关键词: B 样条曲线, 曲线延拓, 相似性, 仿射变换, 最优化

Abstract: For the problem of B-spline curve extension in computer aided geometric design (CAGD), a new algorithm is proposed such that the extended curve is similar to a given reference curve in shape. Firstly, the knot vector of the extended curve is determined by unifying the knot vector of the original curve and that of the reference curve. Secondly, the control vertices corresponding to the original curve are determined with B-spline unclamping algorithm. Finally, the new control vertices are determined with optimization method. The aim is to minimize the sum of squared distances between the control vertices of affine transformed reference curve and those of the extended curve. A two-stage algorithm is presented to solve this optimization problem. At the first stage, the affine transformation is determined with optimization method. And at the second stage, the new control vertices are calculated by applying the affine transformation. As a further improvement to the algorithm, a smoothing term is introduced at the second stage to make the extended curve smoother. Experimental results show that the extended curve by the proposed algorithm has similar shape to the reference curve to some extent, and the algorithm is practical and flexible.

Key words: B-spline curve, curve extension, similarity, affine transformation, optimization