Abstract: In the existing methods of periodic B-spline interpolation, coefficients of B-spline basis functions are determined by iterative algorithms. To overcome the weakness of the existing methods, new parallel algorithm for computing coefficients of B-spline basis functions were established. First, this paper established orthogonal B-spline basis and derived parallel algorithm for coefficients of orthogonal B-spline basis functions; and then derived parallel algorithm for coefficients of B-spline basis functions by using the relation between coefficients of orthogonal B-spline basis functions and coefficients of B-spline basis functions; at last this paper derived explicit formulas for both coefficients of B-spline basis functions and value of interpolated point with the 2nd, the 3rd and the 4th order periodic interpolating B-spline functions. The presented method retains the simplicity of B-spline basis functions while realizing fast parallel algorithm for coefficients of B-spline basis functions.

Key words: spline, spline interpolation, periodic spline, orthogonal spline, parallel algorithms

摘要： 在现有周期B样条插值方法中，需要用迭代算法确定B样条基函数系数。针对现有方法的不足，建立B样条基函数系数的并行算法。首先构造周期区域的正交B样条基，得出正交B样条基函数系数的并行算法；进一步利用正交B样条基函数系数与B样条基函数系数的关系，得出B样条基函数系数的并行算法；最后推导二阶、三阶、四阶周期插值B样条基函数系数及插值点函数值的显式算式。实验证明了该方法在实现B样条基函数系数快速并行算法的同时保持了B样条基函数简单的函数关系。

关键词: 样条函数, 样条插值, 周期样条, 正交样条, 并行算法