For free-form surfaces or curves, it is not the best choice to use traditional G01 or G02 interpolation to generate the reference motion trajectory. Direct interpolation method is a better choice. Direct interpolation is more useful in a free-curve/surface dedicated Computer Numerical Control (CNC) system. A free-curve/surface dedicated CNC system just needs curve/surface information as input, not as a conventional CNC system uses G code as its input. NURBS (Non-Uniform Rational B-spline) is a

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... owerful expression method for free-form curves and surfaces, and so a direct interpolation algorithm based on NURBS curves is studied. In order to realize high speed, high accuracy and stable interpolation, an adaptive prediction-correction with constraint chord error method is presented to define the NURBS curve parameter. S velocity planning is used to make tool move more smoothly. As NURBS curves are piece-wise curves, NURBS direct interpolation must be computed with the parameter within its corresponding sections, and a section transition method is proposed to guarantee computing validity. Also, three reference trajectory generation methods, i.e. position interpolation, velocity interpolation and acceleration interpolation are presented, and their advantages and disadvantages are discussed. The calculation and simulation show that the position interpolation method is more stable and the error is the smallest. The error of velocity interpolation is about 4 times that of position interpolation.