A real-time scheme of cubic parametric curve interpolations for CNC systems

In this paper, the popular finite forward differencing algorithm for fast evaluation of points on a cubic parametric curve is modified for its application to CNC systems so that the inherent accumulative error in the calculation of one piece of curve will not propagate to the whole composite curve. Using specified tolerances, a computationally non-intensive method of analysis for the computation of step size has been developed. Tolerance, velocity, acceleration and jerk analyses are conducted based on computer simulation results. The interpolation scheme method developed in this paper has been analyzed and proven to be accurate, adaptive to the curvature of a curve, reduces jerk, and can be easily implemented in CNC systems. Finally, the paper explains why the algorithm developed here is natural for cubic parametric curve interpolations.