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The Schmidt net is a manual drafting method for the
The Schmidt net is not an appropriate grid for representing the Earth's northern or southern hemisphere (because the lines would not correspond to meridians or parallels in such a projection). However, it can be used as a scalar measuring device for projecting latitude-longitude points onto a blank circle of the same size, to produce a Lambert equal-area projection with the azimuth at the north or south pole. The intersection of the parallels with the outer circle can be used as a ''de facto'' protractor for plotting a point's longitude as the angle in the polar projection. The Schmidt net's horizontal axis can then be used as a scalar measuring device to convert the point's latitude (relative to the pole) into a radial distance from the centre of the circle. Alternatively, the Schmidt net could be replaced entirely with a correctly projected polar grid, and grid squares from a map re-drawn into this disc.
The Schmidt net is a manual drafting method for the Lambert azimuthal equal-area projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Swiss mathematician Johan ...
using graph paper. It results in one lateral hemisphere of the Earth with the grid of parallels and meridian
Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to
Science
* Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon
* ...
s. The method is common in geoscience
Earth science or geoscience includes all fields of natural science related to the planet Earth. This is a branch of science dealing with the physical, chemical, and biological complex constitutions and synergistic linkages of Earth's four spher ...
.
Construction
In the figure, the area-preserving property of the projection can be seen by comparing a grid sector near the center of the net with one at the far right of the net. The two sectors have the same area on the sphere and the same area on the disk. The angle-distorting property can be seen by examining the grid lines; most of them do not intersect at right angles on the Schmidt net. A single Schmidt net can only represent one hemisphere of the earth; typically a pair of Schmidt nets is used to represent both sides of the globe. It is relatively simple to re-plot a gridded map of the world onto a Schmidt net if the azimuth is chosen to be the junction of the equator with any particular meridian from the world-map's grid. Each grid square surrounding this chosen longitude is simply re-plotted into the corresponding distorted grid-square in the Schmidt net. Points of latitude-longitude can be plotted relative to the azimuth's longitude, interpolating between grid lines in the Schmidt net. For greater accuracy, it is helpful to have a net with finer spacing than 10°; spacings of 2° are common.
The Schmidt net is not an appropriate grid for representing the Earth's northern or southern hemisphere (because the lines would not correspond to meridians or parallels in such a projection). However, it can be used as a scalar measuring device for projecting latitude-longitude points onto a blank circle of the same size, to produce a Lambert equal-area projection with the azimuth at the north or south pole. The intersection of the parallels with the outer circle can be used as a ''de facto'' protractor for plotting a point's longitude as the angle in the polar projection. The Schmidt net's horizontal axis can then be used as a scalar measuring device to convert the point's latitude (relative to the pole) into a radial distance from the centre of the circle. Alternatively, the Schmidt net could be replaced entirely with a correctly projected polar grid, and grid squares from a map re-drawn into this disc.
Use
Researchers instructural geology
Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover informati ...
use the Lambert azimuthal projection to plot lineation and foliation
In mathematics ( differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition ...
in rocks, slickenside
In geology, a slickenside is a smoothly polished surface caused by frictional movement between rocks along a fault. This surface is typically striated with linear features, called slickenlines, in the direction of movement. Geometry of slickensid ...
s in faults, and other linear and planar features. In this context the projection is called the equal-area hemispherical projection. The Schmidt net is often used to sketch out the Lambert azimuthal projection for these purposes.Borradaile (2003). Conversely, the Wulff net
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (the ''projection plane'') perpendicular to the diameter thr ...
("equal-angle projection") is used to plot crystallographic
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...
axes and faces.
Sources
* * *References
{{reflist Technical drawing Map projections