This paper presents a new method to generate tool paths for machining freeform surfaces represented either as parametric surfaces or as triangular meshes. This method allows for the optimal tradeoff between the preferred feed direction field and the constant scallop height, and yields a minimized overall path length. The optimality is achieved by formulating tool path planning as a Poisson problem that minimizes a simple, quadratic energy. This Poisson formulation considers all tool paths at once, without resorting to any heuristic sampling or initial tool path choosing as in existing methods, and is thus a globally optimal solution. Finding the optimal tool paths amounts to solving a well-conditioned sparse linear system, which is computationally convenient and efficient. Tool paths are represented with an implicit scheme that can completely avoid the challenging topological issues of path singularities and self-intersections seen in previous methods. The presented method has been validated with a series of examples and comparisons.

中文翻译：

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具有首选进给方向的自由曲面的长度优化刀具路径规划

本文提出了一种生成刀具路径的新方法，用于加工以参数化曲面或三角形网格表示的自由曲面。这种方法允许在首选进料方向场和恒定扇贝高度之间进行最佳权衡，并产生最小的总路径长度。最优性是通过将刀具路径规划制定为泊松问题来实现的，该问题使简单的二次能量最小化。该泊松公式一次考虑所有刀具路径，而不像现有方法那样求助于任何启发式采样或初始刀具路径选择，因此是全局最优解。寻找最佳刀具路径相当于求解一个条件良好的稀疏线性系统，这在计算上既方便又高效。工具路径用隐式方案表示，可以完全避免在以前的方法中看到的路径奇点和自相交的具有挑战性的拓扑问题。所提出的方法已通过一系列示例和比较得到验证。