COGO, short for coordinate geometry, is a set of tools for (or the act of) converting between local polar and rectangular plane coordinates.

COGO (or coordinate geometry) tools are used extensively by land surveyors and civil engineers who make detailed measurements of (or calculations using) distances and angles among sets of points on a plane, within a relatively small area. They are less commonly used by geographers and cartographers who are more concerned with points on a spheroid or map over a relatively large area.

In surveying or engineering, points are invariably stored as rectangular coordinate pairs (i.e., X-Y or E-N) on a plane reference surface. However, between points, both raw field measurements and parcel map lines are usually represented by some form of polar coordinates (i.e., pairs of angles and distances).

The simplest and most common COGO tasks, both involving simple trigonometry, are:

  • Given a known point and an azimuth (or bearing) and a distance to a new point, calculate the new X-Y (or E-N) coordinates. This is known as a direct (or traverse) calculation.
  • Given two known points, calculate the azimuth (or bearing) and distance between them. This is known as an inverse (or join) calculation.

Other COGO tasks include the following:

  • Given azimuths (bearings) from two known points to a new point, calculate the coordinates of the target. Known as triangulation or bearing-bearing (or line-line) intersection.
  • Given distances from two known points to a new point, calculate the coordinates of the target. Known as trilateration or distance-distance (or arc-arc) intersection.
  • Several variations of the above.

COGO purists might claim that a true COGO tool must allow distances and angles to be entered implicitly, by identifying the end-points of lines, as an alternative to the (possibly more time-consuming and possibly less accurate) explicit entering of numerical quantities.

In a surveying/engineering context, examples of popular COGO tools are the commercial AutoCAD Map 3D and the free Copan. In a GIS context, where COGO tends to be more limited, ArcGIS has it built in and QGIS has a plugin.

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