FRACTAL ANALYSIS OF TOPOGRAPHIC DATA BY THE PATCHWORK METHOD
FRACTAL ANALYSIS OF TOPOGRAPHIC DATA BY THE PATCHWORK METHOD
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DOI：
10.1016/0043-1648(93)90453-s
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发表时间：
1993-04-01
期刊：
影响因子：
5
通讯作者：
CHESTERS, S
中科院分区：
文献类型：
--
作者：
BROWN, CA;CHARLES, PD;CHESTERS, S
提出了一种基于分形的工程表面地形数据分析方法。该方法，我们称之为拼接方法，类似于著名的分形分析的海岸线方法，它使用线段来估计作为段长度的函数的锯齿状线的长度。拼块法使用三角形拼块来估计作为拼块面积的函数的表面积。斑块面积既可以解释为观察尺度，也可以解释为形态依赖现象的相互作用尺度。使用拼接方法，可以识别尺度上的交叉或阈值，该交叉或阈值将相对较大的尺度（其中表面是光滑的并且最好由欧几里得几何描述）与那些较小的尺度（其中表面是粗糙的并且最好由分形几何描述）分开。人们还获得了一个参数，该参数表征了低于阈值的地形的复杂性或复杂性。这些参数，结合其规模的相互作用的概念，表征地形依赖的现象，似乎有很好的潜力，阐明表面相互作用的机制。这些参数还可以作为支持曲面设计过程及其制造的工具。
A new, fractal-based method is described for analyzing topographic data sets from engineering surfaces. The method, which we call the patchwork method, is analogous to the well-known coastline method of fractal analysis, which uses line segments to estimate the length of a jagged line as a function of the segment length. The patchwork method uses triangular patches to estimate surface area as a function of patch area. The patch area can be interpreted either as the scale of observation, or as the scale of interaction for morphologically dependent phenomena. Using the patchwork method one can identify the crossover, or threshold, in scale which separates the relatively large scales, where the surface is smooth and best described by Euclidean geometry, from those smaller scales where the surface is rough and best described by fractal geometry. One also obtains a parameter that characterizes the complexity, or intricacy, of the topography, below the threshold. These parameters, combined with the concept of characterizing topographically dependent phenomena by their scales of interaction, appear to have good potential for elucidating mechanisms of surface interactions. These parameters can also serve as a tool for supporting design processes for surfaces and for their manufacture.