Date of Award

1993

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computer Science

First Advisor

S. Sitharama Iyengar

Abstract

Two basic approaches to drawing lines on raster devices are discussed and improved upon. The first is the recursive bisection algorithm, a method recently proposed by John Rankin, which uses a fractal approach to draw lines. The second is the double-step algorithm, a method proposed by Xiaolin Wu and Jon Rokne, which is based on the traditional Bresenham approach to drawing lines. Although a number of line drawing algorithms exist, the algorithms presented are of interest because the double-step algorithm is one of the fastest line drawing algorithms. Furthermore, since lines are self-similar and fractals have been found to be useful in drawing other self-similar objects such as coastlines, plants, and terrain, the investigation of such an approach appears to be a worthwhile endeavor. In addition, some of the ideas presented can be applied to other line drawing algorithms and related problems such as incremental linear interpolation. Regarding the recursive bisection algorithm, modifications making it faster than the traditional Bresenham method while reducing the logarithmic space requirements to a constant are discussed. A more detailed examination of the error analysis is presented as well. A parallel version of the algorithm is also developed in which only two operations reducible to multiplication/division are required, equaling the lower bound and half the amount needed by the parallel Bresenham algorithm. In addition, the amount of logic needed is small. In the second part, modifications to the double-step line drawing algorithm are presented that allow additional pixels to be determined during some of the loop iterations. It is then shown that the resulting algorithm reduces the number of iterations by up to 33% while keeping the same worst case performance, code complexity, and initialization costs as the double-step algorithm. Lastly, this approach is generalized and applied to one of the fastest incremental linear interpolation algorithms, giving similar results.

Pages

92

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