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3) Properties of Map Projections 4) The classification of Map Projections |

**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.

The following properties would be present on a map projection without any scale distortions:

- Areas are everywhere correctly represented
- All distances are correctly represented.
- All directions on the map are the same as on Earth
- All angles are correctly represented.
- The shape of any area is correctly represented

It is, unfortunately, impossible to have all these properties together in one map projection.

An **equivalent **map projection, also known as an **equal-area** map projection, correctly represents areas sizes of the sphere on the map. When this type of projection is used for small-scale maps showing large regions, the distortion of angles and shapes is considerable. The Lambert cylindrical equal-area projection is an example of an equivalent map projection.

The Lambert cylindrical equal-area projection as an example of an equivalent, cylindrical projection

An **equidistant** map projection correctly represents distances. An equidistant map projection is possible only in a limited sense. That is, distances can be shown at the nominal map scale -the given map scale- only from one or two points to any other point on the map or in certain directions. If the scale on a map is correct along all meridians, the map is *equidistant along the meridians* (e.g. the Plate Carree projection). If the scale on a map is correct along all parallels, the map is *equidistant along the parallels.*

The Plate Carree projection as an example of an equidistant, cylindrical projection

A **conformal** map projection represents angles and shapes correctly at infinitely small locations. Shapes and angles are only slightly distorted, as the region becomes larger. At any point the scale is the same in every direction. On a conformal map projection meridians and parallels intersect at right angles (e.g. Mercator projection).

The Mercator as an example of a conformal, cylindrical projection

*Note**A map projection may possess one of the three properties, but can never have all three properties. It can be proved that conformality and equivalence are mutually exclusive of each other and that a projection can only be equidistant (true to scale) in certain places or directions. *

There are map projections with rather special properties:

On a *minimum-error *map projection the scale errors everywhere on the map as a whole are a minimum value (e.g. the Airy projection ).

On the Mercator projection, all rumb lines, or lines of constant direction, are shown as straight lines. A compass course or a compass bearing plotted on to a Mercator projection is a straight line, even though the shortest distance between two points on a Mercator projection - the great circle path - is not a straight line.

All rumb lines, or lines of constant direction, are shown as straight lines.

On the Gnomonic projection, all great circle paths - 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

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