Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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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)
  • Received : 2016.05.09
  • Accepted : 2016.06.14
  • Published : 2016.06.25
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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.

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References

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