Using Program Transformations to Derive Line-Drawing Algorithms

Abstract

A wide variety of line-drawing algorithms can be derived by applying program transformations to a simple, obviously correct algorithm. The transformations increase the speed of the algorithm and eliminate the need for floating-point computations. We show how Bresenham's algorithm can be derived in this way. The transformations are then used to derive several variants of Bresenham's algorithm, designed for use on displays that can generate more than one pixel at a time. The treatment shows a complete, extended example of the practical use of program transformations. © 1982, ACM. All rights reserved.