Part 8 (1/2)
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SHADING EFFECTS.--Now, to examine it properly so as to observe what the draughtsman wishes to express, look at Fig. 138, in which the three diverging lines (A, B, C) are increased in thickness, and the cube appears plainly. On the other hand, in Fig. 139, the thickening of the lines (D, E, F) shows an entirely different structure.
[Ill.u.s.tration: _Fig. 137._]
[Ill.u.s.tration: _Fig. 138._]
[Ill.u.s.tration: _Fig. 139._]
It must be remembered, therefore, that to show raised surfaces the general direction is to shade heavily the lower horizontal and the right vertical lines. (See Fig. 133.)
HEAVY LINES.--But there is an exception to this rule. See two examples (Fig. 140). Here two parallel lines appear close together to form the edge nearest the eye. In such cases the second, or upper, line is heaviest. On vertical lines, as in Fig. 141, the second line from the right is heaviest. These examples show plain geometrical lines, and those from Figs. 138 to 141, inclusive, are in perspective.
[Ill.u.s.tration: _Fig. 140._]
[Ill.u.s.tration: _Fig. 141._]
PERSPECTIVE.--A perspective is a most deceptive figure, and a cube, for instance, may be drawn so that the various lines will differ in length, and also be equidistant from each other. Or all the lines may be of the same length and have the distances between them vary. Supposing we have two cubes, one located above the other, separated, say, two feet or more from each other. It is obvious that the lines of the two cubes will not be the same to a camera, because, if they were photographed, they would appear exactly as they are, so far as their positions are concerned, and not as they appear. But the cubes do appear to the eye as having six equal sides. The camera shows that they do not have six equal sides so far as measurement is concerned. You will see, therefore, that the position of the eye, relative to the cube, is what determines the angle, or $the relative$ angles of all the lines.
[Ill.u.s.tration: _Fig. 142._]
[Ill.u.s.tration: _Fig. 143._]
A TRUE PERSPECTIVE OF A CUBE.--Fig. 142 shows a true perspective--that is, it is true from the measurement standpoint. It is what is called an _isometrical_ view, or a figure in which all the lines not only are of equal length, but the parallel lines are all s.p.a.ced apart the same distances from each other.
ISOMETRIC CUBE.--I enclose this cube within a circle, as in Fig. 143. To form this cube the circle (A) is drawn and bisected with a vertical line (B). This forms the starting point for stepping off the six points (C) in the circle, using the dividers without resetting, after you have made the circle. Then connect each of the points (C) by straight lines (D).
These lines are called chords. From the center draw two lines (E) at an angle and one line (F) vertically. These are the radial lines. You will see from the foregoing that the chords (D) form the outline of the cube--or the lines farthest from the eye, and the radial lines (E, F) are the nearest to the eye. In this position we are looking at the block at a true diagonal--that is, from a corner at one side to the extreme corner on the opposite side.
[Ill.u.s.tration: _Fig. 144._]
Let us contrast this, and particularly Fig. 142, with the cube which is placed higher up, viewed from the same standpoint.
FLATTENED PERSPECTIVE.--Fig. 144 shows the new perspective, in which the three vertical lines (A, A, A) are of equal length, and the six angularly disposed lines (B, C) are of equal length, but shorter than the lines A. The only change which has been made is to shorten the distance across the corner from D to D, but the vertical lines (A) are the same in length as the corresponding lines in Fig. 143.
Notwithstanding this change the cubes in both figures appear to be of the same size, as, in fact, they really are.
[Ill.u.s.tration: _Fig. 145._]
In forming a perspective, therefore, it would be a good idea for the boy to have a cube of wood always at hand, which, if laid down on a horizontal support, alongside, or within range of the object to be drawn, will serve as a guide to the perspective.
TECHNICAL DESIGNATIONS.--As all geometrical lines have designations, I have incorporated such figures as will be most serviceable to the boy, each figure being accompanied by its proper definition.
[Ill.u.s.tration: _Fig. 146._]
[Ill.u.s.tration: _Fig. 147._]
Before pa.s.sing to that subject I can better show some of the simple forms by means of suitable diagrams.
Referring to Fig. 145, let us direct our attention to the body (G), formed by the line (D) across the circle. This body is called a segment.
A chord (D) and a curve comprise a segment.
SECTOR AND SEGMENT.--Now examine the shape of the body formed by two of the radial lines (E, E) and that part of the circle which extends from one radial line to the other. The body thus formed is a sector, and it is made by two radiating lines and a curved line. Learn to distinguish readily, in your mind, the difference between the two figures.