基于Gauss-Legendre求积的参数曲线实时插补

提出一种基于Gauss-Legendre求积和多项式插值的复杂参数曲线（包括高次多项式曲线、Bezier曲线、B样条曲线、NURBS曲线等）实时插补算法。该算法分插补预处理和实时插补两大部分，首先通过auss-Legendre求积公式计算曲线的弧长，然后将曲线按参数范围等分成若干区间，建立等分点参数值与弧长的对应表，再按多项式插值的方法计算各插补周期末的曲线参数值。文中还对曲线插补中进给速度平滑控制和减速点参数值的预测作了详细分析。对扩充数控系统的轨迹控制功能，简化零件程序，提高加工精度具有重要的意义。

Real-Time Curve Interpolator Based on Gauss Quadrature and Polynomial Interpolation

A new real time interpolation algorithm for complex parametric curve, including high order polynomial curve, Bezier curve, B spline curve, NURBS curve, etc, was developed, which is based on Gauss Legendre quadrature and polynomial interpolation. Firstly, the curve arc length is calculated by using piecewise Gauss Legendre quadrature. Then, the curve is divided into small sub intervals according to the parameter value, and a table of relationship between sub parameter value and sub arc length is created. Lastly, the parameter value of each interpolation cycle is calculated by using the polynomial interpolation. The strategy of smooth motion control and the calculation of declaration point's parameter were also analyzed. The proposed algorithm can extend the CNC's trajectory control function, simplify the part program, and improve machining precision.