Consider two lines of different orientation (e.g. the ‘edges’ q and r of the house in Fig. 14a). Provided the pair of lines pass through a common point (as lines q and r do in Fig. 14a) it is always possible to fit a plane through them (here, the gable wall of the house). Where two lines of different orientation do not share a common point (e.g. the lines p and s in Fig. 14a) no plane can be fitted through them. When two lines are plotted in stereographic projection, however, they are treated as if they pass through a common point: the centre of the projection sphere (see p. 12). This means that a plane can always be fitted through any pair of lines. In other words, the stereographic projection takes account only of orientations of structures and ignores their locations.

We now take an example of the need for this construction. The axial surface of a fold (Fig. 14b), being the surface which contains the hinge lines of successive surfaces in a sequence of folded surfaces, is often difficult to measure in the field because it may not correspond to a real, visible plane at the outcrop. Instead, what we usually see are axial surface traces: lines of outcrop of the axial surface (lines x and y in Fig. 14b). These lines are geometrically parallel to the axial surface and can therefore be used to construct it (Fig. 14c).