# CIRCLE APPROXIMATION BY QUARTIC G2 SPLINE USING ALTERNATION OF ERROR FUNCTION

• Kim, Soo Won (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY) ;
• Ahn, Young Joon (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
• Accepted : 2013.06.04
• Published : 2013.09.25

#### Abstract

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

#### Acknowledgement

Supported by : Chosun University

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