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The dual basis functions for the Bernstein polynomials

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Abstract

An explicit formula for the dual basis functions of the Bernstein basis is derived. The dual basis functions are expressed as linear combinations of Bernstein polynomials.

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References

  1. P.J. Barry and R.N. Goldman, What is the natural generalization of a Bézier curve?, in: Mathematical Methods in Computer Aided Geometric Design (Academic Press, Boston, 1989) pp. 71–85.

    Google Scholar 

  2. P.J. Barry and R.N. Goldman, Three examples of dual properties of Bézier curves, in: Mathematical Methods in Computer Aided Geometric Design (Academic Press, Boston, 1989) pp. 61–69.

    Google Scholar 

  3. Z. Ciesielski, The basis of B-splines in the space of algebraic polynomials, Ukrainian Math. J. 38 (1986) 311–315.

    MATH  MathSciNet  Google Scholar 

  4. C. de Boor and G. Fix, Spline interpolation by quasi-interpolants, J. Approx. Theory 8 (1973) 19–45.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Dong-Bing, Dual bases of a Bernstein polynomial basis on simplices, Comput. Aided Geom. Design 10 (1993) 483–489.

    Article  MathSciNet  Google Scholar 

  6. R. Farouki and V.T. Rajan, Algorithms for polynomials in Bernstein form, Comput. Aided Geom. Design 5 (1988) 1–26.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design (A.K. Peters, Wellesley, 1993).

    Google Scholar 

  8. D.E. Knuth, The Art of Computer Programming, Vol. 1, Fundamental Algorithms (Addison-Wesley, Reading, MA, 1972).

    Google Scholar 

  9. G. Lorentz, Bernstein Polynomials (Toronto Press, 1953).

  10. W.A.M. Othman and R.N. Goldman, The dual basis functions for the generalized Ball basis of odd degree, Comput. Aided Geom. Design 14 (1997) 571–582.

    Article  MATH  MathSciNet  Google Scholar 

  11. K. Zhao and J. Sun, Dual bases of multivariate Bernstein–Bézier polynomials, Comput. Aided Geom. Design 5 (1988) 119–125.

    Article  MATH  MathSciNet  Google Scholar 

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Jüttler, B. The dual basis functions for the Bernstein polynomials. Advances in Computational Mathematics 8, 345–352 (1998). https://doi.org/10.1023/A:1018912801267

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  • DOI: https://doi.org/10.1023/A:1018912801267