一对Bézier曲线基于控制顶点优化的显式G2约束拼接

针对一对Bézier曲线的G2约束拼接，提出了通过最小化l2距离的一种简单且显式方法。将l2距离表示成具有两个参数的二次函数，最优的拼接曲线以优化控制顶点使得l2距离最小的方式得到。通过证明l2距离是凸的，说明了唯一解的存在性。由于该方法是非迭代的并且表示为已知的控制顶点，所以是显式和高效的。实例表明新方法的有效性。

Explicit G2-constrained Merging of a Pair of Bézier Curves by Control Point Optimization

This paper presents a simple and explicit method for G²-constrained merging of a pair of Bézier curves by mini-mizing the l₂ distance defined in terms of control points. After expressing the l₂ distance as a quadratic function of two param-eters, the optimally merged curve can be explicitly obtained, which is achieved by control point optimization such that the l₂ distance is minimized. The existence of the unique solution is shown by proving that the l₂ distance is convex. The pro-posed method is explicit and effcient since it is non-iterative and expressed by known control points. Numerical examples demonstrate the effectiveness of the new method.