The Internet Collection ofMap Projections and
Reference Systems for Europe
by Stefan A. Voser
Europe is merging closer. Facts for this are the European Community or the
currency Euro. But what about a homogeneous Geospatial Data Infrastructure? The requirements
for that are a common data model, similar data capturing methods and metadata in several
The most fundamental model aspects of geospatial data are coordinate reference
geodetic reference systems and map projections. They are the frame in which coordinates as the
holder of the geometric information get their spatial semantics.
In Europe, the landscape of coordinate reference systems is very heterogeneous
every country built up its own reference systems. Most of them have their own history and lineage.
So, most of them originally have no relations to other nations reference systems: they do not have
a common geodetic datum.
On this level of modelling geospatial data, a comprehensive georeferencing
model is required to
homogenise coordinate reference systems. If homogenisation is reached, geographic locations get
the same mathematical location, i.e. that overlaying data from different sources fit together not
only in reality but also positionally within GIS.
For reaching a homogeneous positional overlay, the first step is the identification
of the coordinate
reference system entity in which your data is stored. A second step is to find the geometric relation
to the target reference system together with the functional model for the changing process.
The MapRef internet collection is an approach to support users when homogenising
from different coordinate reference systems. MapRef collects definitions and parameterisations of
coordinate reference systems like geodetic reference systems and map projections, sorted by
countries. Furthermore, it also includes geodetic datum transformation parameters to global
systems as WGS84, the system in which GPS originally works. In MapRef, you also find other
related information on coordinate reference systems, as theory, related links and additional
The presentation gives you an introduction to the MapRef-pages.
Spatial Reference and Coordinate Reference Systems
The main characteristic of geospatial data is their spatial semantics, meaning that to each spatial
information, a geographical location is assigned. There exist two ways to describe a spatial
location within a GIS:
- Spatial referencing by geographic identifiers
- Spatial referencing by coordinates
The first method is a cognitive one, the second one is a mathematical or geodetic one. Geographic
identifiers use thematic and logic models to describe and assign a geographic location. This
method of spatial referencing is not followed within this discussion.
Spatial referencing by coordinates has its basics in mathematics and analytical geometry.
Generically, a location is described by a set of coordinates which refers to a coordinate system.
But further on, spatial locations need coordinate systems with spatial (or geographic) semantics.
Such spatial coordinate systems are called coordinate reference systems. A coordinate system
is defined by its origin, its axes and units, a coordinate reference system needs its spatial
extension, the position and orientation of the axes in relation to the earth. This spatial extension is
called the datum.
There exist various classes of coordinate reference systems. Here, we only focus on the classes
for geodetic reference systems and map projections. Let's have a look at Fig. 1 what the main
Fig. 1: From the earth surface to the plane of a map projection
A spatial location is related to the earth surface. So we need a mathematical method to describe
the earth shape by a reference surface to which a coordinate reference system may be assigned.
For areas smaller than 10 x 10 km2 a plane may be supposed whereas for larger regions, a curved
surface has to be established. In Geodesy, the science of the determination of the figure and the
size of the Earth, three types of Earth surfaces are used [Moritz 1990]:
- the topographic surface - the physical or geological one (mountains, valleys lakes, the
- the geoid - the geophysical or gravitational one. The geoid is a surface perpendicular to
the plumb lines. It is the continuation of the mean sea level surface at the continents.
The geoid is the reference surface for heights, particularly the orthometric heights.
- the spheroid and sphere - a mathematical and symmetric surface. The spheroid
(ellipsoid) is a sphere flattened at the poles. It mainly is used for describing a horizontal
position (e.g. by geographic coordinates).
Let's conclude: the geodetic reference systems are the geoid for the heights and the spheroid
(ellipsoid) for the horizontal.
In Fig. 1b we see an ellipsoid as a reference for the horizontal position, and for the heights, a digital
elevation model as an approximation of the topographic surface is given. Each height- information is
assigned to a horizontal position, but the height is not referred to the ellipsoid, but influenced by
and related to the gravity field. (this leads to the problem of geodetic hybridity when modelling
coordinate reference systems).
In Fig. 1c,d, it is shown that ellipsoids may vary by their shape and size as well as by their
position. This means that various geodetic datums exist. E.g. in Europe, there is a big
heterogeneity. Mainly each country uses or used its own reference systems. Some may use the
same ellipsoid but a different datum, but also various ellipsoids are in use. Of course, there exist
various efforts to unify the geodetic reference systems. One example is the European Datum 1950
with is/was used by NATO and primarily for militarian mapping. A newer effort is the EUREF
Campaign which led to the ETRS89 (European Terrestrial Reference System 1989) together with its
control point field, the ETRF89- Frame. Since this frame is realised, many countries defined new
national geodetic reference systems which are referred or equal to ETRS.
