Perspective Drawing of Surfaces With Hidden Line Elimination

Abstract

An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding to single-valued, continuous functions which are defined over rectangular domains. The algorithm automatically computes and eliminates “hidden lines.” The number of computations in the algorithm grows linearly with the number of sample points on the surface to be drawn. An analysis of the algorithm is presented, and extensions to certain multi-valued functions are indicated. The algorithm is implemented and tested on two different computers: a large central computer with hard-copy capability, and a small laboratory computer affording interactive use. Running times are found to be exceedingly efficient on both machines. Interactive implementation of the algorithm, with on-line scope display and view-point control, enables effective and rapid examination of a surface from many perspectives.