Description and classification of folds in single surfaces

Abstract

I propose a new three-parameter description of fold style in folded surfaces based on the ratio of the amplitude to the half-wavelength (the aspect ratio P), the maximum angle of relative rotation of opposite limbs of the fold (the folding angle φ), and a measure of the relative curvature at the fold closure (the bluntness b). For symmetric folds, the first two parameters define a trapezoid that circumscribes the fold and provides the primary criterion for the classification of fold style. Within a given trapezoid, fold style variations are defined by the bluntness. Perfect folds in profile are defined to have a single hinge with perfectly straight limbs tangent to hinge zones that are perfect circular arcs. An analytic description of the variation in perfect fold geometry defines the limits for all natural single-hinged folds. The proposed system includes folds with folding angles both less than and greater than isoclinal folds, it applies to both single-hinged and multiple-hinged folds, and it also can be extended to apply to asymmetric folds. Previously proposed two-parameter classification systems can only describe folds that are restricted to a specific surface through the three-parameter fold style space proposed here.