An algorithm for high-speed curve generation

A fast algorithm for the generation of arbitrary curves is described. The algorithm is recursive, using only integer addition, one-bit right shifts, complementation and comparisons, and produces a sequential list of raster points which constitute the curve. The curve consists of concatenated segments, where each segment is smooth and open. The curve may be arbitrarily complex, that is, it may be smooth or discontinuous, and it may be open, closed, or self intersecting. Implementation of the algorithm in a hardware microprocessor is considered as an extension to incremental plotting devices and other numerically controlled machines. An extension of the algorithm to generate 3-D curves is described, along with techniques for their application to surface representation, nonlinear interpolation, and direction of numerically controlled milling machines and similar devices.