1. A method for operating a computer numerical control (CNC) machining tool with the aid of a digital computer, comprising the steps of: providing a computer with parameters for a CNC machining tool comprising a plurality of orientations of the CNC machining tool while longitudinally traversing a rotating cutting edge; providing the computer with a model of a part defining surfaces of the part; providing the computer with a maximal set of translations for the CNC machining tool that avoids collisions between the rotating cutting edge and the surfaces of the part, each translation comprising one of the orientations of the CNC machining tool and a volume removable by the translation; computing in the computer an intersection of the translations within the maximal set and taking in the computer a union of the removal volumes for the intersecting translations; determining in the computer a largest space of the maximal set of the translations of the CNC machining tool outside of the surfaces of the part, which is machinable by the CNC machining tool; taking an intersection of the maximal set of the translations of the CNC machining tool in the computer as a maximal machinable volume for the CNC machining tool; evaluating the part in the computer based upon whether a union of the maximal machinable volumes substantially equals a negative volume of the part; programming the CNC machining tool with process plans downloaded by the computer and comprising machining operations by the CNC machining tool as conditioned upon the union substantially equaling the negative volume of the part; and operating the CNC machining tool per the machining operations in the downloaded process plans by machining off the removal volumes through longitudinal traversals of the rotating cutting edge over the surfaces of the part.