To draw an anamorphosis which will be restored to its proper form by reflection from the surface of a cylin der. Let R be the point situated immediately under the eye, 0 R the height of the eye, a 0 A g the base of the cylinder. Describe a reticular square round the picture to be distorted, and form a cratieular ectypc a g as in the former case ; then the diverging lines R i, R k, R 1, &c. will each cut the circle in two points. From the point a in which R i cuts the circle, draw the straight line a,, equal to a q. and produce it to 1, making a 1 equal to a. i, and from the point in which R k cuts the circle, set off ; A equal to ; c, and produce it to K, making b K equal to b k. In a similar manner draw the several lines y L, a's A1, &c. diverging from the cylinder, and to these lines transfer the points of division on the respective lines a i, C k, &c. Draw regular curves by estimation through the points 1, K, L, AI, N, 0, P, and through A, B, C, D, E, F, G, and through each inter mediate order of points ; the figure ADGPAII thus di vided will be a deformed copy of the reticulated square, described round the original picture, the base of the prototype being represented by the curved line ABCDE FG.
By transferring into each areola of the curved ectype whatever is contained in the correspondent areola of the prototype, an anamorphosis will be formed, which shall be reduced to its just proportions, by reflection from the cylinder a A A.
To draw an anamorphosis upon the convex surface of a given cone, and which shall appear in just propor tion to an eye, elevated at a given height above the ver tex of the cone. Let ACBD, (Fig 3.) the base of the cone, be divided by radii into any number of equal parts ; then let one of the radii be also divided into several equal parts, and through the points of division describe concentric circles, so shall the cmticular prototype be formed.
With EP (Fig. 4.) the side of the cone as radius, de scribe the circle EFL, and from it cut off a sector EFP, such as that the arch EF shall be the same part of the whole circumference, which AB is of twice EP; this sector being plied round the cone, will cover its surface.
Divide the arc EF into the same number of equal parts, which the craticular prototype is divided into, and draw radii to all the points of division. Then in the
circle EFL, place the straight line FL equal to AB the diameter of the prototype, bisect it in K and from K to P draw the straight line KP, and produce it to Q, so that PQ may be equal to the height at which the eye is to be elevated above the vertex of the cone, join LP and divide LK into the same number of equal parts with the radius of the prototype, and from P to the points of divi sion draw lines cutting PL in the points o, a, in. Lastly, from P as centre with the radii P o, P n, P m, &c. de scribe concentric arcs rs, tu,V70, thus shall the craticu lar cctvpe be formed. What is delineated in the seve ral areoh of the prototype, being now transferred to the corresponding areolx of the ectype ; an anamorphosis will be formed, which when wrapped round the surface of the given cone, will seem reduced to its just propor tions, when viewed from a point elevated above the ver tex of the cone at a height equal to EP.
The various kinds of anamorphosis may be formed mechanically in the following manner. Perforate with a fine needle the principal points of the picture which. is to be distorted, and place it before a candle, and then mark on what points of the surface which is to contain the anamorphosis, the rays passing through the small holes WI. These will be the correspondent points in the distorted painting. It is hardly necesary to mention, that when it is intended by this method to draw an atm morphosis, which shall be reformed by reflection, we must place the perforated picture between the candle and the reflecting surface.
These pictures are sometimes contrived so ingeni ously, as when viewed directly to appear like some re gular drawing, such as an encampment, &c. but when viewed obliquely like some di fferent object. See Niceron's Thaunzaturgus Onticu8. Lutman Ill, ni. 1171fier. AClid Peter. vol. iv. \Volfii Elementa Mathedros, vol. iii. c. 5. p. 99. Priestley's Hist. of p. 93-96. Schottus's Magid, vol. i. p. 162. Smith's Omits, von. i. b. 2d. p.
248-25 I. Mutton's Dictionary, art. ANA MOR PHOSIS.
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