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http://dx.doi.org/10.12941/jksiam.2016.20.151

APPROXIMATION ORDER OF C3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC  

BAE, SUNG CHUL (DEPARTMENT OF MATHEMATICS EDUCATION, KOREA UNIVERSITY)
AHN, YOUNG JOON (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.20, no.2, 2016 , pp. 151-161 More about this Journal
Abstract
In this paper, we present a $C^3$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $C^3$ quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the $C^3$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $C^3$ quartic B-spline approximation of a circular arc is also presented.
Keywords
circle approximation; $C^3$ quartic B-spline; quartic $B{\acute{e}}zier$ curve; Hausdorff distance; approximation order;
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