Determining Point Locations on the Stereonet
The intersection of a linear feature with the lower hemisphere (a point) is projected up to a plane cutting through the center of the sphere. The distance of a point from the center of the projection circle is a function of the plunge. This distance is given by:
d = r * tan ( d / 2 )
Equal angle projection
d = 2 * 0.707 * r * sin ( d / 2 )
Equal area projection
where r equals the radius of the circle and d is the complement of the plunge.
Once the distance from the center of the circle has been determined, the azimuth is used to determine the exact location of a point on the stereonet.
Plotting Points and Great Circles on the Stereonet
These values are plotted by utilizing an imaginary Cartesian coordinate system within the graphic vector files created by the program. The radius of the stereonet in vector coordinates is used to calculate the exact coordinate position for a particular linear feature. When the symbols are drawn, they are centered on these coordinates.
For great circle plots, individual points on the great circle are found by calculating the apparent dip at 1 degree intervals from 90 degrees minus the dip direction, to 90 degrees plus the dip direction. Small lines are drawn between these points to form the great circle.
Which Method to Use?
The choice of what projection to use is somewhat arbitrary. However, if a large number of points is being plotted, the equal angle projection will tend to show a weak, yet false, orientation towards the center of the circle. This can occur because a 10 by 10 degree area in the center of the net is smaller than the same angular area at the margin. This is especially important when using the Step Function density grid calculation routine.