A method and software is provided for machining a workpiece, including for determining a machining path for material-removing machining of a workpiece using a multi-axis machine tool, wherein control commands for controlling a number of N different machine axes of a machine tool can be generated from the machining path with computer support, according to which a tool can be moved continuously along the machining path, wherein the machining path comprises a first engagement path segment and a second engagement path segment along which the tool engages with the workpiece at least in sections, and wherein the machining path further comprises a connecting path segment along which the tool does not engage with the workpiece and which connects an end point of the first engagement path segment to a starting point of the second engagement path segment continuously and collision-free with the workpiece.

To smoothen a machining route more appropriately. A numerical controller of the present invention comprises: a machining program look-ahead unit that acquires a program for machining; a command route mathematization unit that expresses a machining route as a parametric line segment or curve on the basis of the program for the machining; and a smoothing processing unit that sets a range of smoothing for a target point of the smoothing along the parametric line segment or curve in an optional range from the target point, and performs the smoothing on the target point on the basis of the set range of the smoothing. The range of the smoothing set by the smoothing processing unit is a range in which a deviation between before the smoothing and after the smoothing on the target point is a set threshold or less.

To smoothen a machining route more appropriately. A numerical controller of the present invention comprises: a machining program look-ahead unit that acquires a program for machining; a command route mathematization unit that expresses a machining route as a parametric line segment or curve on the basis of the program for the machining; and a smoothing processing unit that sets a range of smoothing for a target point of the smoothing along the parametric line segment or curve in an optional range from the target point, and performs the smoothing on the target point on the basis of the set range of the smoothing. The range of the smoothing set by the smoothing processing unit is a range in which a deviation between before the smoothing and after the smoothing on the target point is a set threshold or less.