ANIMATING THE EVOLUTION OF A FIELD

Many problems in electromagnetics involve modeling a changing multi-di mensional field, and one can often gain insight into the underlying ph ysical problem by animating the changes. The ability to view directly the evolving field may also provide a useful debugging tool during mod eling and simulation. In the past, a great deal of programming effort, or the purchase of expensive commercial software, was required to pro duce such animations. Here, we present a relatively simple scheme to a nimate a changing two-dimensional field (which can be a ''slice'' thro ugh a computational domain of higher dimensions). The scheme permits v arious mappings of field values to colors, so that the color of each p ixel in an image indicates the field found at the corresponding locati on within the computational domain. Alternatively, a gray-scale mappin g can be used. A program used to construct individual frames of the an imation is presented in full. Sufficient detail is given so that the c ustomization of the code is straightforward. Public-domain software is used to view the frames as an animated sequence, or to generate an MP EG file. Some aspects of the scheme described here are tailored for us e in an X-Windows or UNIX environment, but most of the important steps are independent of the operating system. Frame-generation routines ar e presented in FORTRAN (C versions of the code are similar and can be obtained ''on-line''). The scheme presented here is relatively fast, e fficient, and flexible, and should serve well as a starting point for those wanting to ''roll their own'' graphics. In addition, for those n eeding more sophisticated renderings, pointers are given to several po werful commercial and public-domain graphics packages.