The completion of fragmented contours is important for several processes of visual perception. However, the shape of the interpolated curves is not unique but rather varies with the completion type (amodal/modal) and contextual information. The solutions represent a balancing between the two constraints of good continuation and minimal path which is controlled by a parameter called GC-MP contrast. In this paper, we propose an integration of such a parameter into the tensor voting approach which has been proposed as a general-purpose model for perceptual grouping mechanisms. The results of this extension are demonstrated on typical configurations of rectilinear and curvilinear fragments. 1