【摘要】 针对计算机辅助几何设计(CAGD)中B样条曲线延拓问题提出了一种新的算法,可以使延拓后的曲线和给定的参考曲线形状尽量相似。首先通过统一待延拓曲线和参考曲线的节点矢量来确定延拓后曲线的节点矢量;然后,利用B样条端点松弛算法确定延拓后曲线中和原曲线对应的控制顶点;最后,通过优化方法确定新增加的控制顶点,优化的目标是经仿射变换后的参考曲线和延拓后的曲线对应控制顶点之间距离的平方和最小。提出了一种两步法求解该优化问题,先通过优化方法确定仿射变换,然后利用该仿射变换计算新增加的控制顶点。为了使延拓后的曲线光顺性较好,通过引入光顺项对该算法进行了进一步的改进。实验结果表明,该算法得到的延拓曲线和参考曲线形状具有一定的相似性,算法具有很好的实用性和灵活性。更多还原

【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.更多还原