b. Inverse Computation

An inverse computation is used to determine the distance and direction between two coordinate pairs. The computations involved are basically the same as those for determining a line's new length and direction from its adjusted lats and deps.

For the traverse shown in Figure F-7, how would we determine the length and direction of the line from point T to point R?

img18
Figure F-7
Length and Direction Between Nonadjacent Points

 

Knowing the coordinates of the two points, we can determine the latitude and departure of the line from the coordinate differences, Figure F-8.

img19

Figure F-8
Length and Direction from Coordinates

 

img20        Eqn (F-4)

 

Note that the differences are the To point values minus the From point values.

img21        Eqn (F-5)
and    
img22   Eqn (F-6)
where    
-90° ≤ ß ≤ 90°    

 

The mathematic signs on the coordinate differences determine the direction quadrant, Figure F-9.

img14 2 
Figure F-9
Converting ß to a Direction

If X and Y coordinates are used, remember that Y corresponds to N and X corresponds to E.