Two Methods of Modelling a Curved Surface in a Ray Tracing Model

This paper describes two methods of modelling a curved surface in ray tracing computer models: an approximate method in which the surface is modelled as a series of planes, and an exact method which uses the precise analytical description of the surface. The focusing effects predicted using the two models in a hypothetical cylindrical space have been examined and compared. It was found that the approximate method of modelling the curved surface predicted focusing effects that were significantly different from those predicted using the exact method. However, the larger the number of planes used in the approximation, the closer the agreement between the two methods. The effects of source position and number of sources on focusing were also examined, and showed that focusing effects are stronger when the source position is on the axis of the cylinder. Propagation of sound across and along the cylinder has also been studied.