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Analyses of fold profiles using cubic Bézier curve
International Journal of Earth Sciences ( IF 2.3 ) Pub Date : 2020-11-01 , DOI: 10.1007/s00531-020-01945-2
Manash Pratim Gogoi , Soumyajit Mukherjee , Tapos K. Goswami

Matching curves to represent diverse fold morphologies is an active research field in structural geology that can have far-reaching implication in resource studies and in engineering geology. Further, some of the recent literatures show that 2D and 3D restoration and best fit of folds have been researched actively in petroleum geosciences. The significant advantage of the method presented here using cubic Bézier curve is that the profile of a fold could be represented in terms of four “controlling points”, which can be re-synthesized in 2D graphical plot using the spreadsheet programme such as Microsoft Excel, Apache Open Office Spreadsheet etc. by simply developing a tabular spreadsheet based on the equation of cubic Bézier curve. The method is simple and has been tested successfully to synthesize a few fold profiles by changing the values of coordinates of the controlling points and on photographs of two natural examples of folds. Bézier curves of different order have been used along with multi-paradigm programming/numerical computing software such as MATLAB, mathematical symbolic computation program: Wolfram Mathematica, and vector graphics designing. However, it is not easy for all learners or researchers to rapidly use or develop such programmes. On the other hand, spreadsheets programmes, both commercial and open-source, well known to the majority of the population having a general knowledge in computers.



中文翻译:

使用三次贝塞尔曲线的折叠轮廓分析

匹配曲线代表不同的褶皱形态是结构地质学的活跃研究领域,在资源研究和工程地质学中具有深远的意义。此外,最近的一些文献表明,在石油地球科学中已经积极地研究了2D和3D恢复以及褶皱的最佳拟合。此处使用三次贝塞尔曲线表示的方法的显着优点是,可以用四个来表示折线的轮廓通过简单地根据三次贝塞尔曲线方程式开发表格电子表格,可以使用电子表格程序(例如Microsoft Excel,Apache Open Office Spreadsheet等)在2D图形图中重新合成“控制点”。该方法很简单,并且已经通过改变控制点的坐标值以及在两个自然的折叠示例的照片上成功地测试了一些折叠轮廓。已经使用了不同阶数的Bézier曲线以及诸如MATLAB之类的多范式编程/数值计算软件,数学符号计算程序:Wolfram Mathematica和矢量图形设计。但是,并非所有的学习者或研究人员都很难快速使用或开发此类程序。另一方面,电子表格计划,包括商业计划和开源计划,

更新日期:2020-11-02
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