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Freehand Perspective and Sketching
By Dora Miriam Norton
Dover Publications, Inc.Copyright © 2006 Dover Publications, Inc.
All rights reserved.
MATERIALS. — Any paper having a fine and fairly soft texture can be used. It should produce an even grain in both vertical and horizontal pencil strokes. Pencil exercises such as those reproduced in this book are usually drawn on paper of quarter imperial size (11" x 15"), on which at least an inch and a half of margin is allowed. This is a good size for the student's drawings, whether copied from these exercises or drawn from objects. Have two pencils, one fairly soft (as No. 2 Faber, SM Dixon, or 2 B Koh-i-noor), and a harder one; also a good eraser.
Line Practice. — Cut the pencil like the illustration (Fig. 3), and rub on practice paper till a broad line, firm at the edges and transparent (that is, with the grain of the paper slightly showing through it) can be made. Sit erect, with the paper directly in front, and have the desk top inclined, or use a drawing board (Fig. 4), that the paper may be as nearly as possible parallel with the face. Hold the pencil almost flat, as in the illustration (Fig. 5), and as loosely as is consistent with a steady control. For horizontal lines use position A, Fig. 5, moving the pencil from left to right; for vertical lines use position B, moving from the top downward. Practice vertical, horizontal, or oblique lines persistently; moving the hand freely from the shoulder, not resting it on the wrist or elbow. If the muscles acquire an unpleasant tension, relax by dropping the hands at the sides and loosely shaking them. Unfamiliar or difficult exercises should be first carefully sketched with a thin, light line. If wrong, draw over without erasing until a satisfactory form is obtained. Erase the incorrect part, and render expressively (Ch. IV). But after the composition of the exercise is planned, such straight lines as margins, cylinder sides, and many ellipses may be drawn in full at once. And as the student gains in skill, more and more of the work should at the first touch be put on the paper as it is intended to remain. Exact knowledge is to be acquired only that artistic interpretations may be expressed with ease and certainty.
Models for Work. — Objects in common use have been chosen for most of these exercises. Geometric solids are assigned only as needed for the clearer elucidation of perspective truths. Necessary models, as the cylinder, the cube, and others, should be made by the student as directed. For forms (as the hexagonal frame) too complicated to be easily made, the well-known wooden models have been used. But after thorough mastery of the simpler forms, most of the later lessons can be understood without models.
Placing of Models. — All objects for study should be placed so as to present their vertical surfaces in nearly their true shape to the student. Thus if the model is to be near, as on the table at which the student sits, it is better to raise it a few inches (Fig. 4). This will not be necessary if it can be placed four or five feet distant. If the study is seen too much from the top, the perspective will be unpleasantly violent, as in a photograph where the camera has been pointed too much downward.
The Table Line. — To indicate a supporting surface under the objects a horizontal line (A, B in Fig. 6) is used. It stands for the back edge of the table or other horizontal supporting surface, and is called the Table Line. It should be represented as further back than any portion of the study. As will be observed later, it need not be used if the supporting surface is otherwise suggested, as by a cast shadow (Fig. 34).
All Work Freehand. — All work is to be done freehand, that is, with no ruling, and no measuring other than by the eye and pencil.CHAPTER 2
PENCIL MEASUREMENT AND THE PICTURE PLANE
PENCIL Measurement. — Before studying the exercises which follow, the beginner should become familiar with Pencil Measurement. Place a book upright directly in front of the eye. With one eye shut and the arm at full length (to ensure a uniform distance from the eye) measure on the pencil held horizontally the apparent width of the book. Then turning the pen-cil, compare this distance with its height (Fig. 7). (It is better to take the smaller distance first, and to measure it into the larger.) Compare the proportions so found with those obtained by actual measurement of the book. But always get the pencil measurement first, for this compels the eye to do all that it can unaided before showing by actual measurement how much better it can learn to do.
Now turn the book away a little, and compare this new appearance of the width with the height (Fig. 12).
The Picture Plane. — Here we must learn to keep the pencil parallel with the face in order that the pencil measurement may be reliable. For this, go to the window, and stand facing the glass, so the face is parallel with it. Choose some object seen through the window, as another house, and resting the pencil against the glass measure its width and compare that with its height (Fig. 8).
