A New Line Drawing Algorithm Based on Sample Rate Conversion

1 Overview In this paper, a new method for drawing straight lines suitable for use on raster scan displays and plotters is presented. Unlike previous methods which are based on DDA or midpoint algorithms, this technique is based on signal processing concepts related to resampling, multirate processing and sample rate conversion generally, and decimation in particular. An algorithm based on spatial decimation is developed which has attractive features including the elimination of test, compare and branch operations within the inner plotting loop. Furthermore, all multiplies, divides, shifts and other complex CPU operations are eliminated from the inner loop, as well. Lines can be drawn in any orientation with 'nearest pixel' accuracy using only the primitive CPU operations of addition (subtraction) and incrementing (decrementing). With some CPU architectures, including current Intel and AMD processors, it is possible to hold all variables in CPU registers so that the only memory accesses required in the inner loop relate to the plotting function. A variety of line drawing algorithms have been published in the literature. Among these are algorithms by Bresenham [1], Wu [5] and others. The central problem solved by these algorithms is to find a 'best fit' to an ideal line, given the constraints imposed by a raster scan or integer grid limited display. See also Pitteway [3], and Foley [2]. These prior art solutions are typically derived from the differential quantities associated with a straight line and focus on correct pixel selection or 1