一种基于矩阵LU分解的分段B样条插值法

采用分段三次b样条曲线来光滑地连接采样点，满足了连续性要求；由于分段b样条插值控制点形成三对角线性方程组，通过矩阵的LU分解来求解该控制点方程组，实验结果表明，该方法快速地生成了通过所有采样点的光滑连续自由曲线，完全可以达到实时任务的要求。

A Segmental B - Spline Interpolation Algorithm Based on Matrix LU Decomposition

This paper applies the segmental three order b-Spline to smoothly connect all sampling points,which satisfy the continuity requirements and cause the segmental b-spline controlling points being triple diagonal linear equations.This paper uses the matrix LU decomposition to resolve the b-spline controlling points linear equation.The test result proves that this proposed method can rapidly create the smooth and continuous free curve which crosses all sampling points,and meets the real time task requirement.