Computational Mathematics and Mathematical Physics

, Volume 46, Issue 11, pp 1872–1881 | Cite as

Bernstein polynomials and composite Bézier curves

  • M. I. Grigor’ev
  • V. N. Malozemov
  • A. N. Sergeev


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.


Bernstein polynomials constructing Bézier curves on the basis of Bernstein polynomials geometric design 


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  1. 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. 2.
    I. P. Natanson, Constructive Function Theory (Fizmatgiz, Moscow, 1949) [in Russian].MATHGoogle Scholar
  3. 3.
    V. S. Videnskii, Bernstein Polynomials (Leningr. Gos. Ped. Inst., Leningrad, 1990) [in Russian].MATHGoogle Scholar
  4. 4.
    V. S. Videnskii, Linear Positive Operators of Finite Rank (Leningr. Gos. Ped. Inst., Leningrad, 1985) [in Russian].Google Scholar
  5. 5.
    P. De Casteljau, “Pole Theory,” in Mathematics and CAD 1 (Mir, Moscow, 1988), pp. 130–200 [in Russian].Google Scholar
  6. 6.
    P. Bézier, “Geometric Methods,” in Mathematics and CAD 2 (Mir, Moscow, 1989), pp. 96–257 [in Russian].Google Scholar
  7. 7.
    G. Farin, Curves and Surfaces for CAGD (Academic, New York, 2002).MATHGoogle Scholar
  8. 8.
    P. Bézier, Numerical Control: Mathematics and Applications (Wiley, New York, 1972).Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

  • M. I. Grigor’ev
    • 1
  • V. N. Malozemov
    • 1
  • A. N. Sergeev
    • 2
  1. 1.Faculty of Mathematics and MechanicsSt. Petersburg State UniversityPetrodvoretsRussia
  2. 2.Engineering and Economical AcademySt. PetersburgRussia

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