Consider a plane P and a line L which is not parallel to it (Fig. 19a). Imagine now a distant light source which is shining directly onto the plane, i.e. the plane is facing the light. The line L will cast a shadow onto the plane A. This shadow defines a line L′ in the plane P. We say that L′ is the orthogonal projection of L on plane P. Constructions involving orthogonal projection find a none of important applications in structural geology.

Calculating the projection of a line L onto a plane P

To calculate the direction of L′ use is made of the fact that lines L′, L and N (the normal to plane P) all lie in the same plane (Fig. 19b). This plane intersects plane P along the sought direction L′. Details of this construction are as follows.

1. 1 Plot the great circle for the plane P and its pole, N (Fig. 19c).

2. 2 Plot line L and then fit a plane (great circle) through N and L (Fig. 19c).

3. 3 L′ is given by the point of intersection of the great circle drawn at Stage 2 and that of plane P (Fig. 19c).

Application: slip direction of faults

The idea of projecting a line onto a plane is relevant to the problem of predicting the movement direction on a potential fault plane.