Fig. 1e finally shows the way from geodetic or geographic coordinates to the national grid
coordinates or generically to the planar coordinates of a map projection. A national coordinate grid,
as used for topographic mapping, is based on a map projection, mostly based on a conformal one.
But for thematic mapping also other geometric properties as equal-
area projections and equidistant
projections are in use. In Fig. 1e, it is shown that most projections use a conic map projection
surface (cylinder, cone, plane) which is flattened to the plane.
The implementation of map projections has a much wider amount of map projection instances for
authoritative mapping than for Earth models. Why? Map projections have distortions. Only for a
characteristic and type dependent area, these distortions are small enough that they are smaller
than the accuracy of drawing the map elements. Because of that, for larger counties as e.g.
Austria, Germany, France, Sweden etc, map projection zones are used. In various European
countries, also different projections are used for mapping at different scales.
We have seen, there exist various ways for choosing a coordinate reference system for mapping. In
other words, the same spatial location may have different coordinates in different maps or datasets.
When using datasets from different sources but covering the same area, it may require a
homogenisation of these sets by means of coordinate reference systems.
Such a coordinate reference system homogenisation is a georeferencing process. There exist
two groups of georeferencing processes:
- Conversions: the relation between the coordinate reference systems is set by definition (the
method as well as the parameters). E.g. the application of a map projection is a conversion of
coordinates from the reference surface to the projection plane or vice versa.
- Transformations: the relations between the coordinate reference systems is determined based
on measurements. Normally, the mathematical method is known, but the parameters have to be
estimated. For that, fiducials or control points are used (the coordinates are known in the source
as well as in the target system). Typically the following two types of transformations are used for
- Planar transformations: e.g. used for georeferencing map sheets or scanned maps.
- Geodetic datum transformations: used for changing the geodetic reference system.
In Fig. 2, these main georeferencing processes are shown. Planar transformations, used e.g. when
digitising or scanning maps, inverse projections as conversions, and geodetic datum
transformations for the change between two geodetic reference systems.
Fig. 2: Georeferencing Processes: a Chain of Transformations and Conversions
Applications of Coordinate Reference Systems
Various coordinate reference systems were defined and implemented by authoritative bodies and
organisations. These systems have a specific datum based on their definition (initialisation). E.g.
national mapping agencies decided for a map projection (system) together with its underlying
geodetic reference system. Their definitions are constant, and this information may be required for
many georeferencing processes.
For these two groups of coordinate reference systems, it is a comfort to have the required
parameters and methods collected and published or implemented. Many GIS- Software
implementations support the functionality for georeferencing, as well for planar transformations as
for map projections and datum transformations. A lack still is to get the correct parameters.
Therefor, the MapRef- pages are built up.
The MapRefWeb Pages
The MapRef Web- Site is an internet collection of information about map projections and reference
systems. The main focus is done on the definitions and parameters for map projections and
geodetic reference systems in Europe.
Fig. 3: The Internet Home of the MapRef-Collection
The MapRef pages are designed for the following information. Not all themes are included or
Definitions and parameters of map projections, sorted by European countries;
parameters, sample data; references.
Definitions and Parameters of geodetic reference systems, sorted by European
countries; parameters, sample data; references.
Map Series, sorted by European countries; related reference
The mathematical basics of mapping. Links to tutorials and
other related sites.
Terms, glossaries and acronyms; links.
Publications, books and libraries; links.
National offices for mapping and geodesy; links.
National or international bodies in the field of Cartography
What are the standardisation efforts for Coordinate Reference
Data Exchange Formats. Ready for CRS?
Technical applications for georeferencing.
Internet applications for georeferencing.
Metadata about the MapRef-Pages.
If you have questions, please check here first.
If you really need help or have interesting information
to be included.
In the following, only the main characteristics of the definitions or specifications of map projections
and geodetic reference systems are discussed more in detail.
How to specify a map projection
A map projection is classified as a conversion between geographic and planar coordinates based
on a method with its geometric properties. There exist various ways to classify map projections.
See e.g. [Richardus/Adler 1972, Snyder 1987]. The methods for the classifications are:
- the extrinsics of geometry (mapping surface)
- The nature of the mapping surface (plane, cone, cylinder)
- The coincidence (tangency, secancy)
- The position or alignment (normal, transverse, oblique)
- The intrisics of geometry (properties)
- Deformation method (conformal, equidistant, equivalent, compromise)
- The generation (geometric, semi- geometric, conventional)
- The geographic use and extent
- World mapping
- Large and medium scale maps
- Polar, equatorial, other area
- Visual effects
- Mathematical systematics
These characteristics are all important when choosing a map projection for a certain purpose. A
main problem when using implemented methods is their identification. The same method may have
different names, or also different mathematical approaches etc.
