复杂空间参数曲线加工的插补算法

Interpolation Algorithm for Machining Complex Parametric Curves in Space

以一阶泰勒展开式插补算法和平面参数曲线插补算法为基础,提出引入误差补偿值的复杂空间参数曲线插补算法(IAIECCS).该算法是在粗确定插补点参数后,引入误差补偿值,通过求解矩阵方程提高插补点的计算精度.根据IAIECCS算法与一、二阶泰勒展开式算法在对插补点参数值计算时产生误差的原因,给出3种算法的插补点参数值误差表达式.Nurbs曲线仿真实例表明该算法所计算的插补点参数值误差小,实时性好.

The interpolation algorithm of introduced error compensation for complex parametric curves in space （IAIECCS） was proposed on the basis of the first order Taylor expression interpolation algorithm and the plane parametric curves interpolation algorithm. The interpolation precision was improved by introducing error compensation and solving the matrix equation after interpolated points＇ parameter had been computed roughly, The different interpolated points＇ parameter errors of the IAIECCS, the first order Taylor expansion and the second order Taylor expansion algorithms were provided according to the error different algorithms. The simulation of Nurbs curve proves that the parametric value error computed by IAIECCS algorithm is small and the real-time performance is good.