Curvature analysis of triangulated surfaces in structural geology

This paper addresses the problem of characterizing the shape of a geological surface on the basis of its principal curvatures. The surface is assumed to be modeled as a set of adjacent triangles defined by the location of their vertices and a method is proposed for estimating numerically the principal curvatures at the vertices of the triangles using a local C-2 interpolant. Also shown is how principal curvatures can be useful for studying the deformation of a geological surface (with application to 3D balanced unfolding), and analyzing the folding or faulting of the interface between two adjacent layers.