Resection (orientation)

The planar resection is a trigonometric method of land surveying (see Geodesy ). The coordinates of a new point N by three points A, B and C are determined with known coordinates, when the horizontal angle ANB = φ and ψ = BNC ( seen by N of ) are known.

This angle can be calculated from the three measurements in the direction of new point N to the points A, B, C. Cutting through the two peripheral angle circles (see peripheral angle theorem ) with the angles φ ( on the chord AB ) and ψ (above the chord BC ) gives us a solution.

Pothenot or Snell?

The task of the planar backward -section is also called Pothenotsche task to Laurent Pothenot; However, before this already Willibrord van Roijen Snell ( Snell ) published a solution. Therefore, some authors speak of the task Snell's Pothenotschen. Numerical solution methods for this task have been proposed among others by Cassini, Abraham Gotthelf Kästner, Collins, Carl Friedrich Gauss and Ansermet.

Dangerous circle

Failure of the reverse step if the points A, B, C, N are on a circle. Then the two peripheral angle circles are to one another and found no distinct intersections. This case is called a dangerous circle. In the figure to the right of the point A lies almost on the arc of CBN. Measurement error smear the exact location of the circles. Instead of a unique intersection at N we obtain an intersection N'- N '.

Experienced surveyors islets also avoid the circle close to the dangerous effect ( concrete already on about 10 percent of the point distances ) location error of a few centimeters to meters.