Observe that if the outline of the house could be traced by the pencil on the glass it would form correctly the apparent shape of that house.
This leads us to see that all perspective drawing may be regarded as placing on paper the equivalent of such a tracing on the glass. It will therefore be apparent at once that pencil measurement, to be correct, must be taken with the pencil held as if laid on such a pane of glass; or in other words, on a plane parallel with and in front of the face. This imaginary transparent plane is called the Picture Plane, and is a most important factor in all freehand drawing. Thus, by turning or revolving the pencil on the glass in front of the face, that is, by revolving the pencil in the picture plane, it can be made to cover the appearance of any possible line or direction. For example, the sloping gable edge of the outside house, though retreating from the eye and therefore foreshortened, can be covered by the revolving pencil (Fig. 9), thus giving the appearance or picture of its direction. Its apparent or foreshortened length can also be taken on the pencil and compared with any other dimension, as the height of the nearest corner. The essential requirement is that the pencil shall constantly lie flat on this pane of glass; that is, on the picture plane.
We have therefore, in the use of pencil measurement on the picture plane, a ready and accurate means of ascertaining any direction or any proportionate dimension seen by the eye. It cannot give us actual sizes, as the length of the gable in feet; but it will tell us how long the slanting line representing the gable must be drawn in proportion to other parts of the house. In this case, for instance, the sloping edge appears three-fourths of the gable width. The difficulty in using this valuable aid with exactness lies in the beginner's trouble in keeping the pencil always in his invisible picture plane. Any distance between the eye and the object may be assumed for the picture plane. But for accuracy this assumed distance must be kept the same while comparing sizes. This is easily done by sitting erect and measuring at arm's length, supporting the elbow with the other hand if needful. The student should then mentally see the picture plane, recalling that it is vertical, or parallel with the face when looking at the middle of the objects to be drawn. That is, it is at right angles to what we may call the Central Direction of Seeing.
The Central Direction of Seeing. — This extends from the eye to the center of the objects observed, while the face and the picture plane are parallel to each other and at right angles to it. The picture plane may then be thought of as a transparent vertical plane pierced in its middle by the direction of seeing.
We have said the central direction of seeing is at right angles to the face. Since the face is generally vertical, the direction of seeing is generally horizontal (A in Fig. 14, Ch. III). The commonest exception is that of being directed slightly downward (B in same Fig.). In this case it cannot be at right angles to the picture plane. It will, however, always appear at right angles to it when looked at from above. That is, it is at right angles from side to side, and in a plan will always be shown at right angles, as in Fig. 8.
Return now to the seat (Fig. 7), and try pencil measurement on the turned book. Imagine as clearly as possible the transparent picture plane at arm's length, on which the pencil may be revolved, but through which it must never be thrust. Starting with the pencil erect (Fig. 10) drop it directly over to the left (Fig. 11), watching carefully to keep it from leaning back or forward. Let another person help by turning the book away while you measure it and at the same time keep the pencil from following it backward as it is turned away (Fig. 12). Thus as the book is turned, the pencil, if it remains on the picture plane, shows the book to appear narrower or be foreshortened. What is now sought for is that which the eye really sees as the width, not what the mind knows it to be. It is of great importance to distinguish sharply between actual facts of form and size and the perspective appearance of them as presented to the eye.
An excellent object for practice is a door. Stand facing a closed door, and take its proportions by pencil measurement. Then let some one open it, and observe the apparent decrease in width.
For further consideration of the picture plane see Chapters XXXIV, XLI, and XLIII.CHAPTER 3
HAVING learned that the book cover and door appear foreshortened in proportion as they are near to coinciding with the direction in which they are seen, we naturally look for the same change in the Circle.
Making a Cylinder. — Fold the long edges of a piece of stiff paper (A in Fig. 12a) and roll it into a cylinder, tucking one end of the paper under the folds of the other (B in Fig. 12a).
