Abstract: A three dimensional surface shaping tool comprising a machining portion, wherein a graphical projection of the outermost locus of the motion of the machining portion, onto a plane parallel to the longitudinal axis of the tool, has a shape comprising a curve expressed by at least one equation or a combination of at least one straight line and at least one of the curve, and a three dimensional surface shaping method using the above mentioned tool, which comprises the steps of determining the desired shape of the surface; choosing a shape of the tool based on the desired shape of the surface; and contacting the tool with a workpiece under tool motion control such that the contact with the tool occurs at points along the machining portion of the tool where a curvature thereof is most appropriate for the desired surface shape.

Abstract: A data processing device for machining a three dimensional surface includes a tool locus data generator providing tool shape and dimension indicative information of a machining tool and machining route information, calculating information selected from a curvature, a normal line and a tangential line at a machining point of the three dimensional surface, and calculating the optimum shape of a machining tool and/or controlling condition of the tool based on the calculated information; a device for checking the tool locus data of a machining tool based on a predetermined pattern; and a processor for converting the checked tool locus data into data which is to be inputted into a machine which conducts three dimensional surface machining.