WSB型曲线的细分算法

Subdivision algorithm for WSB curves

WSB型曲线以不同的2个参数表示一族有用的曲线,Bézier曲线、Wang-Ball曲线、Said-Ball曲线均为WSB型曲线的特例。文章利用对偶泛函,给出了WSB型曲线的一种显式细分算法,该算法可归结为曲线的控制顶点向量与细分矩阵的乘积,与传统算法相比,该算法避免了繁琐的矩阵求逆及基转换的运算。

With two different parameters,WSB curves represent a number of useful curves with the uniform expression.Bézier curves,Wang-Ball curves and Said-Ball curves are a special case of WSB-type curves.By using dual function,an explicit subdivision algorithm about WSB curves is given.This algorithm can be implemented by multiplying the vector of control points and the subdivision matrix.Comparing with the traditional subdivision algorithms,this algorithm avoids complicated computation about the matrix inversion and the conversion of basis function.