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