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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.
Map Projection in Common Use
Several hundreds of map projections have been described, but only a smaller part is actually used. Most commonly used map projections are:
- Universal Transverse Mercator (UTM),
- Transverse Mercator (also known as Gauss-Kruger),
- Polyconic,
- Lambert Confomal Conic,
- Stereographic projection.
These projections and a few other well-known map projections are briefly described and illustrated.
Cylindrical projections
Mercator projection The Mercator projection is a conformal cylindrical projection. Parallels and meridians are straight lines intersecting at right angles, a requirement for conformality. Meridians are equally spaced. The parallel spacing increases with distance from the Equator.
Mercator: conformal cylindrical projection
The ellipses of distortion appear as circles (indicating conformality) but increase in size away from the equator (indicating area distortion). This exaggeration of area as latitude increases makes Greenland appear to be as large as South America when, in fact, it is only a quarter of the size.
The Mercator projection is used for long distance navigation because of the straight rhumb-lines. It is more convenient to steer a rumb-line course if the extra distance travelled is small. Often and inappropriately used as a world map in atlases and for wall charts. It presents a misleading view of the world because of excessive area distortion towards the poles.
Transverse Mercator projection The Transverse Mercator projection is a transverse cylindrical conformal projection.
The Transverse Mercator projection is based on a transverse cylinder
Versions of the Transverse Mercator Projection are used in many countries as national projection on which the topographic mapping is based. The Transverse Mercator projection is also known as the Gauss-Kruger or Gauss Conformal projection. The figure below shows the World map in Transverse Mercator projection.
The world mapped in the Transverse Mercator projection (at a small scale)
The Transverse Mercator is the basis for the Universal Transverse Mercator projection, as well as for the State Plane Coordinate System in some of the states of the U.S.A.
Universal Transverse Mercator (UTM) The UTM projection is a projection accepted worldwide-accepted for topographic mapping purposes. It is a version of the Transverse Mercator projection, but one with a transverse secant cylinder.
The UTM is a secant, cylindrical projection in a transverse position
The UTM projection is designed to cover the world, excluding the Arctic and Antarctic regions. To keep scale distortions within acceptable limits, 60 narrow, longitudinal zones of six degrees longitude in width are defined and numbered from 1 to 60. The figure below shows the UTM zone numbering system. Shaded in the figure is UTM grid zone 3 N which covers the area 168o - 162o W (zone number 3), and 0o - 8o N (letter N of the latitudinal belt).
The UTM zone numbering system (click to enlarge)
Each zone has it's own central meridian. Along each central meridian, the scale is 0.9996. The central meridian is always given an Easting value of 500,000 m; to avoid negative coordinates sometimes large values are added to the origin coordinates, called false coorinates. For positions north of the equator, the equator is given a Northing value of 0m. For positions south of the equator, the equator is given a (false) Northing value of 10,000,000 m.
2 adjacent UTM-zones of 6 degrees longitude
Other Cylindrical projections Pseudo-cylindrical projections are projections in which the parallels are represented by parallel straight lines, and the meridians by curves. Examples are the Sinusoidal, Eckert, Winkel, Mollweide, DeNoyer and the Robinson projection.
The Mollweide projection as an example of a pseudo-cylindrical projection
The Robinson projection is neither conformal nor equal-area and no point is free of distortion, but the distortions are very low within about 45o of the center and along the Equator and therefore recommended and frequently used for thematic world maps. The projection provides a more realistic view of the world than rectangular maps such as the Mercator.
The Robinson projection as an example of a pseudo-cylindrical projection
Conic projections
Three well-known conical projections are the Lambert Conformal Conic projection, the Albers equal-area projection and the Polyconic projection.
The Lambert Conformal Conic projection in normal position is an example of a conic projection
Polyconic projection The Polyconic projection is neither conformal nor equal-area. The polyconic projection is projected onto cones tangent to each parallel, so the meridians are curved, not straight.
The polyconic projection is an example of a conic projection, equidistant along the parallels
The scale is true along the central meridian and along each parallel. The distortion increases away from the central meridian in East or West direction.
The polyconic projection is used for early large-scale mapping of the United States until the 1950's, early coastal charts by the U.S. Coast and Geodetic Survey, early maps in the International Map of the World (1:1,000,000 scale) series and for topographic mapping in some countries.
Azimuthal projections
The five common azimuthal (also known as Zenithal) projections are the Stereographic projection, the Orthographic projection, the Lambert azimuthal equal-area projection, the Gnomonic projection and the azimuthal equidistant (also called Postel ) projection.
For the Gnomonic projection, the perspective point (like a source of light rays), is the centre of the Earth. For the Stereographic this point is the opposite pole to the point of tangency, and for the Orthographic the perspective point is an infinite point in space on the opposite side of the Earth.
The projection principle for the Gnomonic, Stereographic and Orthographic projection
Stereographic projection The Sterographic projection is a conformal azimuthal projection. All meridians and parallels are shown as circular arcs or straight lines. Since the projection is conformal, parallels and meridians intersect at right angles.
In the polar aspect the meridians are equally spaced straight lines, the parallels are unequally spaced circles centered at the pole. Spacing gradually increases away from the pole.
The transverse (or equatorial) stereographic projection is an example of a conformal azimuthal projection
The scale is contant along any circle having its centre at the projection centre, but scale increases moderately with distance from the centre. The areas increase with distance from the projection center. The ellipses of distortion remain circles (indicating conformality).
The Stereographic projection is commonly used in the polar aspect for topographic maps of polar regions. Recommended for conformal mapping of regions approximately circular in shape (e.g. The Netherlands)
Gnomonic projection The Gnomonic (also known as central azimuthal) projection is neither conformal nor equal-area. The scale increases rapidly with the distance from the center. Area, shape, distance and direction distortions are extreme, but all great circles - the shortest routes between points on a sphere - are shown as straight lines.
all great circles - the shortest routes between points on a sphere - are shown as straight lines on the Gnomonic projection
In combination with the Mercator map where all lines of constant direction, are shown as straight lines it assist navigators and aviators to determine appropriate courses. Since scale distortions are extreme the projection should not be used for regular geographic maps or for distance measurements.
Other map projections
The table below gives an overview of other commonly used map projections.
Map Projection LinkS:
- More Map Projections (classification and properties)
- Demonstration of different Map Projections
- Picture Gallery of Map Projections
- Understanding Map projections
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