The Word is Greek; compounded of ἀνά (ana), and μόρφωσις (morphe), formation, of μορφή (morphe), form.
To make an Anamorphosis, or monstrous Projection on a Plane—Draw the Square ABCD, (Tab. Perspective, Fig. 18.)
In this Square, or Reticle, called the Craticular Prototype, let the Image to be distorted be drawn.
Then draw the Line AE = AB; and divide it into the same Number of equal Parts, as the Side of the Prototype AB; and in E, the middle thereof, erect the Perpendicular EV, so much the longer; and draw VS perpendicular to EV, so much the shorter, as the image is desired to be distorted. From each Point of Division draw right Lines to V, and join the Points A and E; as also the right Line AS. Through the Points d e f g, draw Lines parallel to AE; then will abcd be the Space that the Monstrous Projection is to be delineated in; called the Craticular Epitype. Lastly, in every Areola, or small Trapezium of the Space abcd, draw what appears delineated in the corresponding Areola of the Square ABCD: by this means you will obtain a deformed Image, which yet will appear in just Proportion to an Eye distant from it the length FV, and raised above its height, VS.
See DESIGNING.
It will be easy to manage it so, that the deformed Image does not represent a mere Chaos; but some other Image: Thus, we have seen a River with Soldiers, Wagons, &c., marching along the side of it; so drawn, that when viewed by an Eye in the Point S, it appears to be the figural Face of a Man. An Image also may be distorted mechanically, by perforating it here and there with a Needle, and placing it against a Candle, or Lamp; and observing where the Rays which pass through these little Holes fall on a plane, or curved Surface; for they will give the corresponding Points of the Image deformed: by means whereof, the Deformation may be completed.
To draw the Anamorphosis, or Deformation of an Image upon the convex Surface of a Cone. It is manifest from the former Case, that all here required, is to make a Craticular Epitype on the Surface of the Cone, which shall appear to an Eye duly placed over its Vertex, equal to the Craticular Prototype. Let the Base ABCD, therefore, of the Cone, be divided by Diameters into any Number of equal Parts, that is, the Periphery thereof: And let some one Radius be likewise divided into equal Parts, and through each Point of Division draw concentric Circles: thus will the Craticular Prototype be made. With double the Diameter AB, as a Radius, describe the Quadrant EFG, so as the Arch EG be equal to the whole Periphery: then this Quadrant folded duly up, will form the Surface of a Cone, whose Base is the Circle ABCD. Divide the Arch AB into the same Number of equal Parts as the Craticular Prototype is divided into, and draw Radii from each of the Points of Division. Produce GE to I, so that FI equals FG, and from the Centre I, with the Radius IF, draw the Quadrant FKH, and from I to E draw the right Line LE. Divide the Arch KF into the same Number of equal Parts, as the Radius of the Craticular Prototype is divided into; and draw Radii through each of the Points of Division, from the Centre I meeting EF, in 1, 2, 3, etc. Lastly, from the Centre F, with the Radii, F1, F2, F3, etc., describe the concentric Arches. Thus will the Craticular Epitype be formed, each Areola whereof will appear equal to another. Hence, what is delineated in every Areola of the Craticular Prototype; being transferred into the Areolas of the Craticular Epitype: the Image will be distorted or deformed; yet an Eye being duly raised over the Vertex of the Cone, will perceive it in just proportion. If the Chords of the Quadrants be drawn in the Craticular Prototype, and Chords of their fourth Part in the Craticular Epitype, all things else remaining the same; you will have the Craticular Epitype on a quadrangular Pyramid. And hence it will be easy to deform any Image, in any other Pyramid, whose Base is any regular Polygon. Because the Eye will be more deceived, if from contiguous Objects it cannot judge of the distance of the Parts of the deformed Image; therefore, these kinds of deformed Images are to be viewed through a small Hole.