In this thesis, we presents a new algorithm that finds the longest partial match between two space curves. The algorithm iteratively extends an initial matching portion of two curves within some tolerance over the matching quality. Each iteration adjusts the matching transformation (rotation, scale, and translation) to handle noisy data more robustly and to enlarge the matched portion. To control the matching accuracy, a statistical threshold is introduced to stop the iterative extension. Experiment shows that the algorithm has a comparable accuracy to that of the well known ICP algorithm but its efficiency is improved by an order of magnitude. The algorithm has been demonstrated over synthetic and range data. Experiment shows that it adjusts well to noise distributions and performs effectively over curves of complex shapes.