Computer graphics, peripheral vision and non-Euclidian geometry

Abstract

Computer graphics is often confronted with the task of providing the viewer with a visual picture of some object that is too large to fit on a computer screen unless the image is scaled down so drastically that much of the detail is lost. The viewer is then asked to work with a partial view of the object, and use a keyboard or a mouse to (a) scroll this image horizontally or vertically, or (b) zoom in or out, or (c) rotate the object. These techniques are strikingly similar to those that the human visual system uses to deal with a similar problem. One crucial difference is that of peripheral vision—the human eye, while concentrating on a small part of the field of vision, still retains a hazy view of the peripheral region preventing it from losing sight of the total picture. This paper argues that the lack of a similar peripheral vision is a major deficiency in computer graphics today. It then goes on to develop a mapping technique that tries to simulate this peripheral vision, and, thereby, make computer graphics more powerful and versatile. The paper analyses the distortions induced by such a mapping, and argues at length why these do not pose serious problems. The suggested mapping is closely related to non-Euclidian geometry; this ties in with the fact established by experimental psychologists over 50 years ago that the perceptual geometry of human vision is strongly non-Euclidian. Thus, if one were to adapt the Turing test for artificial intelligence to computer vision, then non-Euclidian geometry can be expected to play a key role in any attempt to satisfy that test. Building on these ideas, the paper demonstrates that computer graphics has a great deal to learn from non-Euclidian geometry, and that, in turn, computer graphics can contribute significantly to the intelligent application of non-Euclidian geometries to real life problems.