Fast real-time NURBS path interpolation for CNC machine tools

In this paper, a novel fast real-time non-uniform rational B-spline (NURBS) path interpolation method is presented. This method efficiently integrates the data processing of a NURBS path in a CNC controller, from pre-processing to real-time interpolation. In the calculation of the total length of the NURBS path, the numerical adaptive quadrature method adapts to the integrand, i.e. the first derivative of the length function, automatically, dividing the parameter interval into subintervals with fine or coarse spacing according to the varying condition of the integrand. This new method takes full advantage of the subdivision scheme. The key point is to generate inverse length functions (ILF) for each resulting subinterval. In the real-time NURBS path interpolation, the new setting path parameter can be calculated directly using the ILF without the need for any time-consuming computation of NURBS derivatives and iteration. The proposed method is extremely fast, accurate and suitable for real-time implementation, and simulations and practical tests proved its effectiveness.