Explicit G2-constrained Merging of a Pair of Bézier Curves by Control Point Optimization
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摘要: 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。Abstract: 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.
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Key words:
- Bé /
- zier curve /
- merging /
- l2 distance /
- G2 continuity /
- optimization
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