Bezier Curves and Surfaces Based on Modified Bernstein Polynomials

被引：0

作者：

Khan, Kh ^{[1
]}

Lobiyal, D. K. ^{[1
]}

Kilicman, A. ^{[2
]}

机构：

[1] JNU, SC & SS, New Delhi 110067, India

[2] Univ Putra Malaysia, Fac Sci, Dept Math, Serdang, Malaysia

来源：

AZERBAIJAN JOURNAL OF MATHEMATICS | 2019年 / 9卷 / 01期

关键词：

degree elevation; degree reduction; de Casteljau algorithm; Bernstein blending functions with shifted knots; Bezier curve; tensor product; shape preserving; LUPAS Q-ANALOG; (P; APPROXIMATION; Q)-ANALOG;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, Bezier curves and surfaces have been constructed based on modified Bernstein bases functions with shifted knots for t is an element of[alpha/n+beta, n+alpha/n+beta]. Various properties of these modified Bernstein bases are studied. A de Casteljau type algorithm has been developed to compute Bezier curves and surfaces with shifted knots. Furthermore, some fundamental properties of Bezier curves and surfaces with modified Bernstein bases are also discussed. Introduction of parameters alpha and beta enable us to shift Bernstein bases functions over subintervals of [0,1]. These new curves have some properties similar to classical Bezier curves. We get Bezier curves defined on [0,1] when we set the parameters alpha, beta to the value 0: Simulation study is performed through MATLAB R2010a. It has been concluded that Bezier curves that are generated over any subinterval of [0,1] based on modified Bernstein bases functions are similar to the Bezier curves that are generated based on classical Bernstein bases functions over the interval [0,1].

引用

页码：3 / 21

页数：19

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