A High Precision Digital Differential Analyzer for Circle Generation
In most applications of computer graphics, circles and circular arcs are frequently displayed. It is possible to contruct a DDA that draws a true circle; however, the logic needed for multiplications and trigonometric functions makes it less suited to hardware implementation, and the computations are performed to slowly by software on a computer to be acceptable. Other incremental methods perform computations without multiplications and trigonometric functions, but the common weakness of these methods is lower accuracy.
In this paper the author presents a new incremental algorithm for circle-generating DDA. The accuracy of this algorithm is much higher than that of others, and almost the same as that of the equation for the true circle. The logic of this method is as simple as the other incremental algorithms. Furthermore, where line-generating hardware exists, if we decrease the accuracy of this algorithm by one order of magnitude, the speed of drawing the circle may be raised considerably. Because of its simplicity and use only of elementary addition, subtraction, shift and sign testing, this method is also appropriate for use in numerical control, drafting machines or raster display, where closeness of fit is necessary.
KeywordsComputer Graphic Hardware Implementation Incremental Algorithm Radial Error Peak Error
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