Schmidt's network
The Schmidt net or the layer sphere is an aid for the representation of geological or crystallographic directional data, devised by Walter Schmidt (1925). This is a geometrical technical term. Since these data only represent directions in most cases and therefore do not have a defined amount (e.g. length), they can be understood as unit vectors. If one lets all these unit vectors begin at a point, then their tips lie on a spherical surface, the layer sphere. Line-shaped (i.e. linear) elements are drawn in in the form of the point of contact (intersection point) of the vector with the spherical surface. Flat elements are represented by the point of contact between the surface normal and the layer sphere. The position of such a point, like the position of a geographic point on the earth's surface, is indicated by longitude and latitude. A planar element can also be represented by a great circle that is normal (i.e. perpendicular) to the intersection point of the surface normal.
application
The great advantage of the layered sphere representation lies in the comparability of different amounts of data and the possibility of carrying out various geometric operations with this data. The geometry of geological bodies can also be determined very clearly with this aid. In crystallography, the layered sphere is an important tool to clearly demonstrate the symmetry relationships of crystallographic surfaces and axes. When presenting geological facts on the layer sphere, however, one must be aware that the geographical position of each element shown is lost and only its direction remains. So you can z. B. Do not distinguish between saddles and hollows (= geological folds) on the layer sphere.
Since most of the structure data are bipolar axes, i. d. Usually the representation on a hemisphere. In geology, the lower hemisphere is usually used, while crystallographic elements are usually represented in the upper hemisphere. The layer ball is also ideal for displaying large amounts of data for which directional statistical parameters can also be determined on the layer ball. In order to show the layer sphere clearly and unambiguously in a drawing plane, different layer sphere projections are used.