Coordinate Reference Systems

A Coordinate Reference System is a method of projecting positions in the world onto screen/paper.

The surface of the Earth is curved, but paper is flat. These two facts mean that paper maps will always be slightly distorted.

Different coordinate reference systems are designed to minimise the distortion in different ways. Some coordinate reference systems show orientation accurately, some show areas accurately etc.

There are many different ways to classify Coordinate Reference Systems: some are based on cylinders or cones wrapped around a sphere (Earth); whereas others are based on a Plane, tangential to the sphere either at a Pole, the Equator or any other point on the surface. The most common are:

Cadcorp SIS Desktop 9.1 uses this classification model and the following table briefly describes the supported Coordinate Reference Systems, some of their properties and their possible uses:

  Meridians
(Lines of Longitude) 		Parallels
(Lines of Latitude) 		Graticule Spacing Linear Scale Notes Uses

Cylindrical
Cassini Central Meridian, each meridian 90°
from it and Equator are straight lines.
Others are complex curves.		 Parallels are complex curves.   Scale is true along Central Meridian and along lines
perpendicular to CM.		 Conformal. Still in limited use outside USA although largely replaced
elsewhere by Transverse Mercator. Used for topographic
mapping.
Cylindrical Equal-Area Parallel straight lines Parallel straight lines Meridians and parallels intersect at right angles. Scale diminishes polewards. At any point, the scale along
meridians is too small as the parallel scale is too large,
i.e. meridian and parallel scales are compensatory.		 Direction is not correctly represented. Areas are represented
equally.		 Has often been used for distribution maps in Tropical areas.
Equirectangular Equidistant straight lines. Equidistant straight lines. Meridians and parallels intersect at right angles. Scale is true along the central parallel, normally the Equator. Neither Equal Area nor Conformal. Poles shown as lines. Primarily used for display of general World or Regional
information where distortion is considered to be unimportant.
Gall Stereographic Parallel straight lines. Parallel straight lines. Parallels are projected
Stereographically i.e from one end of the Equator.		 Meridians and parallels intersect at right angles. Scale is true only along parallels 45° N and 45° S. Scale
along Meridians expands towards the Poles but is only correct
around latitude 45°. 		Neither Equal Area nor Conformal. Areas of land progressively
diminished equatorwards but polewards of Latitude 45° they are
progressively enlarged.		 Used in Atlases to show distribution examples.
Mercator Parallel straight lines. Parallel straight lines. Meridians and parallels intersect at right angles.
Meridian spacing is equal and parallel spacing
expands polewards.		 Scale is true only at the Equator. Conformal. Poles cannot be represented. Reasonably accurate
within 15° of the central parallel (Equator).		 Universally used for Marine navigation because all straight
lines on the map are lines of constant Azimuth (Rhumb lines).
Also used for display of Equatorial regions.
Miller Cylindrical Parallel straight lines. Parallel straight lines. Meridians and parallels intersect at right angles.
Meridians are equidistant. Parallel spacing expands away from the Equator.		 Scale is true only at the Equator. Poles shown as lines. Less scale exaggeration than Mercator. Used for World maps as an alternative to Mercator.
Oblique Mercator Complex curves towards the line of tangency. Complex curves concave towards the nearest Pole. Graticule spacing increases away from the line of
tangency.		 Scale is true along the line of tangency or along two lines
equidistant and parallel to the line of tangency.		 Conformal. Mathematically based on a cylinder tangent along
any Great Circle other than the Equator or any Meridian.		 Most often used for Navigation strip charts and satellite
tracking charts.
Transverse Mercator Complex curves concave to a straight
central meridian that is tangent to the
globe. The straight central meridian
intersect the Equator at 90°.		 Complex curves, concave towards the nearest pole.
The equator is straight.		 Parallels are spaced at their true distances on the
central meridian. Spacing increases away from the
tangent meridian.		 Scale is true along the line of tangency or along two lines
equidistant and parallel to the line of tangency.		 Conformal. Shape is true only within a small area.
A real enlargement increases away from the tangent meridian. Cannot be edge-joined in an East West direction if each sheet has its own central meridian.		 Used where the North-South dimension is greater than the
East-West. Used for National Topographic maps.

