A rapid Bézier curve method for shape analysis and point representation of asymmetric folds

Abstract

Point representation of fold shapes is useful, in particular, for classification of a large number of folds into different geometric populations. The methods for shape analysis and point representation of asymmetric folds are a few and tedious, although several methods exist for the analysis of the individual fold limbs, or symmetric folds. This article gives a rapid method that uses the Bézier curve tool, available in any common computer graphics software, for the analysis of a complete asymmetric fold and its point representation in the two-dimensional frame. The new method is based on the reduction of variables in the parametric equations of a cubic Bézier curve. It makes the length of one Bézier handle zero, pins the end point of the other Bézier handle at the origin of the X-Y frame and drags its control point along the Y-axis to fit the Bézier curve on the given asymmetric fold. A Cartesian plot between normalised length of the Bézier handle and the lift, i.e., difference between the heights of the two inflection points, gives the unique point that represents the given asymmetric fold shape. We test the validity of the new method on several computer simulated asymmetric folds and demonstrate its usefulness with the help of a natural example.