Error Analysis of Circle Drawing Using Logarithmic Number Systems

Tomio KUROKAWA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E75-D   No.4   pp.577-584
Publication Date: 1992/07/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing, Computer Graphics and Pattern Recognition
Keyword: 
computer graphics and pattern recognition,  logarithmic number systems,  circle drawing,  error analysis,  

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Summary: 
Logarithmic number systems (LNS) provide a very fast computational method. Their exceptional speed has been demonstrated in signal processing and then in computer graphics. But the precision problem of LNS in computer graphics has not been fully examined. In this paper analysis is made for the problem of LNS in picture generation, in particular for circle drawing. Theoretical error analysis is made for the circle drawing. That is, some expressions are developed for the relative error variances. Then they are examined by simulation experiments. Some comparisons are also done with floating point arithmetic with equivalent word length and dynamic range. The results show that the theory and the experiments agree reasonably well and that the logarithmic arithmetic is superior to or at least comparable to the corresponding floating point arithmetic with equivalent word length and dynamic range. Those results are also verified by visual inspections of actually drawn circles. It also shows that the conversion error (from integer to LNS), which is inherent in computer graphics with LNS, does not make too much influence on the total computational error for circle drawing. But it shows that the square-rooting makes the larger influence.