Direction Cosines and Vector Geometry

Abstract

The orientations of structural elements are most readily obtained analytically by 3-D vector geometry. A line is represented by a vector of unit length and a plane by its pole vector or its dip vector. The direction cosines of a line describe the orientation of the unit vector parallel to the line. Structural information such as bearing and plunge is converted into direction cosine form, the necessary operations performed, and then the values converted back to standard geological format. This chapter gives the basic relationships and outlines some of the ways vector geometry can be applied to structural problems involving lines and planes.