Read an Excerpt
A Guide to Pictorial Perspective
By Benjamin R. Green
Dover Publications, Inc.Copyright © 2005 Dover Publications, Inc.
All rights reserved.
APPEARANCES OF OBJECTS.
ON viewing any object except a sphere, we find its appearance not only differing from its actual form, but varying with every change of position. Thus we have a variety of objects represented in the following plates, in which we observe many of their edges or bounding lines seemingly tending upwards, downwards, or sideways, which we know in reality to be perfectly level, and others apparently converging towards certain points though actually parallel; so, also, surfaces equidistant in nature, approaching each other and diminishing as their distance from us increases, and circular forms appearing as ellipses, or merging into right lines; yet so familiar are their appearances as there represented, that we recognize in each one the object intended. Now, the chief end of drawing is to give such a representation of an object that it may convey to the eye as nearly as possible the same appearance as that of the object itself. Accustomed, however, as we are from childhood to the exercise of our sense of sight, so intuitive may be said to be its results, that we are rarely led to enquire into the differences subsisting between the forms and appearances of objects, and to acquaint ourselves with the causes of such changes. This investigation, nevertheless, constitutes the basis of all correct drawing, since we are thereby enabled to deduce the rules for our guidance in the pictorial representation of objects. We shall, therefore, after a brief summary of the principal definitions, proceed to consider the circumstances under which objects are seen.CHAPTER 2
FREQUENT misconceptions having arisen in treatises on perspective, from the incompleteness of a few definitions. relative to lines and angles, together with the conventional terms and figures applied to them, we shall briefly enumerate, in this place, the most essential points to be observed in connection with them.
Lines represent the extremes of the intersection of surfaces; their positions abstractedly considered are three: viz., HORIZONTAL, VERTICAL, and Oblique (see plate 1). But their positions to one another, also three in number, are distinguished by the terms, PARALLEL, PERPENDICULAR, and INCLINED—terms, it will be seen, different in their signification from the former three, though too often confounded with them.
PARALLEL LINES are such as are equidistant from each other in every part, whether they be horizontal, vertical, or oblique. Lines are said to be PERPENDICULAR to each other when they meet or intersect so that the angles on either side are equal to each other, and these angles being right angles, the lines are also said to be at right angles to each other: it will be seen by the illustration that the perpendicularity of the lines is mutual, and that an oblique line may be perpendicular to another oblique line. Lines INCLINED to each other are those which meet or intersect at an angle greater or less than a right angle.
In illustration of the above terms, the front edges of the flight of steps in the same plate would, in nature, be parallel to one another, but at right angles to the upright edges, in the same manner that the treads of each step are parallel to one another, but perpendicular or at right angles to their sides and fronts. The walls of an apartment are, in like manner, at right angles to the floor; in a pyramidal roof, however, all the lines or edges as well as the surfaces are oblique to each other. Mention being frequently made in perspective works of the position of lines and surfaces to the eye or to the spectator, to which the above terms of parallel, perpendicular, and inclined, could not strictly apply (seeing that the eye is considered as a point)—a classification somewhat analogous is adopted in its stead. Thus, a line or a surface is said to be square to the spectator, in lieu of parallel, when it is so situated as to preserve its true shape and proportions; it need not, however, to this end be directly fronting us. Again, a line or surface is said to go direct from the spectator, or be at right angles to us, when not inclined to the horizon, or to either side. Of this description, consequently, are all level surfaces, as the Chess-board (plate 1), also the fronts of the buildings in the Street view (plate 2), and the walls of the Interior (plate 3), which only apparently incline towards each other, but are in nature parallel. If we stand with our back against one side of a room of the ordinary square form, the side opposite would be square to us, the floor, ceiling, and two remaining sides going off direct.
The walls of the Observatory (plate 2) exhibit a familiar example of surfaces oblique to the spectator; next to these may be instanced roofs, which are also inclined to the horizon.
The HORIZONTAL LINE is a level line crossing the drawing from side to side, the exact height of the eye, and corresponding with our horizon or line of distance, and in a marine view with the junction of sky and ocean. The height of it on the drawing will depend upon the nature of the view to be represented.
PRIME VERTICAL LINE.