Pseudo-Cylindrical
Craster Parabolic Meridians are parabolic curves concave
towards a straight central meridian.		 Straight parallel lines. Meridian spacing is equal and decreases toward the poles. Parallel spacing is equal. Scale is true on the parallels and the central meridian.   Used to display areas that have maximum extent in a
North-South direction. Also used in atlases as a World map
to show distribution patterns.
McBryde-Thomas flat
polar quartic 		Meridians are equally spaces sinusoidal curves. Straight parallel lines. Parallels decrease spacing polewards. Scale is true on the parallels and the central meridian. Equal Area. Used in atlases as a World map to show distribution
patterns, particularly in Equatorial and mid-latitude areas.
MollWeide Central meridian straight line. 90th meridians
are circular arcs. All other meridians are equally
spaced elliptical arcs.		 Unequally spaced straight lines, parallel to each other.
Poles are points.		 An Equal Area projection within an ellipse. Scale is true along 40° 44' North and South. Equal Area. Used for world maps with single central meridian or in
interrupted form with several central meridians. Also
used for regional maps of the Pacific.
Robinson Meridians are complex curves.

Unequally spaced straight lines, parallel to each
other. Equidistant only between ±38° latitude, the only
lines true to scale.

   True to scale only along parallels ±38° latitude Based on table of co-ordinates, not mathematical expressions.
Distorts shape, area, scale and distance.		 Used for World maps.
Sinusoidal Equal Area Meridians are sinusoidal curves concave
towards a straight central meridian.		 Straight parallel lines. Meridian spacing is equal and decreases toward the poles.
Parallel spacing is equal. The graticule spacing retains the property of equivalence of area.		 Scale is true on the parallels and the central meridian. Projection may have several central meridians and may be
interrupted on any meridian to help reduce distortion at high
altitudes.		 Used to display areas that have maximum extent in a
North-South direction. Also used in atlases as a World map
to show distribution patterns.

Conical
Albers Conic Equal-Area Meridians are straight lines converging on the
polar axis but not at the pole.		 Parallels are arcs of concentric circles concave
toward a pole.		 Meridian spacing is equal on the standard parallels and decreases toward the poles. Parallel spacing decreases away from the standard parallels and increases between them. Scale is true on the standard parallels. No areal deformation. Individual sheets can be joined along
their edges.		 Used for thematic maps of large countries with a large
East-West orientation.
Equidistant Conic Meridians are straight lines converging on a
polar axis but not at the pole.		 Parallels are arcs of concentric circles concave
toward a pole.		 Meridian spacing is true on the standard parallels and decreases toward the pole. Parallels are spaced at true scale along the meridians. Meridians and parallels intersect at right angles. Scale is true along all meridians and along the standard
parallel(s).		 North or South pole is represented by an arc. Used in atlases for maps of mid latitude areas. Good for
representing regions with a few degrees of latitude lying
on one side of the equator.
Lambert Conformal
Conic (2SP) 		Straight lines converging toward the pole. Arcs of concentric circles concave toward a pole
and centred on a pole.		 Meridian spacing is true on standard parallels, and decreases
toward the pole. Parallel spacing increases away from the standard
parallels and decreases between them.		 Scale is true on standard parallels. A real distortion is minimal but increases away from the standard
parallels. Opposite pole cannot be projected. Great Circle lines are approximately straight. Sheet can be joined along their edges.		 Used for topographic maps of large countries in mid
latitudes having a large East-West orientation.
Polyconic Central meridian and equator are straight lines,
all other meridians are complex curves.		 Parallels are non-concentric arcs of circles. Meridian spacing is equal and decreases toward the poles.
Parallels are spaced true to scale on the central meridian
and the spacing increases towards the East and West borders.		 Scale is true along each parallel and the central meridian. Neither Conformal nor Equal Area. Has both areal and angular deformation. Used for maps of areas with a North-South orientation.

Pseudo-Conical
Bonne Central meridian is a straight line, others are
complex curves.		 Parallels are concentric circular arcs but the
poles are points.		   Scale is true along the central meridian and along all
parallels.		 Equal Area. No distortion along the central meridian and along the
standard parallel.		 Used for atlas maps of continents and for topographic
mapping of some countries.

