2. Coordinates Computations

a. Forward Computation

A forward computation uses a starting coordinate pair along with a distance and direction to determine another coordinate pair.

In Figure F-5, starting with coordinates at P, compute the coordinates at Q.

Figure F-5
Forward Computation


Using Equations D-1 and D-2, the latitude and departure of the line are:

LatPQ= LPQx cos(DirPQ)

DepPQ = LPQ x sin(DirPQ)


L: line length
Dir: line direction

  To compute X and Y coordinates:

YQ = YP + LatPQ

XQ = XP + DepPQ

       Equations F-1 and F-2

To compute N and E coordinates:

NQ = NP + LatPQ

EQ = EP + DepPQ

       Equations F-3 and F-4


For a complete traverse, Figure F-6:

Figure F-6
Coordinates Around a Loop Traverse


Starting with known coordinates at T (NT, ET) and applying Equations F-3 and F-4 around the traverse:

Compute coordinates of Q: img8
Compute coordinates of R: img11
Compute coordinates of S: img7
Compute coordinates of T: img10


Computing back into T gives a math check: the end coordinates should be the same as the start coordinates.

In order for the math check to be met, adjusted lats and deps must be used.

Where do the start coordinates come from? They can be assumed or they could be from a formal coordinate system. We'll discuss formal coordinate systems in a later topic.