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Bernstein polynomials and composite Bézier curves

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Abstract

Analytical principles of the theory of Bézier curves are presented. A new approach to the construction of composite Bézier curves of prescribed smoothness both on a plane and in a multidimensional Euclidean space is proposed.

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References

  1. S. N. Bernstein, “Proof of the Weierstrass Theorem Based on Probability Theory,” in Collected Works (Akad. Nauk SSSR, Moscow, 1952), Vol. 1, pp. 105–106 [in Russian].

    Google Scholar 

  2. I. P. Natanson, Constructive Function Theory (Fizmatgiz, Moscow, 1949) [in Russian].

    MATH  Google Scholar 

  3. V. S. Videnskii, Bernstein Polynomials (Leningr. Gos. Ped. Inst., Leningrad, 1990) [in Russian].

    MATH  Google Scholar 

  4. V. S. Videnskii, Linear Positive Operators of Finite Rank (Leningr. Gos. Ped. Inst., Leningrad, 1985) [in Russian].

    Google Scholar 

  5. P. De Casteljau, “Pole Theory,” in Mathematics and CAD 1 (Mir, Moscow, 1988), pp. 130–200 [in Russian].

    Google Scholar 

  6. P. Bézier, “Geometric Methods,” in Mathematics and CAD 2 (Mir, Moscow, 1989), pp. 96–257 [in Russian].

    Google Scholar 

  7. G. Farin, Curves and Surfaces for CAGD (Academic, New York, 2002).

    MATH  Google Scholar 

  8. P. Bézier, Numerical Control: Mathematics and Applications (Wiley, New York, 1972).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Petrodvorets, 198504, Russia

    M. I. Grigor’ev & V. N. Malozemov

  2. Engineering and Economical Academy, ul. Marata 27, St. Petersburg, 191002, Russia

    A. N. Sergeev

Authors
  1. M. I. Grigor’ev
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  2. V. N. Malozemov
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  3. A. N. Sergeev
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Additional information

Original Russian Text © M.I. Grigor’ev, V.N. Malozemov, A.N. Sergeev, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 11, pp. 1962–1971.

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Grigor’ev, M.I., Malozemov, V.N. & Sergeev, A.N. Bernstein polynomials and composite Bézier curves. Comput. Math. and Math. Phys. 46, 1872–1881 (2006). https://doi.org/10.1134/S0965542506110042

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  • DOI: https://doi.org/10.1134/S0965542506110042

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