两相邻CE-Bézier曲线的近似合并

Approximate Merging of a Pair of CE-Bézier Curves

为了进一步丰富和发展CE-Bézier曲线的相关理论,针对该曲线的近似合并问题,提出了一种将两相邻CE-Bézier曲线合并成1条CE-Bézier曲线的方法.该方法通过将曲线拟合方法与广义逆矩阵理论相结合,直接得到合并后CE-Bézier曲线控制顶点的显示表达式,同时给出了具体的合并误差.实验结果表明,新方法不仅可获得较好的合并效果,而且具有易于实现、误差计算简单的特点,可广泛应用于计算机辅助设计中对曲线的近似合并.

Cubic extension Bézier （CE-Bézier） curve with multiple shape parameters is one of the most important extensions of the cubic Bézier curve. It not only inherits the outstanding properties of the cubic Bézier curve, but with a good performance on adjusting their local shapes by changing the shape control parameters. In order to develop the basic theory of CE-Bézier curve, a new method to deal with approximating two adjacent CE-Bézier curves by one CE-Bézier curve is presented for the approximate merging of existing curve design. By combining the fitting method of curves and the theory of the general inverse matrix, the explicit formula of control points of the merged CE-Bézier curve can be given directly. Eventually, some merging examples are discussed and the errors of approximate merging are given as well. Experiments illustrate that the proposed method not only has a good merging effect, but is easy to implement and simple to error estimation.