Examples of cones

In structural geology applications the concept of a cone is encountered in connection with:

1. 1 The analysis of cone-shaped geological structures, e.g. conical folds, cone sheet intrusions, conical fractures (Fig. 30a).

2. 2 Imaginary cones defined by rotation of a line about a fixed axis (Fig. 30b).

3. 3 A set of variably oriented lines but where each individual line maintains a constant angle (α) with some fixed direction (Fig. 30c), e.g. lineations which have been folded into spiral geometries.

Terms used to describe the shape and orientation of a cone are defined in Figure 30b.

Stereographic projection of cones

On pp. 12 and 14 it was explained how lines and planes are projected stereographically. Cones are projected in a similar fashion; as before, we start by projecting onto a sphere and then projecting onto a plane.

1. 1 The cone is treated as double-ended as shown in Figure 30c. This double cone is shifted (without rotation) until the apex is positioned at the sphere's centre (Fig. 30d).

2. 2 The bundle of lines which make up the cone is projected outwards until the lines touch the sphere's inner surface. The points of contact with the sphere describe circles. These circles have a smaller radius than the sphere itself and are called small circles (see p. 12). Thus the spherical projection of a cone is a small circle.

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