The PRIME VERTICAL LINE, only occasionally used, is a line at right angles to the horizontal line, and crossing it immediately in front of the eye.
SEAT OF THE EYE.
The SEAT OF THE EYE is the point formed upon the drawing by the intersection of the above lines, and is commonly but erroneously called the "Point of Sight." In theory this seat of the eye is designated the Centre of the Picture, whilst the "Point of Sight" is the term applied to the eye of the sketcher, and is a point, therefore, at some distance out of the drawing.
A VANISHING POINT is a point on a drawing towards which any line tends, or into which two or more lines converge.CHAPTER 3
RELATIVE SITUATION OF THE SPECTATOR AND THE OBJECT TO BE DRAWN FROM.
* * *
1.—HEIGHT, ETC., OF THE EYE WITH RELATION TO THE OBJECT—VANISHING LINES.
By the above title we understand if the object viewed be above, below, fronting, or on either side of us, or these conditions may be all united, as in an Interior; they are, however, intended to apply generally to buildings in a landscape, furniture, and miscellaneous articles. Let us now suppose ourselves stationed upon level ground, or at a moderate elevation, and the object before us to be one of considerable height, as the Observatory (pl. 2), and we shall find the upper lines of the building apparently tend downwards towards the horizon; if, on the other hand, the subject be one lying below the eye, as the Railway, we shall find the lines of the rails (equally with the former the representation of level lines) apparently tend upwards towards a point on the horizontal line or level of the eye, called their vanishing point. Again, on looking down a long straight street (see fig. 3), we see the upper lines of the houses represented descending, and their bottom lines ascending, according to their situation, above or below the eye; but which in nature are all parallel amongst themselves. It will be also seen that these lines all tend to the same point on the horizontal line; for the reason that lines parallel to each other have a common point of convergence, or vanishing point: an important principle strikingly exemplified on viewing the Chess-board, in which are a number of lines running parallel to one another; and as this article is usually seen upon a table, the lines going off from the spectator will apparently incline upwards, and meet in a point on the horizontal line.
In all the above cases we have limited ourselves to the consideration of horizontal lines in buildings, going off direct (at right angles), or oblique from the spectator, being those which chiefly concern the painter; but retiring lines in objects, however situate in respect of us, have the property of invariably seeming to tend in the direction towards which the eye is bent.
The view of Edinburgh from the Calton Hill (pl. 3) is a striking illustration of this truth, differing from the preceding from the fact of our looking on the city from an eminence, thereby causing the horizontal line to be situate high up in the drawing; and this line being invariably found on a level with the eye, when we ascend it appears to rise with us. As the upper lines of the Observatory seem to descend, from the circumstance of our being on level ground, so in the present case the corresponding lines of the buildings in front appear to ascend.
It will be observed that in the Street view, the obliquity of the lines is governed by their proximity to the horizontal line, the inclination becoming less and less as they approach it; which brings us to the consideration of Vanishing lines.
are the lines on which the vanishing points alluded to are situate, hence the necessity for them on the drawing; but they are also highly important to the student as governing the appearances of the sides or surfaces of objects.
Having spoken only of lines in buildings, our attention has now to be directed to the surfaces in which these lines are situated, which, as will doubtless have been surmised, are subjected to corresponding changes in their appearance, and in their seeming tendency in the direction towards which the spectator is looking. Thus in the Street view, the front of the houses seem to approach each other as they recede, tending inwards towards the prime vertical line, while the ground appears to rise upwards towards the horizontal line. This tendency of the ground to incline apparently upwards in the drawing we have seen in the view of Edinburgh, owing to the great elevation given to the horizon; but interiors exhibit the most complete elucidation of the principle, the ceilings presenting, in addition, a level surface above the eye, appearing to incline downwards. (See pl. 3, from Da Vinci's celebrated picture of "The Last Supper.") It may be observed, by the way, that the lines forming then junction of the walls with the floor and ceiling, and going off direct from the eye, are common to both surfaces.
