Automatic Stereoscopic Presentation of Functions of Two Variables

Pictorial representations and visual displays are invaluable aids in conveying scientific or technical information. In particular, the problem of presenting three-dimensional d a t a is of interest both from the standpoint of its wide range of applicability and the difficulty involved in the production of such representations. T h e methods usually employed to present functions of two variables in the fields of applied mathematics, engineering, cartography, etc., fall into two categories: 1) two-dimensional and 2) three-dimensional displays. The first has the obvious advantage of being suitable for the printed page, t h u s permitting a wide circulation for the information so GG3 GG4 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , MARCH 1962 presented. The techniques of nomography, orthography, isarithmic (contour line) representations (see Fig. 1) and relief drawings (see Fig. 2) belong to this category and are widely used despite the expense and difficulty in their preparation. However, the greatest objection is perhaps t h e failure of such displays to match the capabilities of human observers, who are equipped to perceive a three-dimensional object in depth. The second category -- t h a t of spatial models or sculpture -- answers this objection, but these models are usually much too difficult to execute and much too limited in their applicability. There is, therefore, a need for a technique which a) eliminates the tedious effort required of draftsmen in producing such displays, b) presents displays complete with the spatial effects inherently belonging to three-dimensional objects and appreciated by human observers, and c) generates displays suitable for the printed page.