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
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