GENERATION OF POLYGONS REPRESENTING CIRCLES, ELLIPSES AND HYPERBOLAS

Algorithms are presented for the computation of vertices of polygons representing circles, ellipses, and hyperbolas. Integers only are used, together with simple operations such as addition and shifting. The curves are represented by parametric differential equations which are solved using techniques based on digital differential analyzer (DDA) principles, but using only the registers of a general purpose computer. By employing modifications to increase the integration stepsize and hence the speed of curve generation, polygon points are generated which may be joined by the display vector generator to produce more pleasing results. The deviation of the generated curve from the true curve may be estimated from a detailed examination of all potential sources of error. Finally, by employing the DDA residue retention principle, these algorithms allows effective, fast curve generation with computer word lengths as small as 12 bits. © 1979.