On a generalization of Bernstein polynomials and Bezier curves based on umbral calculus

被引：5

作者：

Winkel, Rudolf ^{[1
]}

机构：

[1] Univ Appl Sci Bingen, D-55411 Bingen Rhine, Germany

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2014年 / 31卷 / 05期

关键词：

Umbral calculus; Generalized Bernstein polynomial; Generalized de Casteljau algorithm; Interpolation; Efficient evaluation;

D O I：

10.1016/j.cagd.2014.02.010

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Winkel (2001) a generalization of Bernstein polynomials and Bezier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu (1968) and Goldman (1985), i.e., families that include both Bernstein and Lagrange polynomial, are generalized in a new way, (2) a generalized de Casteljau algorithm is discussed, (3) an efficient evaluation of generalized Bezier curves through a linear transformation of the control polygon is described, (4) a simple criterion for endpoint tangentiality is established. (c) 2014 Elsevier B.V. All rights reserved.

引用

页码：227 / 244

页数：18

共 32 条

[21] Frobenius-Euler polynomials and umbral calculus in the p-adic case [J].

Kim, Dae San ;

Kim, Taekyun ;

Lee, Sang-Hun ;

Rim, Seog-Hoon .

ADVANCES IN DIFFERENCE EQUATIONS, 2012,

[22] SOME IDENTITIES OF CATALAN-DAEHEE POLYNOMIALS ARISING FROM UMBRAL CALCULUS [J].

Kim, Taekyun ;

Kim, Dae San .

APPLIED AND COMPUTATIONAL MATHEMATICS, 2017, 16 (02) :177-189

[23] Symmetric q-extension of λ-Apostol-Euler polynomials via umbral calculus [J].

Elmonser, Hedi .

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 54 (02) :583-594

[24] A Novel Generalization of Bezier-like Curves and Surfaces with Shape Parameters [J].

Ameer, Moavia ;

Abbas, Muhammad ;

Abdeljawad, Thabet ;

Nazir, Tahir .

MATHEMATICS, 2022, 10 (03)

[25] Optimum Velocity Profile of Multiple Bernstein-Bezier Curves Subject to Constraints for Mobile Robots [J].

Zdesar, Andrej ;

Skrjanc, Igor .

ACM TRANSACTIONS ON INTELLIGENT SYSTEMS AND TECHNOLOGY, 2018, 9 (05)

[26] Some identities of extended degenerate r-central Bell polynomials arising from umbral calculus [J].

Kim, Taekyun ;

Kim, Dae San .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (01)

[27] Some identities of extended degenerate r-central Bell polynomials arising from umbral calculus [J].

Taekyun Kim ;

Dae San Kim .

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, 114

[28] (Discrete) Almansi type decompositions: an umbral calculus framework based on DSP (1|2) symmetries [J].

Faustino, N. ;

Ren, G. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (16) :1961-1979

[29] An Algorithm to Realize the Real-time Interpolation of Bezier Curves Based on DSP [J].

Zhang, Yujie ;

Zhang, Weijie ;

Xu, Bin ;

Liu, Chang .

PROCEEDINGS OF THE 2015 INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INTELLIGENT COMMUNICATION, 2015, 16 :440-443

[30] Bezier versus Lagrange polynomials-based finite element analysis of 2-D potential problems [J].

Provatidis, Christopher G. .

ADVANCES IN ENGINEERING SOFTWARE, 2014, 73 :22-34

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