Editing Azimuth (section)

==In cartography==
[[File:Brunton.JPG|thumb|right|A standard Brunton Geo [[compass]], commonly used by geologists and surveyors to measure azimuth]]
The '''cartographical azimuth''' or '''grid azimuth''' (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane ([[Spatial reference system|cartographical coordinates]]):

:<math>\alpha = \frac{180}{\pi} \operatorname{atan2}(X_2 - X_1, Y_2 - Y_1)</math>

Remark that the reference axes are swapped relative to the (counterclockwise) mathematical [[polar coordinate system]] and that the azimuth is clockwise relative to the north.
This is the reason why the X and Y axis in the above formula are swapped.
If the azimuth becomes negative, one can always add 360°.

The formula in [[radian]]s would be slightly easier:
:<math>\alpha = \operatorname{atan2}(X_2 - X_1, Y_2 - Y_1)</math>

Note the swapped <math>(x, y)</math> in contrast to the normal <math>(y, x)</math> [[atan2]] input order.

The opposite problem occurs when the coordinates (''X''<sub>1</sub>, ''Y''<sub>1</sub>) of one point, the distance ''D'', and the azimuth ''α'' to another point (''X''<sub>2</sub>, ''Y''<sub>2</sub>) are known, one can calculate its coordinates:
:<math>\begin{align}
  X_2 &= X_1 + D \sin\alpha \\
  Y_2 &= Y_1 + D \cos\alpha
\end{align}</math>
This is typically used in [[triangulation]] and azimuth identification (AzID), especially in [[radar]] applications.

===Map projections===
There is a wide variety of [[Map projection#Azimuthal .28projections onto a plane.29|azimuthal map projections]]. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system.
{|align=left
|{{comparison_azimuthal_projections.svg|820px|}}
|}
{{clear}}