Fig. 12.

Considerations for using map projections. a Typical problem when representing a three-dimensional orientation without using a projection. Consider four points A, B, C, and D with indicated spherical coordinates. Points A and B clearly represent a different orientation that is ${90}^{\circ }$ apart. Points C and D, however, appear to also represent a different orientation, whereas in reality, they are equal (they are both at the “top” of the hemisphere). b The problem in a can be solved using a map projection. By representing the orientations using a projection, points C and D coincide. The projection used is the Lambert azimuthal equal-area projection. c A Lambert azimuthal equal-area projection is created by using a plane tangential to the centre point on the unit hemisphere (point B in this case). All points will be projected on this plane. From all points on the hemisphere, a circular arc is drawn to the projected plane that (1) ends perpendicular to the projected plane and (2) has point B as its centre