This paper has been revised from an earlier draft written by Prof. Irma Ostroff.
All ordinary perspective drawing is based on a simple concept: that between the eye of the observer and the object to be drawn, there stands a transparent plane, a sort of window called the “Picture Plane”, on which the form of the object is projected. This picture plane may be a window in a literal sense, and, if you make the following experiment, the real meaning of the term will be much clearer.
Select a window having large individual panes. Keeping your head as still as possible, using a magic marker, trace on the window the outlines of the things you see through it. (Be sure to stand at the window at a convenient and comfortable distance to mark the window with your arm outstretched.) The result will be a perspective drawing on the picture plane itself.
If you now examine the window, and the scene includes buildings or other objects containing straight lines and right angles within the view, you will notice several important things critical in the practice of drawing perspectives.
- First, all lines appear to be shorter than their true length and the shortening effect increases as the distance of the object increases.
- Second, vertical lines appear truly vertical, whereas horizontal lines, with the exception of lines at eye level, do not appear horizontal.
- Third, groups of parallel horizontal lines, lines running in a single direction, appear to converge towards a single point. Other groups of horizontals having different directions have different points towards which they converge.
- Fourth, these points of convergence for horizontal lines all lie on a horizontal plane, level with the eye of the observer. This effect can be seen most clearly simply by looking down a long straight railway track and noticing that the rails seem to converge on a line emanating directly fro your eye.
You may notice other effects as well. The apparent shortening of a line seen obliquely is called foreshortening: it is more subtle, though often more dramatic, than that of distance, and it exerts a strong effect on the appearance of the object. For example, the apparent flattening of circles results in (slightly distorted) ellipses.
Since vision is impossible without light, it is assumed that a ray of light (line of vision) enters the eye from each (pixel-like) point on the object. On the way from object to eye, each of these rays passes through (pierces) the picture plane. The spot where the ray from any given point on the object pierces the picture plane is the perspective projection of that point. When all the rays from all the (visible) points on the object have produced their perspective projections, the sum total is the perspective projection upon the two-dimensional picture plane of the three-dimensional object beyond.
The “discovery” (distinction) of the principles of perspective was made in the Renaissance by Filippo Brunelleschi. He actually devised a rectangular frame with two cross wires, one horizontal, one vertical, which could be adjusted to intersect at any position within the frame. The intersection then would be positioned so that it corresponded with a particular point on the object that was seen through the frame. Each point on the object had a unique corresponding point in the frame, which was literally, the picture plane. As each point in the frame was identified, it would be transferred to a sheet of paper, thereby constructing, point by point, the two dimensional image of the object. In other words, to make a literal transcription of what you see, simply transfer the projection on the picture plane to paper. Note that this is the transfer of the projection on the picture plane, not the object itself. Interestingly, the computer-aided drawing algorithm for perspectives, engages a digital frame-like device, essentially identical to that which Brunelleschi invented.
The picture plane is usually considered to be perfectly vertical, assuming that you are looking straight ahead. (This is the case in the window drawing described above.) From other points of view (station points), the picture plane may be horizontal (a bird’s eye view) or tilted (looking up at a tall building).
The picture plane may be assumed to be at any given or desired distance from the eye. When it is close to the eye and distant from the object, we see an image small in size, compared to the object; when it is close to the object and distant from the eye, the image approaches the size of the object. In fact, if the picture plane is located beyond the object the resulting image will be larger than the object. Another way to envision this is to imagine that the small image in your eye is projected by a slide or film projector onto a screen. The farther the screen is from your eye (the projector), the larger the image (and the image, aside from its size, is always the same).
In any rectangular object, there are three sets of parallel lines, mutually perpendicular to each other: lines running from top to bottom, lines running from side to side, and lines running from front to back. Each set of lines, actually parallel to the object, tends in the perspective image to converge towards a point in the distance. If there are three such sets of lines, there are consequently three such points. When the picture plane is parallel to any one of these sets of lines, one of the points “disappears” and the lines in question are truly parallel in the perspective image (two-point perspective). Occasionally the picture plane is parallel to two sets of line in the object: in this case, two of the three sets of lines will appear truly parallel in the perspective, and only one point of convergence is needed (one-point perspective).
These points of convergence in perspective images are called vanishing points, and they are fundamental in making perspectives. When the picture plane is vertical, as it is usually, it is naturally parallel to vertical lines in the object, which appear truly vertical in the image, and, naturally, parallel to each other. Moreover, the two vanishing points of the horizontal lines both lie on the same horizontal line, which is also where the station point (where you are looking from) is located. In other words, the vanishing points are on what is called the horizon line which is determined by the height of the station point (eye level). When the picture plane is parallel to both the vertical lines and a set of horizontal lines as well, those horizontals appear as truly horizontal in the image.
When, as often happens, there are sets of lines in an object that are not parallel to the three principle sets, these lines have their own separate vanishing points. Sloping roofs or stairs are examples of this case.
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