Abstract: The mathematical model satisfying the boundary conditions of the cable path curve segment is established by the quintic Hermite curve. By minimizing the approximate strain energy of Hermite curves, the resulting path curves own better fairness which eliminate the unwanted loops and sharp points as far as possible. Meanwhile the analytical formulas to compute the optimal parameters of path curves are deduced. To provide the theoretical foundation for the maximal cable radius evaluation, the minimal curvature radii of path curves are analyzed and computed further.

Key words: Hermite curve, computer aided geometric design, fairness, optimization

摘要： 利用五次Hermite曲线建立了满足电缆路径曲线段边界约束的数学模型，通过最小化Hermite曲线的近似应变能，保证了生成的路径曲线具有较佳光顺性，尽可能避免了多余的环圈和尖点等奇异现象，推导了计算路径曲线段最优参数的解析公式。进一步分析计算了路径曲线段的最小曲率半径，为电缆的最大直径阀值估算提供理论依据。

关键词: Hermite曲线, 计算机辅助几何设计, 光顺性, 优化