Extension of B-Spline Curve Based on Similarity to Reference Curve

In some cases, a B-spline curve needs to be extended such that it is similar to a given reference curve in shape for repair of curves and surfaces. To address this problem, the concept of quasi-curvature is generalized for spatial curves, and a new concept, quasi-torsion, is put forward. Both quasi-curvature and quasi-torsion are invariant under rotation, translation and proportional zooming. Upon these a measurement of similarity between two curves is proposed, and an algorithm for extending B-spline curve based on the curve similarity is given. Firstly, the knots of extended B-spline curve are determined on the basis of those of the original curve and the reference curve. Secondly, the control vertices corresponding to original curve are determined by applying B-spline unclamping algorithm. Finally, remaining control vertices are determined by maximizing the similarity measurement between the extended curve and the reference curve. Experiments were done to extend the curves generated from the simulated data and the measured data on the aircraft blade with our proposed algorithm, results show that the extended curves with our method have good fairness and are similar to the reference curves in some content even if target points are not given.