A fast algorithm for plotting and contour filling radiation patterns in three dimensions

Advanced line drawing algorithms suitable for cylindrical and spherical coordinates have been developed by W.R. Scott Jr. (1988). Unfortunately, all these methods require a significant amount of additional computation to be able to plot the surface with the hidden lines removed, and none allows contour filling. An algorithm is developed and presented in the present work which avoids the extra computation by exploiting known properties of the surfaces being plotted, and contour filling can be easily incorporated in the algorithm. This study is based on the following postulate. If a function f(u,v), where u and v are two coordinates of an orthogonal system, generates a single-valued surface in the variables u and v then there exists a systematic, although not unique, ordered sequence in which to draw the surface from back to front. This sequence is known a priori once the observation angles are specified. Therefore, no hidden line removal is necessary and plotting a function with hidden lines removed takes approximately the same amount of time as plotting without removing the hidden lines.<>