1630

In 1630, on the year of foundation of Boston, Jean-Louis Sieur de Vaulezard published his treatise "Perspective cilindrique et conique, ou Traicté des apparences veuës par le moyen des miroirs cilindriques et coniques, soient convexes ou concaves" (Cylindrical and conical perspective, or Treatise on appearances seen using cylindrical and conical mirrors, either convex or concave). It proposed the first known exact geometric method for the construction of catoptric anamorphosis images. Cylindrical images, which are only seen correctly through a cylindrical mirror, had been popular in Europe for more than a decade, and were also known in China: it has been conjectured by Baltruöaitis that they were introduced to Europe from China, just as tea had been centuries earlier.Vaulezard showed how a rectangular grid projects onto the image surface using geometric optics (we would now call it ray-tracing). The reverse problem, known as Alhazenís problem (after the Arab scholar ibn Al-Haytham), had a known but more complex solution. Before Vaulezard, catoptric anamorphosis were probably realized using polar-grid approximations, or by painting while looking through the mirror. Since approximate solutions such as the one popularized later by Nicéron proved adequate for many contents, they eventually gained favor because of their simplicity.Contemporary lectures of catoptric anamorphosis often depict it as a juncture point between art and science, or mathematics, a position shared by computer graphics. Even in a media-rich era, this geometric optical transformation continues to fascinate. The iconic Utah teapot appeared in the 1976 Newell/Blinn paper describing reflection mechanism and texture mapping: Figure 5 of the paper showed the cylindrical anamorphosis of a photograph as an illustration of the technique.The piece 1630 shows a cylindrical catoptric anamorphic image, combining a diagram from Vaulezard's work with the Utah teapot: the straight lines of light propagation in the diagram warp into curves; the anamorphic images of the diagram resembles that of the teapot in its minimalist wireframe representation. While the cylindrical mirror reveals the original image, the anisotropic scaling of the diagram's pixels induced by the mapping emphasizes the discrete nature of the image.