Map Projections

You probably don’t need to know much about map projections unless you are a cartographer or GIS professional.  They are of little concern to most people and can get rather complicated.

We do need them. They are used to represent the surface of the earth on a flat surface. There are lots of different ways to tackle the problem and they all introduce distortion. It is like trying to flatten out the skin of an orange. You can’t do it unless you cut it, stretch it or scrunch it.

Map projections are actually equations that transform the earth’s angular geographic coordinates (latitude, longitude) to x,y cartesian coordinates on a flat projected surface. Assumptions have to be made about the shape of the earth. The earth is an irregular shape though most projections assume it to be a sphere or an ellipsoid.

There is no limit to the possible number of projections.   And modern technology has made it easier than ever to compute them.

Map projections can be categorised in four ways:
Class, Angle, Fit and Properties.

Class:
The projection class is defined by the shape of the projection surface, commonly either a flat plane, a cylinder or a cone. Note that cones and cylinders are not flat shapes, however they can be rolled flat without introducing additional distortion.

  • Azimuthal: coordinates are projected directly onto a flat planar surface.
  • Cylindrical: coordinates are projected onto a rolled cylinder
  • Conical: coordinates are projected onto a rolled cone

In general, azimuthal projections work best for circular areas (eg: the poles), cylindrical projections work best for rectangular areas (eg: world maps), and conical projections work best for triangle shaped areas (eg: continents)

Angle:
This refers to the alignment of the projection surface, measured as the angle between the main axis of the earth and the main symmetry axis of the projection surface.

  • Normal: the two axes are parallel
  • Transverse: the two axes are perpendicular
  • Oblique: the two axes are at some other angle

Ideally the plane of projection is aligned as closely as possible with the main axis of the area to be mapped.  This helps to minimise distortion and scale error.

Fit:
A measure of how closely the projection surface fits the surface of the earth.

  • Tangent: the projection surface touches the surface of the earth.
  • Secant: the projection surface slices through the earth.

Distortion occurs wherever the projection surface is not touching or intersecting the surface of the earth.  Secant projections usually reduce scale error because the two surfaces intersect in more places and the overall fit tends to be closer.

A globe is the only way to represent the entire earth without any significant scale error.

Properties:

  • Conformal projections preserve shapes and angles
  • Equal Area (or equivalent) projections preserve areas
  • Equidistant projections preserve distance (this is only possible at certain locations or in certain directions)

It is impossible to construct a map that is both equal-area and conformal.

Conformal map projections are recommended for navigational charts and topographic maps.
Equal area projections are generally best for thematic mapping.
Equidistant map projections should be used when measuring distances from a point (air routes, radio propagation strength, radiation dispersal).


1. Azimuthal Projections

Gnomonic
The only projection where the shortest distance (great circle) between any two points is always represented by a straight line.  It is neither conformal nor equal area, and suffers from large scale distortions.  It dates from the 6th century BC and is arguably the world’s oldest map projection.  It is still used to plot radio signals and seismic waves.

Stereographic
A conformal projection, useful for mapping areas that are roughly circular in shape.  Scale distortion is moderate.

Orthographic
The Orthographic projection has a viewpoint at infinity and parallel projection lines.  It shows the earth as seen from outer space.

Azimuthal Equidistant
Frequently used for air-route distance maps.

Lambert Azimuthal Equal Area
Suitable for thematic mapping of continents or regions.

2. Cylindrical Projections

Mercator
A conformal projection dating from 1569. It was used widely for navigation because a compass bearing on the map can be represented by a straight line (rhumb line). There is gross distortion in scale at high latitudes (>70°).

Universal Transverse Mercator (UTM)
A conformal projection, promoted for worldwide topographic mapping by the United Nations Cartography Committee in 1952. To minimise distortion the UTM divides the earth into 60 longitudinal zones, each 6° wide. Several countries, including New Zealand, have adopted a custom Transverse Mercator with coordinates projected to a local cartesian grid.

Equidistant Cylindrical (Plate Carree, Equirectangular)
This projection maps latitude directly to Y and longitude directly to X.  The meridians and parallels form a grid of equal rectangles.  It is neither equal area nor conformal but has become a de-facto standard for global raster datasets.

Lamberts Cylindrical Equal Area, Gall-Peters, Behrmann
These cylindrical equal area projections all suffer some shape distortion but are suitable for thematic mapping.

Pseudo-cylindrical projections
This is a family of projections used for world maps where the earth is displayed with a curved edge and curved meridians. Most pseudo-cylindrical projections are equal area (or close to equal area) and are suitable for thematic or distribution mapping. Examples include  Mollweide, Sinusoidal, Eckerts I–VI, Winkel I–II, Robinson

 3. Conical Projections

 Lambert Conformal Conic
This is the only conformal conic projection and is used for topographic mapping at a regional or continental level.

Albers Equal Area
This is perhaps the most important equal area conic projection. It is best suited for use in the mid latitudes.

 Polyconic
Polyconic projections have non-concentric parallels, and are neither conformal nor equal area. Pseudoconic projections have curved meridians.

4. Other Projections

Interrupted Projections
These are typically cylindrical but display the earth with an interrupted graticule. They are used to project gores (the angled map segments used to construct globes) and where there is a need to focus on particular areas (eg: continents). The example shown is the Goode Homolosine projection, an interrupted version of the Mollweide.

Myriahedral Projections
Possibly the least practical projection for mapping yet the most striking in terms of cartographic art. Myriahedrals are interrupted projections. The surface of the earth is not projected onto a cylinder, cone or plane, but onto a myriahedron (a polyhedral with a very large number of flat faces). The myriahedron is then cut up in various ways and unfolded. Visit the Myriahedral site.

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