Curve-Drawing Algorithms for Raster Displays

Abstract

The midpoint method for deriving efficient scan-conversion algorithms to draw geometric curves on raster displays in described. The method is general and is used to transform the nonparametric equation f(x,y) = 0, which describes the curve, into an algorithms that draws the curve. Floating point arithmetic and time-consuming operations such as multiplies are avoided. The maximum error of the digital approximation produced by the algorithm is one-half the distance between two adjacent pixels on the display grid. The midpoint method is compared with the two-point method used by Bresenham, and is seen to be more accurate (in terms of the linear error) in the general case, without increasing the amount of computation required. The use of the midpoint method is illustrated with examples of lines, circles, and ellipses. The considerzations involved in using the method to derive algorithms for drawing more general classes of curves are discussed. © 1985, ACM. All rights reserved.