 and floors are made with steel reinforcing rods spaced 20 cm or more apart, then the effect on microwave radio is small. If the builders used corrugated steel pans that were left in place as casting molds for the concrete, then the attenuation is much greater, and there is a significant reflected signal. The next level of sophistication in radio path modeling is to go beyond the direct point-to-point path to a ray-tracing model that takes into account multiple paths be- tween the two end points. 47.6 Ray-Tracing Models A ray-tracing model uses a database of all the relevant surfaces between and around the radio path. Not only must we know where the surfaces are, we also must know their radio characteristics at the frequencies we are considering. For microcells in a business district with large buildings, a two-dimensional ray-tracing model may give excellent attenuation and multipath predictions. For a picocell inside the building with its sub- scriber community, we may need a three-dimensional model to get the level of detail re- quired to ensure adequate wireless telephone service. The ray-tracing program calculates all the paths it can find from source A to target B. Radio waves can do three things at a change of medium: They can refract as they go from the old medium into the new medium and change direc- tion according to Snell's law. 9 They can reflect as they bounce back into the old medium. They can diffract in a new radiation pattern from the medium boundary. The ray-tracing program analyzes all the paths that contribute to the total signal. We only need to do this calculation in one direction. The radio paths from A to B are the same as the radio paths from B to A. 10 All the refractions, reflections, and diffrac- tions are going to be the same coming and going. The difference in frequency between the forward and reverse directions is too small to matter in a ray-tracing computation. This is a seriously large computation to do. Recent computer animation has produced astonishingly realistic images in mov