## 1 Introduction
The authors modeled the corner blending behavior of NC systems using FIR filtering applied to a sequence of feedrate pulses, while providing analytical calculation of the minimal cornering feedrate that satisfies both the tolerance and the machining constraints. They demonstrated that the feedrate profile obtained in this way can predict the total cycle to high precision. In [22], the authors proposed a method of spline interpolation based on FIR filtering that does not require look-ahead and is capable of constraining the interpolation error. This result was expanded upon in [23], where the authors presented a method of real-time nonisometric dual-spline interpolation using FIR filtering. The interpolator influences the precision and surface quality through the introduction of transition curves as well as by discrete sampling of the toolpath. While deviations caused by the introduction of transition curves (approximation error) can be controlled by a suitable choice of transition curve parameters [1], controlling deviations caused by discrete sampling of the interpolated toolpath is more complex and requires the introduction of  
Figure 1: The chain of steps from the workpiece CAD model to the finished product. Each step has the potential to add additional inaccuracies that influence the quality of the final product. additional constraints in interpolation algorithms. This type of error, commonly called the chord error, is defined as the Hausdorff distance of the interpolated toolpath from the required toolpath and is typically approximated via higher-order methods [24], due to the computational complexity of the exact evaluation. Several methods have been proposed to constrain the chord error during the interpolation process; see, e.g., [25; 26; 27]. Although the interpolation methods mentioned above are described explicitly in the literature, in practice, the CNC machine is equipped with an interpolator module provided by a commercial manufacturer (Siemens, Heidenhain, Fanuc, and others). The exact design of commercial interpolators is not known to the public, and the operator generally needs to rely on the recommendations provided in the technical manual as well as their personal experience. However, it is difficult to accurately quantify the effect of interpolator parameter settings on the precision and quality of the final workpiece. Thus, the topic of interpolator parameter optimization has recently attracted the attention of several researchers. In [28], the limits of feedrate, acceleration, and jerk served as inputs to adaptive neuro-fuzzy inference systems with the aim of predicting the milling accuracy and surface quality (including the effects of the machine tool control loop and machined dynamics) based on results obtained on a rhombus testing toolpath. In [29], a CNC parameter tuning methodology was presented that focuses on three machining modes: high precision, high speed, and high quality. For each of these modes, the authors studied the effect of jerk and acceleration limits, corner velocity, the smoothing time constant, and radial acceleration on dynamic errors and machining time based on results obtained on several testing toolpaths, including the effects of the servo loop. However, the authors did not specify the interpolator manufacturer. In [30], an optimization algorithm for tuning CNC interpolation parameters based on a back-propagation neural network was presented. The algorithm aims to optimize contour errors, machining time, and corner vibrations simultaneously. The test data were obtained on a square testing toolpath and verified on a toolpath consisting of linear and circular segments. In [31], a genetic algorithm was applied to interpolator setting optimization with the aim to minimize the trajectory error without increasing the cycles. The authors used a simulation approach that combined the CNC interpolator output with a feed drive model to estimate the contour error. They did not, however, use a commercial interpolator as part of their model.