Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
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Comparison of Offset Approximation Methods of Conics with Explicit Error Bounds

  • Bae, Sung Chul (Department of Mathematics Education, Korea University) ;
  • Ahn, Young Joon (Department of Mathematics Education, Chosun University)
  • Received : 2016.01.29
  • Accepted : 2016.03.25
  • Published : 2016.03.30
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Abstract

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

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References

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