Editing Projected coordinate system (section)

=== Projections ===
{{further|Map projection}}

To establish the position of a geographic location on a [[map]], a map projection is used to convert geodetic coordinates to plane coordinates on a map; it projects the datum ellipsoidal coordinates and height onto a flat surface of a map. The datum, along with a map projection applied to a grid of reference locations, establishes a ''grid system'' for plotting locations.  [[Conformal map projection|Conformal]] projections are generally preferred. Common map projections include the [[Transverse Mercator projection|transverse Mercator]] (used in [[Universal Transverse Mercator coordinate system|Universal Transverse Mercator]], the [[Ordnance Survey National Grid|British National Grid]], the [[State Plane Coordinate System]] for some states), [[Lambert conformal conic projection|Lambert conformal conic]] (some states in the [[State Plane Coordinate System|SPCS]]), and  [[Mercator projection|Mercator]] ([[Swiss coordinate system]]).

Map projection formulas depend on the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on the type of project and the conventions chosen for the projection. For the [[transverse Mercator projection]] used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor.<ref name=OGP7_2>{{cite web |title=Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas |url = http://info.ogp.org.uk/geodesy/guides/docs/G7-2.pdf |publisher=International Association of Oil and Gas Producers (OGP) |access-date=5 March 2014 |pages=9–10 |url-status=dead |archive-url = https://web.archive.org/web/20140306005736/http://info.ogp.org.uk/geodesy/guides/docs/G7-2.pdf |archive-date=6 March 2014 }}</ref> Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions.{{r|OGP7_2|page1=45–54}}