So, when specifying an instance of a map projection, it requires the following information:
- Area of use
- Underlying Earth model (incl. datum)
- Control points (for checking)
This information will be collected in the map projection collection, sorted by countries.
How to specify a geodetic reference system
At the beginning, we have seen that geodetic reference systems are used for modelling the figure of
the Earth. When modelling the Earth for flattening it by a map projection, spheroids and spheres
are used because of their geometrical smoothness. Such a model has geometric properties,
describing the shape and size of its figure. And the datum describes the position and orientation
regarding to the Earth (and its surface).
Before artificial satellites became reality, the geodetic datum was determined by astronomical
measurements. Based on such measurements and regarding to the earth curvature for the specific
country, the best fitting spheroid was oriented and positioned in its (national) datum. Normally, a
fundamental point (e.g. the Panthéon in Paris, the old observatory in Berne, the observatory Monte
Mario in Rome etc.) was used for fixing the spheroid in its datum (Fig. 1c,d, Fig. 2c). By this
astronomical definition of the datum, the Earth model stood for its own, and no relations to other
geodetic datums were known or fixed. Important is that by this way, the position and orientation to
the Earth centre (mass point) was unknown.
Since the use of artificial satellites (e.g. TRANSIT, GPS) is applicable for navigation and also for
geodesy, global (world- wide) geodetic reference systems were built up (e.g. WGS72, WGS84,
ITRS89), positioned in the Earth centre, oriented by the mean rotation axis and the meridian of
Since continental (e.g. European Datum 1950) and world- wide geodetic reference systems were
built up, the need for their relations to the national datums raised. The easiest way for that is to
know the geometric relations between the axis of the spheroid between the two systems. (The 3
axis of the spheroid define its "geocentric" Cartesian coordinates (Fig. 1d). Such a modern
definition of a datum is described by the ellipsoid names, and their relational positional information.
Normally, two methods were used:
- translation (3 Parameters)
- Helmert transformation, similarity (7 Parameters: 3 translations, 3 rotations, 1 scale)
These principles may have different implementations. They may vary in its signs, or they are
implemented at curvilinear methods, meaning a direct transformation between the geographic
coordinates related to the two ellipsoids.
So, when specifying an instance of a geodetic reference system, it requires the following
- Fundamental point
- Area of use
- Relation to the global system:
- Parameters + accuracy
- Control points (for checking)
This information will be collected in the reference system collection, sorted by countries.
Not included here are the heights systems or the geoid models, because they belong to a more
Some Meta-Information about the MapRefPages
The MapRef-Pages are not funded by any organisation or institution, they are one aspect of my
work towards my PhD. Because of that, they have an experimental touch, are not complete and
The initiation for the pages was given by the Project "Geodetic Reference Systems and their
Applications to the Field of Nature Conservation", which I realised from 1994-1996 at the Institute
of Geodesy, University of the Federal Armed Forces, Munich, funded by the German Federal Office
for Nature Conservation.
Conclusion and final remarks
Coordinate Reference Systems are the mathematical fundamentals for storing spatial data with its
geometry. A management is required to homogenise spatial data from heterogeneous coordinate
reference systems using georeferencing processes. For many georeferencing processes, the
required information is missing (e.g. the parameters of the map projections and datum
transformations). The MapRef pages are built up to collect such information.
At European level, MEGRIN (Multipurpose European Ground Related Information Network) now
started an initiative to build up a similar European collection.
Bugayevskiy 1995 Bugayevskiy Lev M., Snyder John P.: Map Projections, A Reference Manual,
Taylor&Francis, London, Bristol 1995.
Hooijberg 1997 Hooijberg Maarten; Practical Geodesy – Using Computers. Springer Verlag, Berlin
Moritz 1990 Moritz Helmut: The Figure of the Earth – Theoretical Geodesy and the Earth’s
Interior. Herbert Wichmann Verlag Karlsruhe, 1990.
Richardus/Adler 1972 Richardus, Peter; Adler, Ron K.: Map Projections, for Geodesists,
Cartographers and Geographers. North Holland Publishing Company, Amsterdam 1972.
Snyder 1987 Snyder, John P.; Map Projections - A working manual; U.S. Geological Survey
Professional Paper 1395; Washington 1987.
Voser 1998 Voser S. A.: Schritte für ein automatisiertes Koordinatensystemmanagement in GIS
und Kartographie. (Steps Towards an Automated Coordinate System Management for GIS and
Cartography) Nachrichten aus dem Karten- und Vermessungswesen, Reihe I, Heft Nr. 118, S. 111-
125. Bundesamt für Kartographie und Geodäsie, Frankfurt am Main, 1998.