This paper presents aspects related to the generation and tracking of closed trajectories over an arbitrary surface of unknown geometry. Such a capacity is required in some of the most important industrial robotic tasks, like the cutting or welding of commercial plates. Previous work has shown how a calibration-free, vision-based method can be combined with an optimal geodesic-mapping approach, in order to generate an optimal trajectory that traces a previously defined path, stored as a CAD model, over an arbitrary, curved surface. The application of this technique in the case of nondevelopable surfaces did not achieve closure when a closedtrajectory was attempted. This paper presents a methodology for successfully achieving closure of a given closed-path, when this is traced over a non-developable surface. The proposed technique was tested using an industrial robot and a visionbased system that included structured lighting for imageanalysis simplification. The results of these experiments are reported herein.