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Error analysis for approximation of helix by bi-conic and bi-quadratic Bezier curves

김필수|안영준
대한수학회 (The Korean Mathematical Society)|2005.10|대한수학회논문집 (Communications of the KMS)|제20권 제4호|pp. 861-873

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주제분류수학

초록

Abstract

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic Bezier curves. Each approximation method is end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.

참고문헌 (23)

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  14. "The rational Bezier representation for conics", pp.3~19 (1987), Academic Press.
  15. "Interpolation of helical patches by kinematics rational Bezier patches", pp.275~280 (1990)
  16. "Best approximation of circle segments by quadratic Bezier curves", 1990. Academic Press.
  17. "Curve .tting with conic splines", 2, pp.1~31 (1983)
  18. "The sphere as a rational Bezier surfaces", 3, pp.45~52 (1986)
  19. "Techniques for conic splines in Proceedings of SIGGRAPH 85", pp.151~159 (1985)
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관련 논문AI추천

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