Abstract: Given a point data set that contains several fairly unevenly distributed random points, this paper presents a new paradigm of curve interpolation to fit a curve to the data with end tangent vector constraints. The method uses a base curve, which is subjected to constrained shape manipulations to achieve interpolation, while maintaining end point and end tangent constraints. The algorithm is not sensitive to the distribution or to the randomness of the data, as long as the points represent fairly simple shapes, as in reverse engineering of properly segmented points, or in shape design using simple segments. The method is iterative in nature and allows various forms of adjustments to achieve good results.