Drawings Based on Lines Projected from the Surface of the Circular Cylinder

Abstract

Recently, I have taken an interest in the projection on a flat surface of lines drawn on the surface of the circular cylinder, since in my artworks with nonfigurative constructions during the past four years circular cylinders have been a dominant feature [1,2]. When making these constructions I had to cut fairly complicated shapes out of plastic pipe, and this brought me up against the problem of translating into 3-dimensions shapes drawn on a piece of paper. To draw a curve on the surface of circular cylinder such that it conforms in appearance to a curve drawn on a flat surface requires attention to projective geometry. This geometry excited me beyond its mere utility in terms of my constructions, so I decided to apply it in drawings. I constructed a circular cylindrical grid by drawing first a semicircle and marking off on it points at 5 degree intervals through which I drew vertical parallel lines perpendicular to the diameter of the semicircle. Then I drew horizontal lines at intervals equal to the maximum distance between the vertical lines. The elements of this grid have a constant height and their widths decrease toward the outermost vertical line on each side of the vertical axis. Next, I drew diagonals in the grid, beginning at square elements along the vertical axis and continuing them in neighbouring elements till the outermost vertical lines were met. A set of connected segments of straight lines provided an approximate projection of a line drawn on the surface of a circular cylinder at 45: to its vertical axis. I then made from hardboard a template of this approximate projection. In Fig. 1 is shown a drawing produced by using the template to draw parallel lines positioned along two vertical axes. One in this way obtains the illusion of the appearance of circular cylinders with lines drawn on them at an angle of 45 . The drawing shown in Fig. 2 consists of six squares in which the direction of the lines is reversed in adjacent squares. When the lines are superimposed, interesting textural effects can be produced and, when the lines superimposed are not concisely parallel, the well known moire effect [3] that is often used in Op artworks is