The hinge lines of non-cylindrical folds

摘要

Hinge lines are loci of high curvature points on folded surfaces. They are significant geometrical features of geological folds, and the arrangement of hinge lines constructed for the surface serves to characterize important aspects of the fold pattern. Since the current definition of hinge line is only appropriate for cylindrical folds, we propose a new definition for use with folds of general shape. Like the concept of ridge lines used in differential geometry, the new definition uses the lines of curvature (principal curvature trajectories) as a reference frame for comparing curvatures across the surface. A hinge line passes through points of extreme principal curvature magnitude observed along the corresponding principal curvature trajectory. Two types of hinge lines are defined and methods for constructing hinge lines are suggested.