Analysis of complete fold shape based on quadratic Bézier curves

Abstract

Six segments of quadratic Bézier curve are joined together according to some geometrical rules to approximate fold shape. In a classification of folds based on this method, an ideal fold shape is determined by two parameters. The first one, u c , termed the axial lift-up ratio of the central part, generates the folds within a broad spectrum of forms ranging from box folds to chevron folds. The other one, γ, is the interlimb angle. In the quantitative description of complete folds with multiple layers, three new parameters, θ, T and E are used to describe the deflection angle of the axial plane, the thickness increment of hinge zone and the limb elongation, respectively. Based on the modeling method, the program “Bézier Fold Profiler” has been developed, with which most types of folds can be simulated by varying thirteen parameters. Two description methods, complete fold description and individual layer description, can be used for the quantitative analysis of folds. The description methods are carried out by the visual matching of the fold profile displayed on-screen from an imported digital image. The layer curves of the model are displayed on the fold image. This method has the advantage of speed and simplicity.