arXiv:2606.21209cs.CGcs.CV2026-06
提出一种精确插值点列且参数化为弧长的样条计算方法。
Arc-Length Parameterized Interpolating Splines
- 基于迭代法构造弧长参数化样条，确保通过所有输入点
- 支持任意维度D≥2，平面曲线验证效果稳定
- 适合需要精确路径参数化的应用，如机器人轨迹规划
我们提出一种迭代算法，用于计算通过一组点的弧长参数化样条。与现有方法不同，该方法生成的样条不仅精确插值原始点，且参数化严格对应曲线的弧长。该方法适用于任意维度D≥2，文中以平面曲线为例展示数值结果。
原文摘要 · Abstract (English)
We present an iterative algorithm to compute an arc-length parameterized spline interpolating a set of points. This differs from other methods where the computed spline either does not interpolate the original points or the parameterization is not the arc-length of the returned curves. Our method is applicable in any dimension $D \ge 2$, and we illustrate it with numerical results for plane curves.
样条插值弧长参数化数值计算
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