中文摘要：

针对圆柱螺旋线不能用多项式或有理多项式精确表达的缺陷,提出一种二次非均匀有理B样条逼近算法。通过组合平面圆弧和轴向二次非均匀有理B样条直线构成初始非均匀B样条螺旋曲线;为了减小逼近误差,根据权因子影响非均匀有理B样条曲线形状的特性,提出了修正de Boor细分算法中新控制点轴向坐标的逼近细分算法。实例表明,该逼近算法不仅简单,而且能够稳定地逼近原曲线以满足给定的误差要求,并且为构造非均匀有理B样条螺旋曲面和螺旋体提供了数据。

英文摘要：

Since circular helix couldn＇t be represented by polynomials or rational polynomials in explicit form,an approximation algorithm with quadratic Non-Uniform Rational B-Spline（NURBS） was proposed.An initial approximation circular helix with NURBS curve was represented by combining planar NURBS circular arcs and axial quadratic NURBS line.Utilizing the weight modification to attain local shape,a subdivision scheme was proposed which modified the axis coordination of the new control points in the de Boor algorithm to reduce the approximation tolerance.Examples showed that this approximation algorithm was simple and steadly keeping on improvement the approximation values.It also provided data for NURBS helicoids construction.