A novel method for calculating interpolation points of NURBS curves based on chord length-parameter ratio.

Interpolating non-uniform rational B-spline (NURBS) curves often leads to undesirable feedrate fluctuations due to the non-analytic relationship between the spline parameter and arc length. In this paper, we introduce a feedback method that effectively reduces feedrate fluctuations while maintaining simplicity in the interpolation process. Our approach begins by defining the chord length-parameter ratio (CPR), which we then predict for the current interpolation point using Newton's divided difference interpolation polynomial and historical CPR data. Subsequently, we calculate the compensation length based on tangent and chord directions, and we correct the initial parameter using the second-order Runge–Kutta method. Importantly, our method involves only two calculations of the first derivative of the NURBS curve, making it computationally efficient compared to most approximation methods. To validate our proposed method, we conduct numerical simulations and compare its performance against several approximation methods and a recent feedback method. The results demonstrate that our approach excels in terms of both efficiency and accuracy, making it a promising solution for improving NURBS curve interpolation. [ABSTRACT FROM AUTHOR]