αβ-Bézier曲线的类De Casteljau算法

A De Casteljau-type algorithm for theαβ-Bézier curves

带形状参数的样条曲线比传统样条曲线有更丰富的曲线表达能力,应用广泛.本文研究了一类带形状参数αβ-Bézier曲线的类De Casteljau算法。首先对带形状参数的αβ-Bernstein基函数进行了扩展,讨论了基函数的相关性质,并给出了任意次数αβ-Bézier曲线的定义。在此基础上基于基函数的递推关系给出了αβ-Bézier曲线的快速求值算法。该算法类似于经典的De Casteljau算法,通过对曲线控制顶点的一系列线性运算来实现。操作简单,比基于参数表达式计算曲线上点值的方法更为高效。计算实例表明了算法的可行性与有效性。

The splines with shape parameters have more expressive ability than the traditional splines,and theyare widely used in various fields.In this paper,a De Casteljau-type algorithm for a class ofαβ-Bézier curves with shape parameters was studied.Firstly,theαβ-Bernstein basis function with shape parameters was extended,the related properties of the basis function were discussed,and the definition of arbitrary degreeαβ-Bézier curve was given.Then based on the recurrence relationship of basis function,the geometric drawing algorithm ofαβ-Bézier curve waspresented.Similar to the classical De Casteljau algorithm,the algorithmwas implemented by a series of linear operationsof the control vertices of the curve.Compare to calculating the point value directly based on parameter expression,the algorithmwassimpler and more efficient.The calculation examplesshowed the feasibility and effectiveness of the algorithm.