The fuzzy curve-tracing (FCT) algorithm can be used to extract a smooth curve from unordered noisy data. In this paper, we analyze the convergence property of the algorithm based on the diagonal dominance requirement of the matrix used in the clustering procedure and prove that the algorithm is guaranteed to converge if the weighting coefficient for the smoothness constraint is chosen properly. Based on the convergence condition, we develop several methods for fast and reliable implementation of the algorithm. We show that the algorithm can be initialized with a user-defined curve in many cases, that a multiresolution clustering based approach and an image down-sampling scheme can be used to improve the algorithm stability and speed and that two types of traps can be removed to correct the mistakes in curve tracing. We demonstrate several advantages of our algorithm over the commonly used snake models for boundary detection and several methods for principle curve extraction.