【摘要】 通过把曲线拟合方法与广义逆矩阵理论相结合,给出了把两相邻n次和m次Bézier曲线合并成一条k次Bézier曲线的方法。该方法可直接得到合并Bézier曲线控制顶点的显示表示式,且不论相邻Bézier曲线是否为同次,均可直接合并。在合并过程中,分别考虑了不具有端点插值条件和具有端点高阶插值条件的情形。最后给出数值实例,并把本文方法所得结果与采用已有方法所得结果进行了比较,显示该方法的有效性。更多还原

【Abstract】 By combining the fitting method of curves with the theory of the general inverse matrix, an approach is proposed which deals with approximating two Bézier curves with adjacent degrees by one Bézier curve. The explicit formula of control points of the merged Bézier curve can be given directly, and two adjacent Bézier curves can be merged into a single Bézier curve directly whether the degrees of the two adjacent Bézier curves are equal or not. In the merging process, two cases are considered respectively. One is the case without constraints of endpoints interpolations. The other is the case with constraints of endpoints interpolations. Finally, the numerical examples are presented,and the results obtained by the presented approach are compared with those got by the current method,which shows the effectiveness of the presented method.更多还原