A data processing apparatus generates data denoting a predetermined point on a virtual surface shape formed denoting the basis of digitized data on a tool path for an inverted shape work piece, to thereby facilitates examination of the size of the inverted shape work piece. That is, digitized data obtained by scanning a model shape is input and edited to prepare digitized data representing a tool path for machining a work piece. The digitized data representing the tool path is converted to prepare a numerical control working program. Work piece examination data are also prepared based on denoting an arbitrary measurement point of a scanning probe, data denoting the measuring direction at the measuring point and the digitized data representing the tool path for machining the work piece.