Two-dimensional analysis of shape-fabric using projections of digitized lines in a plane

Abstract

A method of two-dimensional shape-fabric analysis is presented which is based on the projection of lines or ellipses on the x-axis. If a set of lines or ellipses displays a preferred orientation, the average length of projection of the lines or ellipses on the x-axis changes with direction in the x-y plane. The proposed method involves use of Fortran programs which evaluate the average length of projection of lines (e.g., outlines of ooides, pressure solution seams) while the fabric is rotated by small increments in a counterclockwise sense about the origin of the x - y plane. Data acquisition is by digitizing the lines on an enlarged photograph. The sets of x-y coordinates that are thus obtained serve as input for the programs. The basic equations of the method are explained and application to a sedimentary fabric is demonstrated. The proposed method is both fast and sensitive. It is especially useful if the particle outlines are closely spherical or if the fabric is only weakly developed. Yet, the method is not restricted to weak fabrics only. Also, if the fabric is due to deformation this method yields the axes of the two-dimensional strain ellipse.