Rapid analysis of fold shape using Bézier curves

Abstract

We approximate and classify the forms of profile sections of folded surfaces by comparison with cubic Bézier curves. The method analyses a digital image of the fold profile, by interactive visual comparison, with the curves generated by the Bézier drawing tool available commonly in graphics software products. Simplified equations of cubic Bézier curves form the basis of the classification in terms of two parameters. The first parameter, L, is related to the distribution of curvature on a single limb of a fold between the hinge point and the inflection point. It places the fold within a shape spectrum that ranges from straight-limbed chevron folds (L=0) in which curvature is concentrated in the hinge region through to rounded folds with a uniform curvature distribution (L=1). The second parameter, R, is related to the ratio of amplitude to wavelength. A graph of L against R serves to group samples of folds into 'shape groups'. This classification can be used as a tool to assist the determination of relative competence of folded layers and of the folding mechanism. The new method, which has the advantages of speed and simplicity, is applied to examples of natural and experimentally developed folds to demonstrate its versatility for analysing a wide range of fold geometries.