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1.
Bézier曲面有两种不同的形式:三角Bézier曲面和四边Bézier曲面,它们有着不同的基底和不同的几何拓扑结构,但是它们也有很多共同的性质,因此三角Bézier曲面和四边Bézier曲面之间的相互转化就成为CAGD里一个重要研究课题.在本文中,我们用函数复合的方法实现两者之间的相互转化.被复合的两个函数,一个用Polar形式表示,另一个用常见的Bernstein基形式表示.  相似文献   

2.
给出了n阶带形状参数的三角多项式T-Bézier基函数.由带形状参数的三角多项式T-Bézier基组成的带形状参数的T-Bézier曲线,可通过改变形状参数的取值而调整曲线形状,随着形状参数的增加,带形状参数的T-Bézier曲线将接近于控制多边形,并且可以精确表示圆、螺旋线等曲线.阶数的升高,形状参数的取值范围将扩大.  相似文献   

3.
《大学数学》2016,(1):33-37
给出了一组含有两个形状参数α,β的四次多项式基函数,是四次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线不仅保留了四次Bézier曲线一些实用的几何特征,而且具有形状的可调性,在控制多边形不变的情况下,改变参数α,β的取值,可以生成不同的逼近控制多边形的曲线;通过分析该曲线与四次Bézier曲线之间的关系,给出了α和β的几何意义,并利用Bézier曲线递归分割算法给出了这种曲线的几何作图法,同时还讨论了曲线间的拼接问题.  相似文献   

4.
构造了一类新的带双参数形状可调的拟Bernstein基函数,它是在三次Bernstein多项式的基础上扩展而成的一组n次拟Bernstein基.在此基础上,定义了带双形状参数的拟Bernstein-Bézier曲线,它保留了Bézier曲线的几何特征,并具有形状可调的特性.在控制点给定的情况下,可通过改变形状参数的值整体或局部地调控曲线的形状,同时给出参数控制及曲线拼接应用的实例.  相似文献   

5.
以sint,cost,t3,t2,t,1为基底构造了一组类似于Bernstein多项式的基函数,它们依赖于参数a,用这组基函数表示的自由曲线称为五次C-Bézier曲线,它不仅具有一般五次Bézier曲线所具有的各种几何性质,同时又可以精确地表示一些圆锥曲线,例如圆弧甚至整圆.  相似文献   

6.
翟芳芳 《大学数学》2012,28(3):59-63
给出了一组含有两个形状参数α,β的六次多项式基函数,是五次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线具有五次Bézier曲线的性质,改变参数α,β的取值,曲线具有更灵活的形状可调性,而且能向上或从两侧逼近控制多边形.另外,经典的五次Bézier曲线和有关文献中带一个形状参数的曲线均是该文所定义曲线的特例.实例表明,定义的曲线为曲线/曲面的设计提供了一种有效的方法.  相似文献   

7.
利用指数平均族与Béier曲线结合定义了指数平均Bézier曲线族.首先研究了指数平均族,阐述了指数平均族的单调性和正规性,其次由Bernstein函数定义得到n次s阶指数平均Bernstein函数,讨论了它与函数f之间的关系,最后,研究指数平均Bézier曲线族的性质,讨论了它的升阶,de casteljan算法,分割定理等.  相似文献   

8.
洪玲  邢燕 《大学数学》2015,31(1):26-30
将B样条曲线转换为Bézier曲线,基于Bézier曲线间的光滑拼接的理论,研究了带多形状参数的Bézier曲线(CE-Bézier曲线)与均匀B样条曲线的拼接问题,得出均匀B样条曲线与CE-Bézier曲线的G0,G1,G2光滑拼接条件.在达到拼接条件的前提下,通过改变CE-Bézier曲线的形状参数的数值大小,可以灵活调整拼接曲线的形状.  相似文献   

9.
本文研究具有Pythogorean Hodograph (PH)性质的C Bézier曲线的几何性质.以PH C-曲线的代数性质为基础,应用平面参数曲线的复表示方法,本文证明一条C Bézier曲线是PH C-曲线的充分必要条件是其控制多边形的两内角相等,且其第2条边长为首末边长的等比中项.该性质与三次多项式PH曲线相类似,可以用于PHC-曲线的判别.此外,该性质可以很好地应用于解决PH C-曲线的Hermite插值问题,本文构造了PH C-曲线的G1 Hermite插值实例,指出对于给定的G1 Hermite端点条件,存在不超过2条PH C-曲线满足约束.  相似文献   

