The Incremental Display of a Single-Valued Curve

A new algorithm is described for the drawing of a single-valued smooth function on a raster screen. It first approximates the function by a spline, normally cubic, and then displays the spline using a combination of finite differences and a special Bresenham type algorithm in integer arithmetic. Finite difference have not been successful previously, partly because of the build up of rounding errors. We show that for a modern workstation with 32 bit-integers these errors can be estimated and the algorithm modified to minimise their effect.
The result of combining all of these factors, spline, finite differences, error control, geometry and integer arithmetic is a powerful algorithm which we believe is generally more accurate and faster than previous algorithms for smooth curves.
It is worth noting that when the curve is a straight line, our algorithm becomes an extension (and minor improvement) on Bresenham's algorithm.