The topology of isosurfaces changes at isovalues of critical points, making such points an important feature when building contour trees or Morse-Smale complexes. Hexahedral elements with linear interpolants can contain additional off-vertex critical points in element bodies and on element faces. Moreover, a point on the face of a hexahedron which is critical in the element-local context is not necessarily critical in the global context. Weber et al. (2002) introduce a method to determine whether critical points on faces are also critical in the global context, based on the gradient of the asymptotic decider (G. M. Nielson and B. Hamann) (1991) in each element that shares the face. However, as defined, the method of Weber et al. contains an error, and can lead to incorrect results. In this work we correct the error.

中文翻译：

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非结构化六面体网格轮廓树构建的离顶点临界点的识别与分类


等值面的拓扑在关键点的等值处发生变化，使得这些点成为构建等高线树或 Morse-Smale 复合体时的重要特征。具有线性插值的六面体单元可以在单元体和单元面上包含额外的离顶点临界点。此外，六面体表面上在元素局部环境中至关重要的点在全局环境中不一定是关键的。韦伯等人。 (2002) 引入了一种方法，基于共享面部的每个元素中的渐近决策器 (GM Nielson 和 B. Hamann) (1991) 的梯度，确定面部上的关键点在全局上下文中是否也是关键的。然而，根据定义，Weber 等人的方法。包含错误，并可能导致不正确的结果。在这项工作中，我们纠正了错误。