The common practice of mapping the axial trace of a fold by connecting points on a geological map where the strata within the fold undergo their most rapid rate of change of curvature is geometrically incorrect in most geological situations. A line drawn in this way will be oblique to or, in the case of an ideal similar-style fold, parallel, but not coincident, with the outcrop of the axial plane.
A method for mapping the true axial trace of a cylindrical fold can be derived by considering the geometry of a cylinder (either circular or elliptical in right section) drawn tangent to a folded surface within the hinge zone of the fold. The axis of such a cylinder will lie along the axial plane. Furthermore, the cylinder will have an elliptical outcrop pattern (outcrop ellipse) on a plane topographic surface, the center of which will lie on the axial trace. The axial trace of a fold can be constructed by drawing the locus of the centers of outcrop ellipses for several stratigraphic contacts within the fold. This technique is nearly universal in its application and is largely independent of fold style.