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

Title & Authors
APPROXIMATION ORDER OF C3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC
BAE, SUNG CHUL; AHN, YOUNG JOON;

Abstract
In this paper, we present a $\small{C^3}$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $\small{C^3}$ 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 $\small{C^3}$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $\small{C^3}$ quartic B-spline approximation of a circular arc is also presented.
Keywords
circle approximation;$\small{C^3}$ quartic B-spline;quartic $\small{B{\acute{e}}zier}$ curve;Hausdorff distance;approximation order;
Language
English
Cited by
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