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Interpolation to Data Points in Plane with Cubic Polynomial Precision

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4469))

Abstract

This paper presents a new method for constructing parametric curve to interpolate a set of data points in plane. The constructed parametric curve has the precision of cubic polynomial function in the sense that if the given data points are taken from a cubic polynomial, then the constructed curve reproduces the cubic polynomial exactly. The comparisons of the precision of the new method with other ones are included.

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References

  1. Schoenberg, I.J.: Contributions to the problem of application of equidistant data by analytic functions, Quart. Appl. Math. (1946)

    Google Scholar 

  2. Farin, G.: Curves and surfaces for computer aided geometric design: A practical guide. Academic press, London (1989)

    Google Scholar 

  3. Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The theory of splines and their applications, p. 51. Academic Press, New York (1967)

    MATH  Google Scholar 

  4. de Boor, C.: A practical guide to splines, p. 318. Springer, New York (1978)

    MATH  Google Scholar 

  5. Faux, I.D., Pratt, M.J.: Computational geometry for design and manufacture, p. 176. Ellis Horwood Ltd (1979)

    Google Scholar 

  6. Buqing, S., Dingyuan, l.: Computational Geometry, pp. 29–32. Academic Press, Shang Hai (1982) (in Chinese)

    Google Scholar 

  7. Lee, E.T.Y.: Choosing nodes in parametric curve interpolation. In: CAD, vol. 21(6), pp. 363–370 (1989)

    Google Scholar 

  8. Zhang, C., Cheng, F., Miura, K.: A method for determining knots in parametric curve interpolation. In: CAGD, vol. 15, pp. 399–416 (1998)

    Google Scholar 

  9. Zhang, C., Cheng, F.: Constructing Parametric Quadratic Curves. Journal of Computational and Applied Mathematics 102, 21–36 (1999)

    Article  MATH  Google Scholar 

  10. Marin, S.P.: An approach to data parametrization in parametric cubic spline interpolation problems. J. Approx. Theory 41, 64–86 (1984)

    Article  MATH  Google Scholar 

  11. Zhang, C., Han, H., Cheng, F.: Determining Knots by Minimizing Energy. Journal of Computer Science and Technology 216, 261–264 (2006)

    Article  Google Scholar 

  12. Xie, H., Qin, H.: Automatic Knot Determination of NURBS for Interactive Geometric Design. In: Proceedings of International Conference on Shape Modeling and Applications, SMI 2001, pp. 267–277 (2001)

    Google Scholar 

  13. Hartley, P.J., Judd, C.J.: Parametrization and shape of B-spline curves for CAD. In: CAD, vol. 12(5), pp. 235–238 (1980)

    Google Scholar 

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Kin-chuen Hui Zhigeng Pan Ronald Chi-kit Chung Charlie C. L. Wang Xiaogang Jin Stefan Göbel Eric C.-L. Li

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© 2007 Springer Berlin Heidelberg

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Han, H., Liu, H., Ji, X. (2007). Interpolation to Data Points in Plane with Cubic Polynomial Precision. In: Hui, Kc., et al. Technologies for E-Learning and Digital Entertainment. Edutainment 2007. Lecture Notes in Computer Science, vol 4469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73011-8_65

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  • DOI: https://doi.org/10.1007/978-3-540-73011-8_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73010-1

  • Online ISBN: 978-3-540-73011-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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