Appendix B:
Hemispherical
projection
Hemispherical projection methods
These methods enable three-dimensional orientation data to be displayed
in two dimensions and manipulated graphically.
Fundumentd geometry
Directions are vectors with unit length. We assume that these vectors
emanate from the origin of a Cartesian co-ordinate system. It is conveni-
ent to use east/north/down for rock mechanics.
0
Directions are measured in terms of
the angles
a = trend
/3 = plunge
a is measured with a compass,
p is measured with a clinometer.
Note that OB = sin acosp
oc = cos acosp
I AD = sin p.
Because every vector has unit length, the tips lie on the surface of a
sphere. We are usually only interested in downward-directed vectors,
lying on the lower hemisphere.
Projection onto two dimensions
One way to form a two-dimensional plot associated with vectors on the
lower hemisphere is to project the tips of the vectors onto the horizontal