Automatic creation of B-rep models of engineering objects from freehand sketches would benefit designers. One step aims to take a line drawing (with hidden lines removed), and from it deduce an initial three-dimensional (3D) geometric realization of the visible part of the object, including junction and line labels, and depth coordinates. Most methods for producing this frontal geometry use line labeling, which takes little or no account of geometry. Thus, the line labels produced can be unreliable. Our alternative approach inflates a drawing to produce provisional depth coordinates, and from these makes deductions about line labels. Assuming many edges in the drawing are parallel to one of three main orthogonal directions, we first attempt to identify groups of parallel lines aligned with the three major axes of the object. From these, we create and solve a linear system of equations relating vertex coordinates, in the coordinate system of the major axes. We then inflate the drawing in a coordinate system based on the plane of the drawing and depth perpendicular to it. Finally, we use this geometry to identify which lines in the drawing correspond to convex, concave, or occluding edges. We discuss alternative realizations of some of the concepts, how to cope with nonisometric-projection drawings, and how to combine this approach with other labeling techniques to gain the benefits of each. We test our approach using sample drawings chosen to be representative of engineering objects. These highlight difficulties often overlooked in previous papers on line labeling. Our new approach has significant benefits.