Research article

Curve construction based on quartic Bernstein-like basis

  • Received: 22 April 2020 Accepted: 08 June 2020 Published: 22 June 2020
  • MSC : 65D07, 65D17

  • A new quartic Bernstein-like basis possessing two exponential shape parameters is developed and the condition of C2FC2l+3 continuity and the definition of such continuity-related curves are discussed. Based on this new basis, a new cubic B-spline-like basis possessing two global and three local shape parameters is presented and the related cubic B-spline-like curves have C2FC2l+3 continuity at each point and include the classical cubic uniform curves as a special case. Representative properties regarding connecting, interpolation and local adjustment of the cubic Bspline-like curves are also discussed.

    Citation: Kai Wang, Guicang Zhang. Curve construction based on quartic Bernstein-like basis[J]. AIMS Mathematics, 2020, 5(5): 5344-5363. doi: 10.3934/math.2020343

    Related Papers:

  • A new quartic Bernstein-like basis possessing two exponential shape parameters is developed and the condition of C2FC2l+3 continuity and the definition of such continuity-related curves are discussed. Based on this new basis, a new cubic B-spline-like basis possessing two global and three local shape parameters is presented and the related cubic B-spline-like curves have C2FC2l+3 continuity at each point and include the classical cubic uniform curves as a special case. Representative properties regarding connecting, interpolation and local adjustment of the cubic Bspline-like curves are also discussed.


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    [1] G. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Academic Press, Inc., 1993.
    [2] L. Piegl, W. Tiller, The NURBS Book, New York, Springer, 1995.
    [3] X. Q. Qin, G. Hu, N. Zhang, et al. A novel extension to the polynomial basis functions describing Bezier curves and surfaces of degree n with multiple shape parameters, Appl. Math. Comput., 223 (2013), 1-16.
    [4] X. A. Han, Y. C. Ma, X. L. Huang, A novel generalization of Bezier curves and surface, J. Comput. Appl. Math., 217 (2008), 180-193. doi: 10.1016/j.cam.2007.06.027
    [5] G. Hu, H. X. Cao, S. Zhang, et al. Developable Bézier-like surfaces with multiple shape parameters and its continuity conditions, Appl. Math. Model., 45 (2017), 728-747. doi: 10.1016/j.apm.2017.01.043
    [6] I. Cravero, C. Manni, Shape-preserving interpolants with high smoothness, J. Comput. Appl. Math., 157 (2003), 383-405. doi: 10.1016/S0377-0427(03)00418-7
    [7] K. Wang, G. C. Zhang, New trigonometric basis possessing denominator shape parameters, Math. probl. Eng., 2018 (2018), 1-25.
    [8] Z. Liu, Representation and approximation of curves and surfaces based on the Bezier method in CAGD, Hefei University of technology, 2009.
    [9] T. Xiang, Z. Liu, W. Wang, et al. A novel extension of Bézier curves and surfaces of the same degree, J. Inf. Comput. Sci., 7 (2010), 2080-2089.
    [10] P. Costantini, Curve and surface construction using variable degree polynomial splines, Comput. Aided Geom. D., 17 (2000), 419-466. doi: 10.1016/S0167-8396(00)00010-8
    [11] P. Costantini, T. Lyche, C. Manni, On a class of weak Tchebysheff systems, Numer. Math., 101 (2005), 333-354. doi: 10.1007/s00211-005-0613-6
    [12] G. Hu, J. L. Wu, X. Q. Qin, A novel extension of the Bézier model and its applications to surface modeling, Adv. Eng. Softw., 125 (2018), 27-54. doi: 10.1016/j.advengsoft.2018.09.002
    [13] G. Hu, C. C. Bo, G. Wei, et al. Shape-adjustable generalized Bézier surfaces: Construction and its geometric continuity conditions, Appl. Math. Comput., 378 (2020), 125215.
    [14] F. Pelosi, R. T. Farouki, C. Manni, et al. Geometric Hermite interpolation by spatial Pythagoreanhodograph cubics, Adv. Comput. Math., 22 (2005), 325-352. doi: 10.1007/s10444-003-2599-x
    [15] C. González, G. Albrecht, M. Paluszny, et al. Design of algebraic-trigonometric pythagorean hodograph splines with shape parameters, Comput. Appl. Math., 37 (2018), 1472-1495. doi: 10.1007/s40314-016-0404-y
    [16] Y. Zhu, X. Han, S. Liu, Curve construction based on four αβ-Bernstein-like basis functions, J. Comput. Appl. Math., 273 (2015), 160-181. doi: 10.1016/j.cam.2014.06.014
    [17] R. Ait-Haddou, M. Bartoň, Constrained multi-degree reduction with respect to Jacobi norms, Comput. Aided Geom. D., 42 (2016), 23-30. doi: 10.1016/j.cagd.2015.12.003
    [18] J. Hoschek, D. Lasser, Fundamentals of Computer Aided Geometric Design, A. K. Peters, Ltd, 1993.
    [19] P. Constantini, C. Manni, Geometric construction of spline curves with tension properties, Comput. Aided Geom. D., 20 (2003), 579-599. doi: 10.1016/j.cagd.2003.06.009
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