Analyses of fold profiles using cubic Bézier curve

Abstract

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 Bezier 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 Bezier 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. Bezier 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.