ANAMORPHOSIS

, in perspective and painting, a monstrous projection; or a representation of some image, either on a plane or curve surface, deformed or distorted; but which in a certain point of view shall appear regular, and drawn in just proportion.

To construct an Anamorphosis, or monstrous projection, on a plane.—Draw the square ABCD (fig. 1), of any size at pleasure, and divide it by crossing lines into a number of areolæ or smaller squares: and then in this square, or reticle, called also the cratioular prototype, draw the regular image which is to be distorted.—Or, about any image, proposed to be distorted, draw a reticle of small squares.

Then draw the line ab (fig. 2.) equal to AB, dividing it into the same number of equal parts, as the side of the prototype AB; and on its middle point E erect the perpendicular EV, and also VS perpendicular to EV, making EV so much the longer, and VS so much the shorter, as it is intended the image shall be more distorted. From each of the points of division draw right lines to the point V, and draw the right line aS. Lastly through the points c, e, f, g, &c, draw lines parallel to ab: So shallabcd be the space upon which the monstrous projection is to be drawn; and is called the craticular ectype.

Then, in every areola, or small trapezium, of the space abcd, draw what appears contained in the corresponding areola of the original space ABCD: so shall there be produced a deformed image in the spacc abcd, which yet will appear in just proportion to an eye distant | from it the length of EV, and raised above it by a height equal to VS.

It will be amusing to contrive it so, that the deformed image may not represent a mere chaos, but some certain figure: thus, a river with soldiers, waggons, and other objects on the side of it, have been so drawn and distorted, that when viewed by an eye at S, it appeared like the face of a satyr.

An image may also be distorted mechanically, by perforating through in several places with a fine pin; then, placing it against a candle or lamp, observe where the rays, which pass through these small holes, fall on any plane or curve superficies; for they will give the correspondent points of the image deformed, and by means of which the deformation may be completed.

To draw an Anamorphosis upon the convex surface of a cone. It appears from the construction above, that we have only to make a craticular ectype upon the surface of the cone, which may appear equal to the craticular prototype, to an eye placed at a proper height above the vertex of the cone. Hence,

Let the base, or circumference, ABCD, of the cone (fig. 3) be divided by radii into any number of equal parts; and let some one radius be likewise divided into equal parts; then through each point of division draw concentric circles: so shall the craticular prototype be formed.

With double the diameter AB, as a radius, describe the quadrant EFG (fig. 4) so as the arch EG be equal to the whole periphery; then this quadrant, being plied or bent round, will form the superficies of a cone, whose base is the circle.

Next divide the arch EG into the same number of equal parts as the craticular prototype is divided into; and draw radii from all the points of division. Produce GF to I, so that FI be equal to FG; and from the centre I, with the radius IF, describe the quadrant FKH; and draw the right line IE. Then divide the arch KF into the same number of equal parts as the radius of the eraticular prototype is divided into; and from the centre I draw radii through all the points of division, meeting EF in 1, 2, 3, &c. Lastly, from the centre F, with the radii F1, F2, F3, &c, describe concentric circles. So will the craticular ectype be formed, whose areolas will appear equal to each other.

Hence, what is delineated in every areola of the craticular prototype, being transferred into the areolas of the craticular ectype, the images will be distorted or deformed; and yet they will appear in just proportion to an eye elevated above the vertex at a height equal to the height of the cone itself.

If the chords of the quadrants be drawn in the craticular prototype, and chords of each of the 4th parts in the craticular ectype, every thing else remaining the same, there will be obtained the craticular ectype in a quadrangular pyramid.

And hence it will be easy to deform an image, in any other pyramid, whose base is any regular polygon.

Because the illusion is more perfect when the eye, by the contiguous objects, cannot estimate the distance of the parts of the deformed image, it is therefore proper to view it through a small hole.

Anamorphoses, or monstrous images, may also be made to appear in their natural shape and just proportions, by means of mirrors of certain shapes, from which those images are reflected again; and then they are said to be reformed.

For farther particulars, see Wolfius's Catoptrics and Dioptrics, and some other optical authois.