B样条基函数在基本计算系统的实现

摘要

提出一个基于CORDIC的计算B样条基函数的移位加算法。该算法可在仅具备移位、加、逻辑运算的基本计算系统中实现，从而可在各类嵌入式系统等小微型应用系统中应用，帮助实现复杂曲线的绘制和其他数值计算。算法的收敛性得到证明，给出了误差估计，讨论了算法的有效性。给出实例计算验证以上结论。算法可以用硬件实现，也可用汇编语言编程实现。用硬件实现时不需用乘法器，实现成本较低。核心迭代次数一般不超过40次。%In this paper we present a shift-add algorithm,which is based on coordinate rotation digital computer algorithm,for computingB-spline basis functions.This algorithm can be implemented in basic computing system which only has the operations of shift,addition andlogic,so that it can be applied in small and miniature application systems of various embedding systems to help the realisation of renderingcomplicated curves and other numerical calculations.The convergence of the algorithm is proved.Besides giving the error estimation,we alsodiscuss the effectiveness of the algorithm.To verify the above conclusion,we present actual calculation instances.The algorithm can beimplemented with hardware as well as with the assembly language programming.The implementation with hardware does not need themultiplier,so the cost is lower.Usually the times of the core iteration will not exceed 40.