Abstract: Interpolation calculation is the key technology of complex curved surface direct interpolation technology, in order to improve the computational efficiency and accuracy in the process of interpolation and ensure the numerical control system of real time capability, in view of the tool path of B-spline curve model, from the direct interpolation algorithm principle and mathematical model, the B spline curve is presented based on the three B-spline curve the rapid evaluation of derivative algorithm, using B spline node into the technology and the differential recursive derive value for three B-spline interpolation, the interpolation process does not involve any evaluation of B-spline basis function derivation calculation. It is applied in numerical control system to interpolate any B-spline curve trajectory for 3 times, which solves the problem that traditional interpolators cannot effectively interpolate this type of trajectory. The simulation and comparison of the existing methods have great advantages in computing efficiency and real-time, and the machining verification is carried out on the open CNC system platform developed independently.