A tool path generation method includes inputting a first function derived from a polynomial expression including a plurality of coefficients representing a first curved surface, generating a first tool path based on the first function, inputting the first tool path to an NC device of a machine tool and machining a workpiece by relative movement between a tool and a workpiece along the first tool path, measuring the shape of the workpiece at a plurality of measurement points on a surface of the machined workpiece, calculating, for each of the measurement points, a symmetrical position with respect to the first curved surface in a direction perpendicular to the first curved surface as a correction point, obtaining a second function representing a second curved surface based on a series of position data of the correction points, and generating a second tool path based on the second function.

A 3D production apparatus and method that receives a 3D production file, the 3D production file containing at least one positional command defined based on an implicit representation, the at least one positional command including at least one parameter of the implicit representation. At least one tool command is generated based on the parameters of the implicit representation. A position of a tool is controlled based on the generated at least one tool command, to produce at least a portion of a 3D part corresponding to the 3D production file.