To plot any cone/small circle with a horizontal axis

The relationship between the cone and the stereographic net is important because of its applications to rotations, borehole problems and geotechnics. The small circles printed on the equatorial net (stereographic or equal-area) represent cones with horizontal axes. The small circle with the required apical angle (2α) can be traced directly (Fig. 31a).

To plot any cone/small circle with a vertical axis

This construction is ideally carried out using a polar net, or since the small circle required is concentric with the primitive circle, with a pair of compasses (Fig. 31a).

To plot any inclined cone/small circle (Lambert/Schmidt or equal-area projection)

Small circles are not true circles with this type of projection. Because of this, the shape of the small circle has to be built up by joining points representing lines lying on the cone.

1. 1 Plot the cone axis, a (Fig. 31b).

2. 2 Using the equatorial equal-area net, plot a none of lines at the given angle (α) from the axis. This is done by rotating the net and, using the great circle on which a lies, measuring out the required angle, α.

3. 3 When a sufficient none of lines from the cone have been plotted, join these to form the small circle (Fig. 31b).

To plot any inclined cone/small circle (Wulff or stereographic projection)

A more direct method can be used here because of the fact that small circles project as true circles in stereographic projection.

1. Plot the cone axis, a (Fig. 31c).

2. […]