Convexity preservation of the interpolating four-point C2 ternary stationary subdivision scheme

被引：24
|
作者：
Cai, Zhijie [1 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 2009年 / 26卷 / 05期
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
Subdivision scheme; Interpolating four-point ternary subdivision scheme; Convexity preservation;
D O I：
10.1016/j.cagd.2009.02.004
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Since subdivision schemes can generate curves and surfaces rapidly, they are widely used in the curve and surface modeling. Such topic is one of the important research fields in computer aided geometric design. The convexity preserving properties of the interpolating four-point ternary subdivision scheme are discussed in this paper. The conditions on the parameter of the scheme to preserve convexity are given. The parameter locates in the interval (1/15, 1/9). thus the limit Curve generated by the scheme is C-2. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：560 / 565
页数：6
相关论文
共 46 条
  • [31] Level Set Shape Analysis of Binary 4-Point Non-stationary Interpolating Subdivision Scheme
    Bibi K.
    Akram G.
    Rehan K.
    International Journal of Applied and Computational Mathematics, 2019, 5 (6)
  • [32] On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming
    Barrera, D.
    Eddargani, S.
    Lamnii, A.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 420
  • [33] C2 subdivision over triangulations with one extraordinary point
    Zulti, A
    Levin, A
    Levin, D
    Teicher, M
    COMPUTER AIDED GEOMETRIC DESIGN, 2006, 23 (02) : 157 - 178
  • [34] Complete characterization of the regions of C2 and C3 convergence of combined ternary 4-point subdivision schemes
    Novara, Paola
    Romani, Lucia
    APPLIED MATHEMATICS LETTERS, 2016, 62 : 84 - 91
  • [35] A Flexible C2 Subdivision Scheme on the Sphere: With Application to Biomembrane Modelling
    Chen, Jingmin
    Grundel, Sara
    Yu, Thomas P. Y.
    SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2017, 1 (01): : 459 - 483
  • [36] Necessary and sufficient conditions for the C2 continuous limit curves and surfaces of 4-point interpolatory subdivision scheme
    Cao, Yuan
    Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics, 2003, 15 (08): : 961 - 966
  • [37] C2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values
    Eddargani, Salah
    Oraiche, Mohammed
    Lamnii, Abdellah
    Louzar, Mohamed
    MATHEMATICS, 2022, 10 (09)
  • [38] Construction of almost everywhere c2 continuous shape interpolating spaces via progressive interpolation of loop subdivision
    Xu L.
    Yao B.
    Nie Y.
    Jiang J.
    Wu S.
    Li G.
    Computer-Aided Design and Applications, 2020, 18 (03) : 486 - 501
  • [39] A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control
    Romani, L.
    COMPUTER AIDED GEOMETRIC DESIGN, 2010, 27 (01) : 36 - 47
  • [40] BINARY 4-POINT C4 NON-STATIONARY SUBDIVISION SCHEME FOR GEOMETRIC MODELLING
    Siddiqi, Shahid S.
    Younis, Muhammad
    APPLIED AND COMPUTATIONAL MATHEMATICS, 2019, 18 (03) : 236 - 246
12345