Different types of spherical projections can be used for visualizing and evaluating the tree dimensional orientation of planes and lines on a two dimensional surface (screen, paper). Redbex supports the visualization of different types of lower hemisphere of spherical projections. These visualizations are used in Axis section drawings and Reports.

A spherical projection shows where lines or planes intersect the surface of a (hemi)sphere, provided that the lines/planes also pass through the center of the (hemi)sphere. The projection of these intersections can be done in different ways, the two ways commonly used in structural geology (and also the two ways supported by Redbex) are Equal-Angle Projection (or stereographic projection) and Equal-Area projection (or Lambert azimuthal projection).

It is common for spherical projections to show a net (i.e. grid) that allows for better interpretation of the drawn intersections. This grid shows the projection of planes through the center of the sphere with an azimuth of 0° and varying dip, as well as the projection of planes with a dip of 90° and orthogonal to the North south axis in varying distances from the center of the sphere.

A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle. Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle.

Equal-Angle Projection (=Stereographic projection)

This type of projection preserves angular relation ships. I.e. the angle between the tangent of two intersecting great circle traces at their point of intersection is the same as the angel the two real planes the great circle traces represent. The Equal-Angle Projection does not conserve area. I.e. projections of identical circles described on different parts of a projection sphere appear as circles of different sizes.

The grid used for manual drawing of an equal angle projection on paper is called a Wulff net.

Equal-Area projection (=Lambert azimuthal projection)

This type of projection conserves area, i.e. identical circles on the projection sphere project as ellipses with various axisal ratios but having the same area. The Equal-Area projection however does not conserve angular relation ships.

A grid constructed on an equal area projection is called a Schmidt net.

Table 1: Summary of characteristics of different spherical projections

Visualization types

Independently of the chosen type of spherical projection Redbex support 3 different ways of displaying a plane on the projection:

•Great circle: Shows the projection of the intersection of the plane with the lower hemisphere

•Pole Point: Shows the intersection of a line orthogonal to the plane through the center of the sphere, with the lower hemisphere.

•Contour lines: Shows contour lines that visualize the distribution of pole points on the projection.

Note that while Redbex can visualize the distribution of pole points as contour lines on a Equal angle projection that kind of visualization should not be used for statistical analysis.