10.
李军成  刘成志 《计算数学》2017,39(2):115-128
构造了一种带两个形状参数的Bézier型曲线,并研究了该曲线的性质、形状参数对曲线的影响及曲线的拼接.所提出的曲线是多项式Bezier曲线的一种同次新扩展,不仅具有传统Bézier曲线的诸多性质,而且可通过修改两个形状参数的取值对其形状进行调节.由于所提出的曲线是一种带有形状参数且与传统Bézier曲线具有相似性质的同次多项式模型,因此比现有的一些带形状参数的Bézier型曲线更有优势.  相似文献   

11.
This paper proposes a novel boundary element approach formulated on the Bézier-Bernstein basis to yield a geometry-independent field approximation. The proposed method is geometrically based on both computer aid design (CAD) and isogeometric analysis (IGA), but field variables are independently approximated from the geometry. This approach allows the appropriate approximation functions for the geometry and variable field to be chosen. We use the Bézier–Bernstein form of a polynomial as an approximation basis to represent both geometry and field variables. The solution of the element interpolation problem in the Bézier–Bernstein space defines generalised Lagrange interpolation functions that are used as element shape functions. The resulting Bernstein–Vandermonde matrix related to the Bézier–Bernstein interpolation problem is inverted using the Newton-Bernstein algorithm. The applicability of the proposed method is demonstrated solving the Helmholtz equation over an unbounded region in a two-and-a-half dimensional (2.5D) domain.  相似文献   

12.
We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.  相似文献   

13.
李宁  黄有度 《大学数学》2006,22(5):59-63
提出了点集Bézier曲线的概念,给出了点集Bézier曲线的性质及细分算法.按照点集算术的定义,当点集是长方形闭域或圆盘时,点集Bézier曲线就是区间Bézier曲线或圆盘Bézier曲线,因此,点集Bézier曲线是对区间Bézier曲线和圆盘Bézier曲线的推广.  相似文献   

14.
A new formulation for the representation and designing of curves and surfaces is presented. It is a novel generalization of Bézier curves and surfaces. Firstly, a class of polynomial basis functions with nn adjustable shape parameters is present. It is a natural extension to classical Bernstein basis functions. The corresponding Bézier curves and surfaces, the so-called Quasi-Bézier (i.e., Q-Bézier, for short) curves and surfaces, are also constructed and their properties studied. It has been shown that the main advantage compared to the ordinary Bézier curves and surfaces is that after inputting a set of control points and values of newly introduced nn shape parameters, the desired curve or surface can be flexibly chosen from a set of curves or surfaces which differ either locally or globally by suitably modifying the values of the shape parameters, when the control polygon is maintained. The Q-Bézier curve and surface inherit the most properties of Bézier curve and surface and can be more approximated to the control polygon. It is visible that the properties of end-points on Q-Bézier curve and surface can be locally controlled by these shape parameters. Some examples are given by figures.  相似文献   

15.
The polynomials determined in the Bernstein (Bézier) basis enjoy considerable popularity in computer-aided design (CAD) applications. The common situation in these applications is, that polynomials given in the basis of degree n have to be represented in the basis of higher degree. The corresponding transformation algorithms are called algorithms for degree elevation of Bernstein polynomial representations. These algorithms are only then of practical importance if they do not require the ill-conditioned conversion between the Bernstein and the power basis. We discuss all the algorithms of this kind known in the literature and compare them to the new ones we establish. Some among the latter are better conditioned and not more expensive than the currently used ones. All these algorithms can be applied componentwise to vector-valued polynomial Bézier representations of curves or surfaces.  相似文献   

16.
Explicit formulae for the Bézier coefficients of the constrained dual Bernstein basis polynomials are derived in terms of the Hahn orthogonal polynomials. Using difference properties of the latter polynomials, efficient recursive scheme is obtained to compute these coefficients. Applications of this result to some problems of CAGD is discussed.  相似文献   

17.
We establish several fundamental identities,including recurrence relations,degree elevation formulas,partition of unity and Marsden identity,for quantum Bernstein bases and quantum Bézier curves.We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bézier curves.Our proofs use standard mathematical induction and other elementary techniques.  相似文献   

18.
Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining Bézier form of the L 2-solution of the problem of best polynomial approximation of Bézier curve or surface. In this connection, the Bézier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the Bézier coefficients of dual bivariate Bernstein polynomials is derived and an efficient algorithm for evaluation of these coefficients is proposed. Applications of this result to some approximation problems of Computer Aided Geometric Design (CAGD) are discussed.  相似文献   

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