Least-squares Analysis of Fabric Data: A Note on Conical, Cylindroidal and Near–cylindroidal Folds

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Abstract
A cylinder and a plane may be considered as special limiting cases for a right circular cone as the semi-apical angle approaches 0° and 90° respectively (Loudon 1964, Kelley 1966). If these forms are viewed as surfaces generated by an array of lines in space, the rotation axis for the array (the axis of the "cone") can be determined from the orientations of the surface-generating lines by a single computational procedure, using least-squares criterion. The mean angle between the rotation axis and the surface-generating lines will be the semi-apical angle of the cone. However, if this method for determination of the semi-apical angle of the cone, and therefore the best-fitting small circle, is extended to fabric diagrams, in which an array of lines may only statistically describe a great circle or small circle on a stereographic projection, ambiguities arise in certain cases and the semi-apical angle obtained may not be the true semi-apical angle. The difficulty arises because the poles to foliation surfaces are arbitrarily assigned "senses".
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