About Map Projection-What is a Map Projection?

This article consists of six parts matter that are;

References

Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.

Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.

Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.

1) What is a Map Projection?

To produce a map of the world in a convenient way we make use of map projections. A map projection is any transformation between the curved reference surface of the earth and the flat plane of the map.

We can as well define a map projection as a set of equations which allows us to transform a set of Ellipsoidal Geographic Coordinates (j, l) representing positions on the reference surface of the earth to a set of Cartesian Coordinates (x, y) representing positions on the two-dimensional surface of the map (see figure above) .

For each map projection the following equations are available:

X,Y = f ( j, l )      Forward equation

j, l = f ( X,Y )      Inverse equation

The forward equations are used to transform geographic coordinates - latitude (j) and longitude (l) - into Cartesian coordinates (X,Y), while the inverse equations of a map projection are used to transform Cartesian coordinates into geographic coordinates. These equations have a significant role in projection change (see section on Coordinate transformations ).

Some examples of map projection equations are given below:

Map projection equations can be considerably more complicated than those introduced here, for example, when an ellipsoid is introduced as reference surface. J. P. Snyder gives an overview of map projection equations in his book entitled 'Map Projections used by the U.S. Geological Survey'. A number of equations are given at World of Mathematics.

Map projection equations have a number of parameters such as

• radius of the sphere (R) or equatorial (a) and polar radius (b) of the reference ellipsoid;
• geodetic datum;
• origin of the coordinate system;
• false easting and northings;
• central meridian ( lo ), standard parallels ( j1, j2 ) or centre of projection ( j1, lo ) ;
• scale factor at the central meridian or standard parallels.

Information about the projection parameters is required to define a countries spatial reference system.

Activity A point P is located on the Stereographic projection at 60o N and 130o E . The sphere is taken as the reference surface of the earth. Use the equations given above to obtain the Cartesian coordinates for point P. The origin of the coordinate system is located on the North Pole (Radius (R) = 6371000 m, Central Meridian (lo) = 0o , equal to the Greenwich meridian).

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