Two-Dimensional Perspectives of Three-Dimensional Surfaces with Automatic Hidden-Line Elimination
N. Y. Graham, Lawrence R. Rabiner · The Journal of the Acoustical Society of America · 1972
In digital signal processing, one is often faced with displaying a function of two variables. To examine this surface on a two-dimensional medium, such as a piece of paper or a computer scope face, one is forced to resort to clever alternatives. For example, a sound spectrogram uses intensity of blackness of the marking to show the spectrum amplitude as a function of time (x-axis) and frequency (y-axis). In a scope display, intensity modulation can serve as a third variable in making a “three-dimensional” display. In this paper we discuss a novel algorithm for perspective display of a three-dimensional surface. The algorithm includes automatic elimination of hidden lines. To produce a perspective of the surface, the program needs only a mathematical description of the surface over a rectangular grid, and the x, y, z coordinates of the viewing (vantage) point. By changing the vantage point in a continuous manner, one is able to “examine” the surface in detail, as though it were physically there. A movie film, composed and generated interactively on the DDP-516 computer, will illustrate the algorithm.