### 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 |

To compute X and Y coordinates:

Y X |
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 (N_{T}, E_{T}) and applying Equations F-3 and F-4 around the traverse:

Compute coordinates of Q: | |

Compute coordinates of R: | |

Compute coordinates of S: | |

Compute coordinates of T: |

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.