, with vanishing points at F and F', which are common to the perspec tives of all other straight lines parallel to that considered.
Such deformations are obviously a drawback in cases where it is desired to represent subjects containing numerous straight lines other than the verticals, such as architectural works or views of towns having straight streets. But the suppression of all deformations due to excessive obliquity of the visual rays relatively to the projection of plane perspectives (§ 28, Fig. 6) gives to panoramic photographs, often limited to a fraction of the complete horizon, a special interest in such cases as the representation of a. very extensive landscape, such as high moun tainous country, or of a large number of people.
Due to its being unfolded to give a plane surface, such an image no longer permits of one viewpoint only, but of an infinite number of them, arranged on a straight line parallel to the horizon line, at a distance from the image equal to the principal distance. Such a projec tion should be considered as the combination of a great number of projections each formed from a straight vertical band, each to be exam ined from its particular viewpoint. The observer moving in front of the projection should thus an average height of 66 in. Equal lengths measured on the horizon-line of the image on the plane correspond with equal angles on the ground. The diminution of the height of the
images being continuous, and the ratio of the dimensions of a person to his image being equal to the ratio of their distances from the view point, the distances of people in the different directions, defined by the angle they make with the direction chosen as origin, may be calculated as follows— only look at the details of the image which he sees exactly opposite to him.
33. In practice, the question has arisen as to how to place a series of people in such a way that, after the panoramic photograph has been flattened out to form a plane surface, the figures appear exactly in line.
To do this the people should be placed along an arc of a hyperbolic spiral (C. J. Stokes, 1919) having its origin at the viewpoint, that is on the axis of the cylinder. To trace the correct curve to give the desired result, the procedure is as follows— With a principal distance of, say, iof in., we may use a projection, which, after being un folded to form a plane, measures 24 in. long, corresponding to an arc of i32® in a circle of rat in. radius. Considering only a part of this, we will include the people within an angle of We will allow a height of 4 in. for the image of the nearest person and 3 in. for the ones farthest away, assuming the people to have Fig. ICA. represents the curve along which people should be placed in order to obtain the effect shown in Fig. I0B. The extensions of the spiral in parts other than those coming into the case considered have been traced. It will be noticed that in one direction it tends to approach more and more nearly to a circle, and in the other, to approach indefinitely to a straight line.
34. Sharpness of Vision. Sharpness of vision, variable with the illumination and the observer, is measured by the distance from centre to centre of black parallel lines of equal width, separated by white spaces of the same width, this distance being expressed as a fraction of the greatest distance at which the lines can still be separately seen when viewed closely, i.e. when their images are formed on the most sensitive part of the retina. A good eye can distinguish two lines the distance apart of which measured from centre to centre corresponds to an angle of i minute. This would be given by a distance of 1/250 in. at 12 in. A kind of fan shaped object such as that shown in Fig. II is used frequently, with equal sectors alternately black and white. In this case the smallest distance from the thin end is determined at which the sectors are still distinguishable from one another. Practically, the sharpness of an eye is considered to be about the average when it can separate lines,A, in. apart at a distance of 8 in., corresponding with an angle of radian.
35. Depth of Field. When the eye is accom modated for regarding an object at a certain distance with maximum sharpness, objects nearer and farther away do not give sharp images on the retina. There exists, however, a certain zone within which all objects appear to the eye with the same sharpness. The depth of this zone is known as the depth of field, which becomes greater as the object viewed is farther away.
In fact, in looking at a scene of which the different elements are at very different distances from the observer, the accommodation varies constantly as the eye concentrates on the various points. Thus, in the average sensation which results, the most important points are seen more sharply than those of only secondary interest, which are, as it were, only seen accidentally.