Conic Display Generator Using Multiplying Digital-Analog Converters

Abstract

A simple waveform generator for display systems has been designed on the basis of homogeneous coordinate mathematics. This generator will draw points, lines, and general conic sections. The fundamental waveform used is the parabola. Circles, ellipses, and hyperbolas are merely perspective transformations of the basic parabola, which is represented by the parametric vector t= [t2, t, 1]. The design of the homogeneous conic generator is based upon the assumption that a multiplying digital-to-analog decoder can be built economically. The decoder produces an output voltage proportional to the product of a ten-bit digital number and a positive reference level; it must maintain 0.1 percent accuracy up to about 100 kHz. In its simplest form the generator would contain 11 decoders. Allowing subpicture scaling and centering requires 14; adding cubics requires 18; and the most complicated system, with three-dimensional cubics with a final perspective transformation as well as the two-dimensional transformation, requires 34 decoders.