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?
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.
Figure F-8 |
Equations F-5 and F-6 |
Note that the differences are the To point values minus the From point values.
Equation F-7 | ||
and | ||
Equation F-8 | ||
where | ||
-90° ≤ ß ≤ 90° |
The mathematic signs on the coordinate differences determine the direction quadrant, Figure F-9.
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.