We introduce in this article a unified algorithm which allows the selection of collocation stencils, based on the visibility criterion, for convex, concave, and singular problems solved using a collocation method. The algorithm can be applied to any 2D or 3D problem. We show the importance of using a threshold angle, in conjunction with the visibility criterion, to assess of the inclusion of a node in the support of a collocation center. We also show how the algorithm can be used to assess the presence of a node in a defined domain. Such algorithm is particularly useful in the context of model refinement.

中文翻译：

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用于凸、凹和奇异问题的搭配模板选择的统一算法

我们在本文中介绍了一种统一算法，该算法允许基于可见性标准选择搭配模板，用于使用搭配方法解决的凸、凹和奇异问题。该算法可以应用于任何 2D 或 3D 问题。我们展示了使用阈值角度和可见性标准来评估节点是否包含在搭配中心的支持中的重要性。我们还展示了如何使用该算法来评估定义域中节点的存在。这种算法在模型细化的上下文中特别有用。