If we now select any objects nearly level with the eye, and having a number of flat surfaces corresponding in size, and at various distances (see fig. 3, pl. 2), it will be seen that, as these surfaces approach the horizontal line, they gradually seem to lessen, becoming narrower and narrower, so that when one of the surfaces is even with the eye, or coincides with the horizontal line (as the top of the small box in the figure), it disappears, or vanishes; and hence the horizontal line is said to be the vanishing line of level surfaces, seeing that as they approach it they gradually seem to lessen, and finally to disappear therein. There is one other circumstance to be remarked consequent upon the above variation in these surfaces, viz., that the inclination or obliquity of their edges (when not parallel to the horizon) necessarily varies with the height of the surface. Thus the inclination of the sides of the shelves is greatest when they are farthest removed from the horizon, and vice versû. An effect analogous to what we have just described, in reference to surfaces bounded by right lines, takes place with those bounded by curved lines, as in the Flower-stand in the same plate, where we have a succession of circles situated horizontally, viz., the several ellipses diminishing as they approach the horizon; the lowest one being fullest and roundest, the middle one materially less so, whilst the curvature of the uppermost one, from its being even with the eye, is entirely lost.
Having determined the situation of objects in reference to the horizontal vanishing line, we have next to determine their situation in reference to the prime vertical line, and thereby fix their place in respect of the seat of the eye, or point formed by their intersection. For this purpose the attention of the student is called to the representation of a Book and a Hoop (see pl. 3), at different distances from the eye, and he will remark the analogy which they bear to the preceding; the prime vertical line in this case being the vanishing line for upright surfaces at right angles to the spectator, as the horizontal line in the former case for level surfaces. These two vanishing lines, having fixed places upon the drawing, will suffice for all the ordinary purposes of the sketcher, indeed they govern all others; for, owing to the predominance of level surfaces in artificial objects, and next to them of upright ones, surfaces oblique to the eye, as the roofs of buildings, are never met with but in combination with one or the other of them, consequently the lines bounding them are common to both, and will have the same vanishing points.
2.—DISTANCE OF THE OBJECT FROM THE SPECTATOR.
Daily experience has familiarized us with the fact that all objects appear to diminish with their remoteness from the spectator; hence the smallness of the off-side of the Chess-board, of the distant arch of the Railway, and the end of the Apartment (pl. 3). Such are amongst the most obvious effects of the above principle as regards lines and surfaces square with the eye, and to its operation is to be traced every variation in the form of a surface inclining off from the spectator; the lessening of the parts as they recede necessarily causing the lines to tend towards each other. The Chess-board is a striking illustration of the principle: in it we have a number of compartments perfectly uniform in size and figure, and not only do the squares diminish as they recede from the eye, but by the closing in of their side lines the form of each one is different.
3.—POSITIONS OF THE OBJECT TO THE SPECTATOR.
Lastly, we have to consider the positions of the object in reference to the spectator. The ordinary forms of buildings and other objects may be classed into, 1st, buildings, &c., of the ordinary square form, having their sides at right angles to each other; 2nd, objects having more than four sides; 3rd, curved-line objects. It is scarcely necessary to observe that by far the greater number of objects fall under the first of these divisions, and, as it will be seen in the sequel that the correct delineation of the objects comprised under the second divisions may be most easily effected by referring them to the square form, it is to that class our attention will be now directed. It will be readily admitted that the position of an object to the eye may be varied almost to infinity, yet there are but two positions which can be considered as distinct in kind from each other. Thus (in pl. 4) are represented different views of a Teachest: in the two upper views, one side is square to the spectator, preserving its true form and proportions; and the adjoining sides, at right angles to the former, go off direct from the spectator. In the lower view the object is seen cornerwise, and has its sides oblique to the spectator. To one or other, then, of these two positions every object we can conceive (bounded by right lines) may be referred; either one side will be square to the spectator, or they will be all fore-shortened.
The former position of the chest is termed the PARALLEL VIEW, its level lines in the near side retaining their parallel position to each other and to the horizon: while the other position of it is designated the OBLIQUE VIEW, of all the lines (not upright) being oblique. The Chess-board, the interior (pl. 3), and the Street view (pl. 3), are all examples of objects in the Parallel view; the Observatory, of one in the Oblique view. Before selecting the different varieties of objects, singly and combined, comprehended under one or the other of these two classes, it will be desirable to compare them with each other, to exhibit more prominently the characteristics of each.
Excerpted from A Guide to Pictorial Perspective by Benjamin R. Green. Copyright © 2005 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.