Mapping Toolbox

Measuring Azimuth and Elevation

Azimuth is the angle a line makes with a meridian, taken clockwise from north. When the azimuth is calculated from one point to another using the Mapping Toolbox, the result will depend upon whether a great circle or a rhumb line azimuth is desired. For great circles, the result will be the azimuth at the starting point of the connecting great circle path. In general, the azimuth along a great circle is not constant. For rhumb lines, the resulting azimuth is constant along the entire path.

Azimuths, or bearings, are returned in the same angular units as the input latitudes and longitudes. The default path type is the shorter great circle, and the default angular units are degrees. In our example, the great circle azimuth from the first point to the second is

• azgc = azimuth(-15,0,60,150)
  azgc =
      19.0391
  

For the rhumb line, the constant azimuth is

• azrh = azimuth('rh',-15,0,60,150)
  azrh =
      58.8595
  

One feature of rhumb lines is that the inverse azimuth, from the second point to the first, is the complement of the forward azimuth and can be calculated by simply adding 180° to the forward value:

• inverserh = azimuth('rh',60,150,-15,0)
  inverserh =
      238.8595
  difference = inverserh-azrh
  difference =
      180
  

This is not true, in general, of great circles:

• inversegc = azimuth('gc',60,150,-15,0)
  inversegc =
      320.9353
  difference = inversegc-azgc
  difference =
      301.8962
  

The azimuths associated with cardinal and intercardinal compass directions are the following:

North	0° or 360°
Northeast	45°
East	90°
Southeast	135°
South	180°
Southwest	225°
West	270°
Northwest	315°

Elevation is the angle above the local horizontal of one point relative to the other. To compute the elevation angle of a second point as viewed from the first, provide the position and altitude of the points. The default units are degrees for latitudes and longitudes and meters for altitudes, but you can specify other units for each. What is the elevation and slant range of a point 10 kilometers east and 10 kilometers above a surface point?

• [elevang,slantrange] = elevation(0,0,0, 0,km2deg(10),10000)
  
  elevang =
  
         44.901
  
  
  slantrange =
  
          14156
  

The answer is slightly different from that expected from plane geometry because of the curvature of the Earth.

Measuring Distance

Reckoning Positions