Process for producing an article from a filamentary construction material in an additive fused deposition modeling process, comprising the following steps: - supplying the construction material; - delivering the construction material into a printhead at a feed rate for the construction material; - melting the construction material by means of a heating device in the printhead; - discharging the melted construction material to a discharge location in accordance with a selected cross section of the article to be produced, at a discharge rate through an orifice of the printhead, with movement of the printhead relative to the discharge location at a predetermined speed of movement along a predetermined path, wherein the path has at each location a curvature that can assume a positive value, zero or a negative value; wherein a control unit controls at least the delivery of the construction material, the heating device in the printhead and the movement of the printhead; wherein in dependence on the curvature of the path at the location at which the printhead is situated during its movement relative to the discharge location: the control unit controls the relative movement of the printhead in such a way that the speed at which the printhead undergoes a relative movement, correlates negatively with the absolute value of the curvature, the control unit controls the feed rate for the construction material in such a way that the feed rate correlates negatively with the absolute value of the curvature, and characterized in that the control unit controls the heating device in the printhead in such a way that the temperature of the heating device correlates positively with the feed rate for the construction material and/or positively with the speed at which the printhead undergoes a relative movement. - supplying the construction material; - delivering the construction material into a printhead at a feed rate for the construction material; - melting the construction material by means of a heating device in the printhead; - discharging the melted construction material to a discharge location in accordance with a selected cross section of the article to be produced, at a discharge rate through an orifice of the printhead, with movement of the printhead relative to the discharge location at a predetermined speed of movement along a predetermined path, wherein the path has at each location a curvature that can assume a positive value, zero or a negative value; wherein a control unit controls at least the delivery of the construction material, the heating device in the printhead and the movement of the printhead; at a discharge rate through an orifice of the printhead, with movement of the printhead relative to the discharge location through an orifice of the printhead, with movement of the printhead relative to the discharge location at a predetermined speed of movement along a predetermined path, wherein the path has at each location a curvature that can assume a positive value, zero or a negative value; wherein a control unit controls at least the delivery of the construction material, the heating device in the printhead and the movement of the printhead; along a predetermined path, wherein the path has at each location a curvature that can assume a positive value, zero or a negative value; the control unit controls the relative movement of the printhead in such a way that the speed at which the printhead undergoes a relative movement, correlates negatively with the absolute value of the curvature, the speed at which the printhead undergoes a relative movement, correlates negatively with the absolute value of the curvature, the control unit controls the feed rate for the construction material in such a way that the feed rate correlates negatively with the absolute value of the curvature, and characterized in that the feed rate correlates negatively with the absolute value of the curvature, and characterized in that the control unit controls the heating device in the printhead in such a way that the temperature of the heating device correlates positively with the feed rate for the construction material and/or positively with the speed at which the printhead undergoes a relative movement.