关键词: Hermite曲线, 计算机辅助几何设计, 光顺性, 优化

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