A method determines a path of a tool machining a pocket shape in a workpiece. The pocket shape is defined by a closed curve in an x-y plane. The method determines positions and velocities of a motion of an oscillator having an energy defined by a function that is positive within a boundary of the pocket shape and equals zero on the boundary of the pocket shape. The method determines coordinates of the path of the tool based on corresponding pairs of position and velocity values of the motion, wherein a position value of each pair represents an x coordinate of the path of the tool in the x-y plane, and a velocity value of each pair represents a y coordinate of the path of the tool in the x-y plane.