计算复杂度自适应的NURBS曲线插补算法

Algorithm of Adaptive NURBS Interpolation Points Calculation

NURBS曲线插补过程中要求高效、准确地计算插补点,但大多数现有的NURBS曲线插补算法是以计算准确性为主要指标来设计的,其插补计算多是通过B样条间接实现,并未充分考虑如何最大限度地利用插补计算中计算结构的特点以及不同插补算法的性能特点提高计算效率.通过对B样条插补算法计算结构的分析,以基函数值共享为基础,给出了NURBS曲线直接插补算法以及相应的计算效率表达式.在与de Boor-Cox算法相比较的基础上,针对不同插补精度的要求,在满足精度要求的前提下,给出了基于插补计算的复杂度进行插补算法自适应选择的新算法,该算法明显提高了插补计算的效率,缩短了插补周期中插补计算所占用的时间.

During interpolation process, NURBS curve requires efficient, accurate calculation of interpolation points. But most of the existing NURBS curve interpolation algorithm puts the accuracy of calculation as the main design index, and achieved by B spline in- directly, which did not fully consider how to improve the computation efficiency by effectively using the characteristics of interpola- tion process and features of different interpolation. Through the analysis of B spline interpolation, to base value sharing basis, the NURBS curve direct interpolation algorithm and the corresponding calculation formula of efficiency are given. In comparison with the de Boor-Cox algorithm, according to the different precision requirements, a new adaptive algorithm is achieved based on the calcula- tion complexity of different interpolation algorithm. The algorithm improves the efficiency of interpolation calculation, shortens the interpolation period occupied by the interpolation calculation time.