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A new approach to online generation of velocity fields for parametric curves is presented for implementation in passive velocity field controllers (PVFC) that enable human-in-the-loop contour following tasks. In particular, a feedback stabilized closest point tracking algorithm is utilized for real-time determination of the contour error and online construction of the velocity field. The algorithm augments the system dynamics with a new state, and implements a uniformly asymptotically stable controller to update this new state to continual track the closest point to the robot end-effector. Thanks to its feedback-stabilized core, the algorithm is immune to initialization errors, and robust against drift and numerical noise. Furthermore, requiring simple evaluations of the curve and its unit tangents, the approach is computationally efficient. Applicability and effectiveness of the approach to implement passive contour following tasks have been demonstrated through simulations and experiments with a two degrees-of-freedom haptic interface.