Automatic stereoscopic presentation of functions of two variables

Spatial models of functions of two variables are often a valuable research tool. Nomograms and artistic relief drawings in two dimensions are difficult to prepare and still lack the direct impact of a spatial object. It has been demonstrated (see Ref. 2) that objects with a randomly dotted surface permit the determination of binocular parallax and, thus, can be seen in depth even though they are devoid of all other depth cues. This random surface presentation has the advantage that the random brightness points can be evenly and densely placed, whereas the classical contour-line projection at equally spaced heights may leave empty spaces between adjacent contour-lines. A digital computer is used to generate the three-dimensional image of a given z = f (x, y) function and to wrap its surface with points of random brightness. The stereo projections of the function are obtained and, when viewed stereoscopically, give the impression of the three-dimensional object as being viewed along the z-axis. The random surface prevents the accumulation of clusters of uniform regions or periodic patterns which yield ambiguities when fused. Two stereo demonstrations are given of surfaces obtained by this method.