Seeing the Ellipse. — Holding the cylinder vertically, as in A, Fig. 13, and with one eye closed, raise it slowly till on a level with the eye. The top now appears as a straight line (B, Fig. 13). It is so foreshortened that its surface is entirely lost to sight, leaving only its edge visible. Now, keeping the cylinder vertical, lower it till the eye sees into it perhaps half an inch. Observe carefully the shape formed by the top. Turn it so the top appears as a circle (A in Fig. 14), then, holding it vertically again (as at B), compare mentally the apparent shapes as the top is placed in the two different positions. Now (keeping it always vertical) raise and lower the cylinder slowly, and note how the form of the top changes, appearing rounder as it is lowered.
Symmetry of the Ellipse. — This peculiar shape, varying in roundness between the straight line and the circle, represents the appearance of the circle seen obliquely, and is the Ellipse, one of the most beautiful, spirited, and subtle of curves. While the circle is formed by a curve bending equally in all parts, the outline of the ellipse is constantly changing in the degree of its curvature. From the middle of each side (A, A in Fig. 15) this curvature increases smoothly to the ends (B, B). Thus the ellipse may be divided by lines through the middle of its sides and ends into four duplicate curves or quarters. These lines are known as the Long and Short Diameters. On these two lines the ellipse must be symmetrical, whatever the proportion of the diameters to each other; that is, whatever the roundness of the ellipse.
Testing the Ellipse. — A test useful to determine the correctness of a drawing of the ellipse is sighting with one eye along the long diameter. If the ellipse is perfect it will appear foreshortened to a circle having a diameter equal to the short diameter of the ellipse. But there is no test of the ellipse like the ellipse itself as seen in objects. The student should compare his drawing of ellipses with the rhythmically varying curves which compose ellipses as seen in real objects, correcting and comparing till the eye is satisfied. If this be faithfully done, the time will be short before ellipses, often deemed a bugbear of freehand drawing, become a pleasure instead of a penance.
Roundness of Ellipses According to Position. — Since the top ellipse appears rounder as it is dropped below the eye level, it must be concluded that could the bottom be fully seen it would appear as a rounder ellipse than that of the top. Place the cylinder on the table and trace around the bottom with a pencil. Move the cylinder to one side and compare the shape of this traced ellipse with that of the top ellipse (Fig. 16). Also compare both with that part of the cylinder bottom which can be seen. There is no difficulty in perceiving that the ellipses in a vertical cylinder below the eye are rounder as they are farther below the eye level.
Now, keeping the cylinder vertical, raise it slowly. When the bottom ellipse reaches the level of the eye, it appears as a straight line (A in Fig. 17), like the top ellipse when at the same height. When the cylinder is moved on above the eye, the bottom becomes an ellipse (B), which as we raise it farther above the eye level appears rounder. We perceive that it appears rounder or less foreshortened in proportion as it is farther from coinciding with the direction in which the eye looks to see it, as was the case with the book cover in Chapter II. Furthermore, if the cylinder be turned horizontally and held at the level of the eye with its length parallel to the picture plane, and one end be brought in front of the eye, we shall again see this circular end as a straight line (B in Fig. 18), because it coincides with the direction of seeing. If the cylinder be moved horizontally to one side, still keeping its length parallel with the picture plane (A in Fig. 18), the ellipse appears to widen exactly as when the cylinder was held vertically and moved above or below the eye level. The circular top appears as a circle only when its surface is at right angles to the direction of seeing (A, Fig. 14). When oblique to this direction, as at B, it appears as an ellipse, or foreshortened circle. The ellipse is plainly, therefore, an illustration of the second great principle, that of Foreshortening.
Practice of Ellipses. — The student should now practice drawing ellipses, both vertical and horizontal, until they can be formed with ease and exactness. Mark the extreme points (A, A, B, B, Fig. 15) first taking care to have B B exactly opposite the middle of A A. Hold the pencil for drawing ellipses as directed in Chapter I for straight lines, using a position of the hand that will bring the pencil at right angles to the long diameter. If the ellipse is horizontal, begin it a little to the left of the middle of the upper side, drawing to the right first. If vertical, begin below the middle of the left side, and draw up. Make the whole outline with one movement, first carrying the pencil evenly several times over the paper without touching it, to gain confidence and certainty of movement.
Excerpted from Freehand Perspective and Sketching by Dora Miriam Norton. Copyright © 2006 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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