## 2.3 Coordinate systems and coordinate frames

To locate and place any object in the plane or in the space, to define their
location are enabled by coordinate systems. In the coordinate systems, or, in other
words, the reference systems, the coordinates of the objects describe its location
exactly. The axes to the coordinate systems are linearly independent from each
other. The system types in the GIS practice:

planar orthographic coordinate system (planar system)

spatial orthographic coordinate system (or Cartesian system, after the
Latin name of Descartes)

spherical polar coordinate system (geocentric or spherical system)

ellipsoidal (geodetic) coordinate system

The axes of the first two types are lines, perpendicular to each other in the
plane or in the space, respectively. In the last two cases, the coordinates are one
distance (from the center, or more practically, from a defined surface) and two
directional angles, the longitude and the latitude. The coordinates are given in
units described in Point 2.1.

Neither the coordinate systems nor the coordinates themselves are visible in the
real world. That’s why the coordinate systems are realized by physically discrete
points and their fixed coordinates in a specific system. This physically existing,
observable point set, characterized by point coordinates is called reference frame.
In fact, all geodetic point networks are reference frames. Any reference frame is
burdened by necessary errors, by theoretical or measure ones, based on the
technology of the creation of the frame. In case of the geodetic frames, the
difference between the Earth’s theoretical shape, the geoid, and its ellipsoidal
approximation causes theoretical errors. Besides, the limited measuring accuracy
results further errors in the coordinate frame.

Longitude of a point is the same both in spherical (geocentric) and ellipsoidal
(geodetic) systems. However, its latitude is different, because of the altered
definition of the angle of the latitude. *In this version of the textbook,
all latitudes and longitudes are interpreted in ellipsoidal (geodetic)
system*.