My Anamorphoses: Types That Produce Three Kinds of Images in Circular Cylindrical Mirrors

Leonurdo. Vol. 14, No. 3, pp. 198-201, 1981. Printed in Great Britain. 0024-094X/8 I /030198-04$02.00/0 Pergarnon Press Ltd. MY ANAMORPHOSES: TYPES THREE KINDS OF IMAGES IN CYLINDRICAL MIRRORS Hans Hamngren" THAT PRODUCE CIRCULAR 1. reflections from the inner mirrored surface and the other glass surface. Finally, by gluing metallized Mylar sheet to a plastic tube I managed to make a satisfactory mirror of this type. The distorted, sometimes unrecognizable images that are Seen in curved mirrors Once aroused my curiosity and engaged my attention. I wondered, for example, how one cokd make a distorted picture on aflat surfacethat when held before a curved mirror would produce a realistic image in the mirror. What line constructions on the surface could enable one to make such a picture? I had no idea that once having satisfied my curiosity the constructions would engage my attention further. I did not realize that there were subtle aesthetic aspects that could be produced. Then, in 1970, I happened to be looking at David Bergamini's book Mathematics, a well-illustrated book written for lay readers in the LIFE Science Library series [I]. What caught my attention was the illustration on page 100 showing a photograph of an 18th-century painting held horizontally. Resting on the painting is what appears to be a short length of a circular stove pipe (with its central axis vertical). The external surface of the cylinder is a mirror. What is remarkable is that the painting shows three highly distorted figures. But, viewed in the circular cylindrical mirror, the scene with the three figures is realistic, with no distortion. Such a picture is called an anamorphosis and Bergamini wrote in the note beneath the reproduction, 'Secrets of the technique are unknown'. On reading this sentence, 1 immediately decided to rediscover how an anamorphosis could be constructed. (I was to learn later that techniques for making anamorphoseswere not secret and that Jurgis Baltrusaitis wrote books on the subject reproducingsome of the constructions employed, namely those of J. F. Niceron and of Le P. Du Breuil [2]. The second book by Baltrusaitis on the same subject has just now been called to my attention [3]. My ignorance added a sense of magic to my rediscovery. The first cylindrical mirror I used consisted of shiny thin brass sheet, of the kind children use to decorate pine trees in Sweden at Christmastime, which I glued to a cardboard cylinder that had served once as the core of a roll of toilet paper. My next mirror was more sophisticated. It was a carefully cut out, turned and polished copper tube that I had chromium-plated. Then I made mirrors from glass tubing that I silvered inside. But the glass tubes were not precisely circular, and double images were produced by 2. Having a satisfactory mirror, I then began to look for a suitable image to be seen in the mirror. I sought, first of all, an object that possessed a circular cylindrical form, having a height-diameter ratio, like that of the mirror, so that the image on the mirror would seem to be the object itself. I chose an old-fashioned cylindrical 2.5-meter-tall ceramic-ware stove that I used for heating my studio. It was built from eight stacked rings of large bricks and was decorated by several plain moldings that encircle it at different heights. These features and the joints between the bricks contributed to making the stove aesthetically interesting to me. My principal task was to make a drawing on a horizontal plane that on reflection in the circular cylindrical mirror would give an image that seemed to be a small replica of the stove. I started by applying black removable adhesive tape along the joints between the bricks to make a rectangular grid directly on the surface of the stove that would serve as a basis for drawing the anamorphosis. Then I constructed on the horizontal plane the projection of the grid, a highly distorted one, which on reflection in the cylindrical mirror would produce an image that was identical to the grid painted on the stove. Then, using the distorted grid, I...