## 1 Introduction  
Several key factors influence the precision and surface quality of the final workpiece: the interpolator, the feed drive system, machine dynamics, and the machining process. The path from the CAD model of the part to the final workpiece can be represented by a chain of steps, as shown in Figure 1. Each step represents a potential source of error and, thus, affects the precision and surface quality of the machined part. The part model in the CAD SW has limited accuracy, especially for free-form surfaces. The CAM software then generates toolpaths based on the CAD model within a certain tolerance band around the nominal shape of the part in the form of CL data. By translating the CL data with a nonuniform point distribution using a postprocessor, a part program (NC program) with identical properties is generated. The conversion of the part program toolpaths from the geometric domain to the time domain is handled by the interpolator of the CNC machine control system. Its task is to achieve the smoothest, most accurate and time-saving tool speed profile along the NC program toolpath, typically represented by a sequence of linear segments and circular arcs. The main constraints of the interpolator are the user-defined tolerance band around the linear sections of the part program and the kinematic parameters defined by the machine manufacturer. The output of the interpolator is the position setpoint and the velocity profile setpoint, the quality of which is strongly influenced by several functionalities (look ahead, filtering, etc.) of the interpolator and their settings. This is the topic this paper focuses on, i.e., the effect of interpolator settings on the geometric quality, resp. surface quality,and accuracy of the output. The realization of tool movements according to the output of the interpolator is the task of the feed drive controller. The accuracy of the movements is determined by the dynamic properties of the controller, which are closely related to the dynamic properties of the feed drive components and the mechanical structure. Lastly, the accuracy and surface quality of the workpiece are influenced by the cutting process that generates the force load, its interaction with the feed drive controller, and the dynamic properties of the workpiece. An interpolator is a component of the CNC system responsible for the transformation of the geometric NC toplath into a vector of tool positions uniformly sampled in time. This vector needs to satisfy multiple conditions, such as acceleration and jerk limits and contour tolerance, all while attempting to keep the actual feedrate as close to the programmed feedrate as possible. It should also include a strategy for continuous transitions at the points of first- and second-order geometric discontinuities. CNC interpolation continues to be a popular research topic. Among the main subtopics of interpolation is the formulation of transition curves used to increase the order of geometric continuity of the original toolpath and the design of algorithms that plan the feedrate along a toolpath. Transition curves typically include circular arcs, B-spline curves [1; 2; 3], or clothoids [4; 5; 6]. The feedrate functions typically have the form of the trapezoid profile with piecewise constant jerk [7; 8], or functions with continuous jerk [9; 10; 11; 12; 13; 14]. The feedrate profile is typically formulated by continuation methods with bidirectional scanning [15; 16], iterative methods [17], or global methods [18; 19; 20]. In recent years, the approach of finite impulse response (FIR) filtering to design feedrate profiles has gathered increasing attention. This approach does not require geometric smoothing of the toolpath by the introduction of transition curves and uses the composition of first-order filters instead. This makes controlling the contour error substantially more complex. In [21], however, this problem was solved by the authors for the case of three-axis machining.