Azimuthal

(There are three different cases for this particular classification: Polar, Equatorial and Oblique. Only outline information is given for typical cases and it is strongly suggested that the recommended reading is consulted for more detailed information.)
Alaska Grid
(Modified-Stereographic
Conformal for Alaska) 		Meridians are normally complex curves. Parallels are normally complex curves. All meridians and parallels are normally complex curves
although some may be straight under certain conditions.		 Scale is true along irregular lines. Conformal. Maps of Alaska.
Azimuthal Equidistant All meridians on the Polar aspect, the central
meridian on all other aspects and the equator
on the equatorial aspect are straight lines.		 Parallels on the Polar aspect sre circles spaced at true intervals (equidistant for the Sphere)   Distances measured from the centre are true. Neither Equal-Area nor Conformal. Polar aspect - World maps and Polar hemispheres.
Oblique aspect - Atlas maps of continents and World maps for aviation and radio use.
Gnomonic All meridians are straight lines. All parallels except the Equator (a straight line) are ellipses, parabolas or hyperbolas. Distortion rapidly increases away from the centre. Scale rapidly increases away from the centre Neither Conformal nor Equal Area. All Great Circles are shown as straight lines. Directions from the centre are true. Used for navigation charts.
Lambert Azimuthal
Equal-Area 		All meridians in the Polar aspect are straight lines. Parallels in the Polar aspect are circles.   Scale decreases rapidly away from the centre. Equal Area. Maps of continents and hemispheres.
Orthographic All meridians are ellipses, circles or straight lines. All parallels are ellipses, circles or straight lines. Closely resembles a Globe in appearance. Radial scale factor decreases away from the centre. Perspective projection from an infinite distance. Used chiefly for pictorial views.
Polar Stereographic Meridians are straight lines, radiating from the pole. Parallels are concentric circles. A perspective projection of the sphere. Scale increases away from the centre. Conformal. Used for Polar maps and miscellaneous special maps.
Stereo Meridians are straight lines, radiating from the pole. Parallels are concentric circles.   Scale increases away from the centre. Conformal. Used for Polar maps and miscellaneous special maps.
Two Point Equidistant Meridians are complex curves Parallels are complex curves. Limited to one hemisphere.   All Great circles are straight lines. Used for navigation charts.

Miscellaneous
General Vertical
Near-Side Perspective 		All meridians are ellipses, circles or straight lines. All parallels are ellipses, circles or straight lines. Closely resembles a Globe in appearance. Radial scale factor Decreases away from the centre. Perspective projection. Used chiefly for pictorial views.
Hammer-Aitoff Central meridian straight line. All other meridians
are equally spaced elliptical arcs.		 Unequally spaced straight lines, parallel to each other. Poles are points An Equal Area projection. Scale decreases away from the centre Equal Area. Used for world maps with single central meridian.
Van Der Grinten Central meridian straight line, all others are arcs of circles. Equator is a straight line, all other parallels are
arcs of circles.		 Shows entire globe enclosed in a circle Equator is true to scale. Expands rapidly towards the Poles. Neither Equal Area nor Conformal. A curved modification of
the MercatorCoordinate Reference System. With great
distortion in the Polar areas.		 Used only in the spherical form. Distribution maps of
mineral resources on the seabed.
Winkel I Meridians are complex curves. Unequally spaced straight parallel lines. Poles are straight lines, half as long as the Equator.        
Eckert I Meridians are equally spaced at Equator. Parallels are equally spaced straight lines. Graticule entirely composed of straight lines.
Poles are straight lines, half as long as the Equator.		   Not Equal Area. Considered to be a novelty projection.
Eckert II Meridians are equally spaced at Equator. Parallels are unequally spaced straight lines. Graticule entirely composed of straight lines.
Poles are straight lines, half as long as the Equator.		   Equal Area. Considered to be a novelty projection.
Eckert III Central meridian is a straight line, 180° is a
semi-circle, all others are elliptical arcs.		 Parallels are equally spaced straight lines. Poles are straight lines, half as long as the Equator.   Not Equal Area.  
Eckert IV Central meridian is a straight line. 180° is a
semi-circle,  all others are elliptical arcs.		 Parallels are unequally spaced straight lines. Poles are straight lines, half as long as the Equator. Scale is true along latitudes 40° 30' N & S. Equal Area. Used for World maps and Atlas maps of
climate and other themes.
Eckert V Central meridian is a straight line. All others are
sinusoidal curves.		 Parallels are equally spaced straight lines. Poles are straight lines, half as long as the Equator.   Not Equal Area. Used for World maps.
Eckert VI Central meridian is a straight line. All others are
sinusoidal curves.		 Parallels are unequally spaced straight lines. Parallels are straight lines, meridians are sinusoidal curves.
Poles are straight lines, half as long as the Equator.		 Scale is true along latitudes 49° 16' N & S. Equal Area. Used in Atlases and text books for World maps.