This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
114. There seems to exist in the minds of some beginners in the study of perspective, the idea that the drawing of an object made in accordance with geometrical rules may differ essentially from the appearance of the object in nature. Such an idea is erroneous, however. The only difference between the appearance of a view in nature and its correctly constructed perspective projection is that the view in nature may be looked at from any pointy while its perspective representation shows the view as seen from one particular point, and from that point only.
For every new position that the observer takes, he will see a- new view of the object in space, his eye always being at the apex of the cone of visual rays that projects the view he sees (see Fig. 1). In looking at an object in space, the observer may change his position as often as he likes, and will see a new view of the object for every new position that he takes.
115. This is not true of the perspective projection of the object, however. Before making a perspective drawing, the position of the observer's eye, or station point, must be decided upon, and the resulting perspective projection will represent the object as seen from this point, and from this point only. The observer, when looking at the drawing, in order that it may correctly represent to him the object in space, must place his eye exactly at the assumed position of the station point. If the eye is not placed exactly at the station point, the drawing will not appear absolutely correct, and under some conditions will appear much dis torted or exaggerated.
116. Just here lies the defect in the science of perspective. It is the assumption that the observer has but one eye. Practically, of course, this is seldom the case. A drawing is generally seen with two eyes, and the casual observer never thinks of placing his eye in the proper position. Even were he inclined to do so, it would generally be beyond his power, as the position of the station point is seldom shown on the finished drawing.
117. As an illustration of apparent distortion, consider the perspective projection shown in Fig. 23. In order that the perspectives of the vanishing points might fall within the rather narrow limits of the plate, the station point in the figure has been assumed very close to the picture plane, the distance from HPP to SPH showing the assumed distance from the paper at which the observer should place his eye in order to obtain a correct view of the perspective projection. This distance is so short it is most improbable that the observer will ordinarily place his eye in the proper position when viewing the drawing. Consequently the perspective projection appears more or less unnatural or distorted. But, for the sake of experiment, if the student will cut a small, round hole, one quarter of an inch in diameter, from a piece of cardboard, place it directly in front of SPV and at a distance from the paper equal to the distance of SPH from HPP, and if he will then look at the drawing through the hole in the cardboard, closing the eye he is not using, he will find that the unpleasant appearance of the perspective projection disappears.
It will thus be seen that unless the observer's eye is in the proper position while viewing a drawing, the perspective projection may give a very unsatisfactory representation of the object in space.
118. If the observer's eye is not very far removed from the correct position, the apparent distortion will not be great, and in the majority of cases will be unnoticeable. In assuming the position for the station point, care should be taken to choose such a position that the observer will naturally place his eyes there when viewing the drawing.
119. As a person naturally holds any object at which he is looking directly in front of his eyes, the first thought in assuming the station point should be to place it so that it will come very nearly in the center of the perspective projection.
120. Furthermore, the normal eye sees an object most distinctly when about ten inches away. As one will seldom place a drawing nearer to his eye than the distance of distinct vision, a good general rule is to make the minimum distance between the station point and the picture plane about ten inches. For a small drawing, ten inches will be about right; but, as the drawing increases in size, the observer naturally holds it farther and farther from him, in order to embrace the whole without having to turn his eye too far to the right or left.
121. Sometimes a general rule is given to make the distance of the station point equal to the altitude of an equilateral triangle, having the extreme dimensions of the drawing for its base, and the station point for its apex.
122. The apparent distortion is always greater when the assumed position of the observer's eye is too near than when it is too far away. In the former case, objects do not seem to diminish sufficiently in size as they recede from the eye. On the other hand, if the observer's eye is between the assumed position of station point and the picture plane, the effect is to make the objects diminish in size somewhat too rapidly as they recede from the eye. This effect is not so easily appreciated nor so disagreeable as the former. Therefoie it is better to choose the position of the station point too far away, rather than too near.
123. Finally, the apparent distortion is more noticeable in curved than in straight lines, and becomes more and more disagreeable as the curve approaches the edge of the drawing. Thus, if curved lines occur, great pains should be taken in choosing the station point; and, if possible, such a view of the object should be shown that the curves will fall near the center of the perspective.
12-4. The student should realize that the so-called distortion in a perspective projection is only an apparent condition. If the eye of the observer is placed exactly at the position assumed for it when making the drawing, the perspective projection will exactly represent to him the corresponding view of the object in space.