基于二项式系数设计矩阵的Bézier曲线扩展  

Extension of Bézier Curves Based on the Design of Matrix Using Binomial Coefficient

作　　者：郭大勇[1] 成佳颐 

机构地区：[1]清华大学机械工程系,北京100084

出　　处：《图学学报》2014年第4期511-517,共7页Journal of Graphics

摘　　要：根据二项式的展开系数,设计出带形状参数的正系数矩阵,并对Bernstein基函数进行具有明显几何意义的构造,推导出同阶带参的A-Bernstein基函数,该基函数具有Bernstein基函数类似的性质。在此基础上推导出对应的A-Bézier曲线,分析了其不但具有Bézier曲线类似的性质,而且在原始控制点不变的情况下,可以通过修改形状参数来对曲线进行调整。此外,还进一步说明了可以通过对正系数矩阵的调整,实现对曲线的调整。通过举例,展现出该方法灵活有效。Based on the binomial coefficient, a matrix with shape parameters is designed. And then it is used for constructing a new type of basis function called A-Bernstein basis function. It has the same degree with the Bernstein basis function and shares several same properties. According to the A-Bernstein basis function, a corresponding curve named A-Bezier curve is derived. It not only shares the same properties with a Bezier curve, but also can be adjusted in shape by modifying the shape parameter without the changing of original control points. Furthermore, the modification of the matrix is illustrated. It can be used for modifying the A-Bezier curve. Examples show this method is intuitive and effective.

关 键 词：曲线设计 A-Bézier曲线 正系数矩阵 形状参数 A-Bernstein基函数 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]