A formal filtering process is used to simplify fields consisting of smooth layers by concentrating them into singular sheets, filaments and points. The approach is based on weighted coordinate smoothing, where the coordinates of nearby material points possessing non-zero values of the field are smoothed, using a nonlinear diffusion equation, thus moving them together. Examples for two and three-dimensional vorticity fields and the simplification of an interface identified by an index function are shown.

中文翻译：

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通过加权坐标平滑将平滑层压缩为单张

正式的滤波过程用于通过将平滑层集中为奇异的片，细丝和点来简化由平滑层组成的场。该方法基于加权坐标平滑处理，其中使用非线性扩散方程式对具有非零值场值的附近材料点的坐标进行平滑处理，从而将它们一起移动。显示了二维和三维涡度场的示例，以及通过索引函数标识的界面的简化。