Dangerous place
In mathematics and applied geometry, a dangerous location is a critical geometrical situation of an intersection process or a location determination in which two or more geometrical locations intersect at a very flat angle. If this situation is not noticed - or if it is defused by redundant measurements - the position of new points can become extremely imprecise.
For the majority of the term, mathematicians use dangerous places , in geodesy and localization, however, dangerous places (analogous to star words ).
Grinding cuts result in dangerous places with obtuse cutting angles greater than 170 °, or less than ten to five degrees for the secondary angle. For this reason, points measured in engineering geodesy are overdetermined one or two times .
Peripheral circles are particularly susceptible to dangerous locations as a result of grinding cuts - for example, if the new point and the three fixed points are located near a circle during the geodetic backward cut ( dangerous circle ). Instead of an unambiguous point of intersection, an intersection area is obtained, which is marked in the figure with N'-N ' .
Certain satellite configurations allow the measurement error in satellite navigation to grow by several orders of magnitude. Their occurrence is recorded by determining the so-called Dilution of Precision .