The antialiasing problem in ray tracing

Ray tracing is one of the most general and powerful techniques for synthesizing realistic images. Unfortu-nately, this method suffers from a notoriously difficult problem with aliasing. This survey will consider why the problem is hard, several classes of solutions, and some of the issues that require further study. Before discussing ray tracing in particular, some general concepts of images and signals will be reviewed. An image is an example of a two-dimensional signal, and can be in one of several different representations. For example, in a television camera, a lens system focuses an optical image onto a target. That image is a two-dimensional region of varying light intensity and color. When the target is scanned, an electrical signal is produced which is "analogous " to the optical image. In this paper, both the optical and the electrical rep-resentations will be called analog images, because they both consist of continuously variable physical quantities. A second possible representation is that of a symbolic image. For example, a "zone plate " pattern can be expresses as a two-dimensional function, I (x, y) = sin(x2 + y2). Symbolic images may be continuously variable, but they consist of mathematical expressions or computer programs rather than tangible physical quantities. A digital image is a two-dimensional lattice of uniformly spaced samples of color, called pixels. Unlike th