Abstract: A CNC machine is programmed to redefine the corner tolerance as a function of the corner angle based on a recognition that corners having angles not equal to 90° have effective corner tolerances that are equal to the corner tolerance specified by the operator divided by the sine of the corner angle. An increase in machining speed is achieved, because, at corner angles not equal to 90°, the redefined corner tolerance is larger than the operator-specified corner tolerance and the CNC machine is permitted to machine the corner at an earlier time than conventional CNC machines. The CNC machine is also programmed to provide the operator with an interactive control of the parameters that control the speed and accuracy of machining. With this feature, the operator is able to observe the effects of changing the control parameters on the speed and accuracy of machining, and to customize the control parameters to a particular type of tool or application based on the observations.