1. A machine tool, comprising: a tool path curve generation apparatus adapted to generate a tool path curve from a tool path designated by command points in a command point sequence, the apparatus comprising a processor configured to: define a tolerance region which is based on a polygonal line path connecting the command points in the command point sequence, which includes the polygonal line path, and in which the tool path curve is to be included, determine whether the tool path curve is included in the tolerance region on the basis of a geometric shape of a surface of the tolerance region, and output the tool path curve which has been determined to be included in the tolerance region, wherein the tolerance region includes a plurality of element regions, each element region among the plurality of element regions is a rotating body having a rotation axis that is a segment of the polygonal line path connecting a pair of adjacent command points in the command point sequence, the tool path curve includes a plurality of curve sections each corresponding to an element region among the plurality of element regions, and the processor is configured to determine that a curve section among the plurality of curve sections is included in the corresponding element region when the element region includes a spheroid having ends of the curve section as focal points, and a length of the curve section as a sum of distances from points on the spheroid to the focal points, wherein the processor is configured to determine that the element region includes the spheroid by projecting the spheroid and the element region onto a plane that is orthogonal to the rotation axis of the element region, and the machine tool is configured to machine a workpiece in accordance with the outputted tool path curve.