Coordinate Systems

Any geographic object, like a city, a river mouth, or a mountain peak, can only be localized if it is possible to describe it in relation to other objects with known position. It is a matter of determining its position in a coherent network of coordinates.

When we have a coordinate system as a reference we can define the localization of any point on the surface of the Earth.

SPRING works with the systems of geographic and plane coordinates.


Geographic Coordinates System

Is the oldest coordinate system. There, any point on the surface of the earth is located in the intersection of a meridian with a parallel.

Meridians are maximum circles of the sphere, whose planes contain the axis of rotation or the axis of the poles.

Meridian of Origin (also known as prime or fundamental meridian) is the one that passes over the british Greenwich Observatory, chosen as the origin (0°) of the longitudes on the surface of earth and serves also as the basis for the division in Time Zones.

To the East of Greenwich the meridians are measured in ascending values up to +180°. Towards the West, the values decrease down to -180°.


The parallels are circles of the sphere whose plane is perpendicular to the axis of the poles. The Equator is the parallel that divides the Earth in two hemispheres (North and South) and is considered the parallel of origin (0o). Starting from the Equator towards the poles we have many planes parallel to the Equator, whose sizes gradually decrease until becoming a point in the North (+90o) and  South (-90o) poles.


A point on the surface of the Earth is represented by a latitude and longitude values.

The Longitude of a place is the angular distance between any point on the surface and the initial meridian or meridian of origin.

Latitude is the angular distance between any point on the surface of the earth and the Equator.

For example, the city of Leme in the state of Sao Paulo, is located to the south of the Equator and west of Greenwich, having negative latitude and longitude. Since latitude and longitude are angles, their values are traditionally given in degrees, minutes and seconds. Thus the geographic coordinates of leme are:

  • S 22° 11' 04": south  latitude
  • W 47° 23' 01": west  longitude

Being a system that considers angular deviations from the center of the Earth, the geographic coordinates system is not a convenient system for applications that are interested in distances or areas.

In these cases, it is recommended the use of a suitable coordinate system, like, for example, the plane coordinate system, described as follows.


Plane Coordinates System

The plane coordinate system, also known as cartesian coordinate system, is based in the choice of two perpendicular axes, usually the horizontal and vertical axes, whose intersection is called the origin, serving as the base for the localization of any point on the plane. The origin usually has the coordinates (0,0), but could, by convention, have different values, named offsets. Thus we could have the origin with the coordinates (offset_X, offset_Y).

On this coordinate system a point is represented by two numbers: one corresponding to its projection on the X axis, usually associated to the longitude, and the other corresponding to its projection on the Y axis (vertical), usually associated to the latitude.

The x and y values of the coordinates of the city of Leme, for example, are:

where: x = 254.000 m and y = 7.545.000 m

In a GIS the plane coordinates normally represent a cartographic projection and so mathematically related to the geographic coordinates, so that one can be transformed in the other.

Cartographic Concepts 


Cartographic Projections

All the maps are approximate representations of the earth surface. They are approximate because the Earth, spherical, is drawn on a plane surface.

The elaboration of a map consists in a method whereby each point on the earth, in geographic coordinates, corresponds to a point, in plane coordinates, on the map. To obtain this correspondence we use the cartographic projection systems.

There are different cartographic projections, since there is a great variety of ways to project on a plane the geographic objects that characterize the earth surface. Consequently, is becomes necessary to classify it on its many aspects in order to better study them.

Classification of the Projections

We analyze the cartographic projection systems by the type of surface adopted and the degree of the deformation.

Regarding the type of projection surface adopted we classify the projections in: planes or azimuth, cylindrical and conical, depending how we represent the curved surface of the Earth on a plane, a cylinder or a cone tangent or secant to the earth sphere.


1- Plane or azimuth projection:

The map is built as if it was on a plane that is tangent or secant to a point on the surface of the Earth.

Example: polar stereographic projection.

2- Conic Projections:

The map is obtained by imagining it drawn on a cone that surrounds the earth sphere. The cone is then unrolled over a plane. The conic projections can be either tangent or secant.

In every conic projection the meridians are straight lines that converge to a point (representing the vertex of the cone) and all the parallels are circles concentric to that point.

Example: Lambert's conic projection.

3-Cylindrical Projection:

We obtain the map by imagining it is drawn on a cylinder that is tangent or secant to the surface of the Earth. The cylinder is then unrolled over a plane.

In every normal cylindrical projection the meridians and the parallels are represented by perpendicular lines.

Example: Mercator's projection.

Following we present a comparison between the representation of a quarter hemisphere in three different projection systems.


Plane Projection
Conic Projection
Cylindrical Projection

The surface of the Earth is a curved irregular surface that resembles that os an ellipsoid (described in the item Ellipsoid Models in this same chapter). One can transform  the ellipsoid into a sphere with the same surface:  the earth globe is constructed.

Since the surface of the Earth is curved and irregular it is impossible to make a plane copy of such surface without introducing errors. Although in this process some features can be kept untouched. One should, thus, choose among the possible conservation of the angles, of the surface areas, or some other method that might reduce the effects of deformation, taking into account what one wants to analyze in the map. This leads us to the concept of degree of deformation.

The projection systems are thus classified according to the degree of deformation as:

  • Conformal or orthomorphic: preserve the angles observed on the reference surface of the Earth, this means that the shapes of  small features are preserved. That leads to distortions in the areas of the objects represented in the map. Example: Mercator.
  • Equivalent or equal-area: Preserve the surface relationship (no deformation of the areas). Examples: Albers Conical, Lambert Azimuth.
  • Equidistant: Preserve the proportion among distances, in certain directions, on the represented surface. Example:  Equidistant Cylindrical.

SPRING offers the user the possibility of selecting among the cartographic projections listed in the table below. The choice of the projection should be based upon the desired precision, on the impact over what is being analyzed and on the type of the available data. It is up to the project manager to take this decision.

Cartographic Concepts