Abstract: This invention relates to controlled apparatus having a tool including a plurality of directions of movements with the directions interrelated, such as an arc welding unit having an electrode for contouring of similar work parts along a seam contour. The apparatus includes a logic system and memory such as a computer and a tracer to follow an original contoured curve or shape in space and generate a position-related signal. The computer includes a self-programming program in memory in which control program particulars of a contour are generated and introduced by an initial movement of the tracer over an original contour under a closed-loop position control program in a trace-record mode. During the trace-record mode the computer reads the necessary inputs and creates a set of data at points along the contour. The data sets are fitted together by a spline function (third-degree polynominal) to produce a close approximation of the weld seam in its multi-dimensions.