Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
권호 표지
DOI QR코드

DOI QR Code

Construction of Logarithmic Spiral-like Curve Using G2 Quadratic Spline with Self Similarity

  • Lee, Ryeong (Department of Mathematics Education, Chosun University) ;
  • Ahn, Young Joon (Department of Mathematics Education, Chosun University)
  • Received : 2014.04.06
  • Accepted : 2014.06.25
  • Published : 2014.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

Keywords

References

  1. G. Farin, J. Hoschek, and M.-S. Kim, "Handbook of computer aided geometric design", Amsterdam, Netherlands, Elsevier, 2002.
  2. Y. Mineur, T. Lichah, J. M. Castelain, and H. Giaume, "A shape controled fitting method for Bezier curves", Comp. Aided Desi. Appl., Vol. 15, pp. 879-891, 1998. https://doi.org/10.1016/S0167-8396(98)00025-9
  3. G. Farin, "Class a Bezier curves", Comp. Aided Geom. Desi., Vol. 23, pp. 573-581, 2006. https://doi.org/10.1016/j.cagd.2006.03.004
  4. C. Baumgarten and G. Farin, "Approximation of logarithmic spirals", Comp. Aided Geom. Desi., Vol. 14, pp. 515-532, 1997. https://doi.org/10.1016/S0167-8396(96)00043-X
  5. J. Cao and G. Wang. "A note on Class A Bezier curves", Comput. Aided. Geom. D, Vol. 25, pp. 523-528, 2008. https://doi.org/10.1016/j.cagd.2007.10.001
  6. R. Schaback. "Interpolation with piecewise quadratic visually C2 Bezier polynomials", Comp. Aided Geom. Desi., Vol. 6, pp. 219-233, 1989. https://doi.org/10.1016/0167-8396(89)90025-3
  7. G. Farin, "Curvature continuity and offsets for piecewise conics", ACM Trans. Graph., Vol. 8, pp. 89-99, 1989. https://doi.org/10.1145/62054.62056
  8. G. Amati, A. Liverani, and G. Caligiana. "From spline to Class-A curves through multi-scale analysis filtering", Comp. Grap., Vol. 30, pp. 345-352, 2006. https://doi.org/10.1016/j.cag.2006.02.005
  9. D. A. Dietz and B. Piper. "Interpolation with cubic spirals", Comp. Aided Geom. Desi., Vol. 21, pp. 165-180, 2004. https://doi.org/10.1016/j.cagd.2003.09.002
  10. K. Miura, "A general equation of aesthetic curves and its self-affinity", Comp. Aided Desi. Appl., Vol. 3, pp. 457-464, 2006. https://doi.org/10.1080/16864360.2006.10738484
  11. Y. J. Ahn and H. O. Kim, "Curvatures of the quadratic rational Bezier curves", Comp. Math. Appl., Vol. 36, pp. 71-83, 1998.

Cited by

  1. Comparison of Offset Approximation Methods of Conics with Explicit Error Bounds vol.9, pp.1, 2016, https://doi.org/10.13160/ricns.2016.9.1.10