Copying by Triangulation

To enlarge or reduce one may resort to any of the following methods:

(1) Photography.

(2) The mechanical instrument known as the pantograph.

(3) The mechanical instrument known as the proportional dividers.

(4) Free hand drawing. Good practice, but not conducive to accuracy.

(5) Squaring the original by means of intersecting horizontal and vertical lines. This requires great care in preparation and use. The squares must be square and usually require numbering along at least two sides of the original and of the copy.

(6) Triangulation. An old and simply made geometrical form which I have adopted for the purpose of enlarging and reducing.

In my practice it has, since my discovery of its new use, entirely superseded the laborious, if time-honored, methods. By its use ordinary care produces accurate work, no measurements being required except when laying out the perimeters.

In the squaring method even an ordinary reduction or enlargement requires from 16 to 64 squares, the latter with boundary numbers 1, 2, 3,4, 5,6, 7 and 8 on at least two sides of both original and copy. In this maze the draftsman is apt (to become “lost.” In the method I have adopted, the triangulation forms a pattern which aids the eye to keep within the proper corresponding spaces. That is, each triangle, in the original and in the drawing under way, occupies a distinctive and individual position not observable in the squares.

I have not space here to describe the numerous applications and advantages of the triangular method, nor even to describe its operation beyond giving a diagram of its most primitive, simplest form, as shown in the accompanying figures.

These figures merely show the progress of the method. A square or other parallelogram is drawn first, the oblique, vertical and horizontal lines being added.

In a drawing in which the detail is complex, the triangles are easily subdivided, both in the original and in the drawing to be made from it.

Not alone is this method superior in every way to the “squaring” process, but it provides a sure and easy way to make regularly proportional distortions.

Not long ago an engraver on old gold and silver ware came to me. He was distressed. An order had been given to him in which it was required that certain heraldric devices should appear on some silver plate. The devices included the pleasant-looking creature shown in Fig.1.

The engraver’s trouble was that the mythological animal had to be reproduced in narrow vertical and horizontal panels, respectively, of certain definite dimensions. My engraver friend did not know how to get the “critter” squeezed and distended into anything like proper proportions.

Figs. 2 and 3 show the engraver’s purpose was satisfactorily accomplished.

It is to be hoped that the result pleased his customer. It was my conjecture that the griffons might be intended for evolutional ancestral portraits and if my surmise was correct the two distortions might serve as portraits of two of his ancestors-one attenuated and the other obese. Anyway, I would as soon trace my origin to a fine official and officious looking griffon – or whatever it is – as to a grinning, chat. tering chimpanzee.

Another Example – Fig. 4 is another example of what may be done in the way of varying the form of an area in which any design may be placed.