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The Central European Net (CEN )

The European datum began its life as the Central European First-Order Triangulation Adjustment (Hough, 1947) this project began in April 1945 after the U.S Third Army with the HOUGHTEAM captured the trigonometrical section of the Reichsamt für Landesaufnahme in the town of Friedrichsroda, Thuringia (after the raid in Saalfeld - part 2). This group were taken to Bamberg, in the United States Occupation Zone, for interrogation.


It was discovered that the captured Germans, led by Professor Erwin Gigas, had been completing an adjustment of the first-order triangulation of the Greater Reich with the intent to expand this adjustment across the German occupied territories...


“…the material of observation for the triangulation of Central Europe available at the end of the war was almost entirely based on new observations. Thus it appeared advisable to readjust this new material, introducing all astronomical data and the base lines remeasured in the meantime. This task was assigned to the Central Survey Office -- now known as the Land Survey Office -- an organization founded in Bamberg by the U S. Army.” Hough 1948


The assigned Land Survey Office (operating under the Army Map Service and U.S Coast and Geodetic Survey) based in Bamberg commenced the adjustment of the first-order triangulation in June 1945 (Whitton, 1952). It was here, overlooked by the US Army and led by Erwin Gigas, that the German trigonometrical section started a review of all points previously calculated highlighting those of sufficient reliability to be used in the first-order triangulation…


…by adopting the area of the whole of North Western Germany unchanged [,] use of the numerous astronomic observations was rendered impossible. Therefore, the so arising final German Reiehsdreieeksnetz, though constituting a sufficient basis for Germany herself, was no adequate nucleus for any Central European or even European Network…” Hough 1948


This review of German triangulation points created a list of data points that were originally used as area controls rather than individual arcs.  Selecting from the list of first-order points arcs were chosen and thus the framework for the triangulation adjustment was constructed. The captured Germans at Bamberg performed a least-squares adjustment of Western Europe utilising the HOUGHTEAM’s captured data (see list at the end of this blog). The work plan for the adjustment is laid out as 10 points in Hough, 1947.


The adjustment was conducted using methods like the Bowie Junction method (Adams and Oscar, 1930)  which was previously incorporated into the successful adjustment of the North American Datum 1927 (EPSG: 6267). Work was designed to follow a network of arcs following as much as possible meridians and parallels from the existing triangulation.


Bowie method is an arc method of adjusting a triangulation network, where length and azimuth of one side of a triangle at every junction between arcs (chains) are assumed correct and carried into a suitable figure of the junction. Directions or angles in arcs between these figures are then calculated, the corrections in the individual chains calculated, and the misclosures passed into the longitudes and latitudes of the initially fixed sides in the junctions by an adjustment of the entire network, using the method of least squares.


Locational calculations were incorporated from over 140 years of German records choosing the most logical values for astronomic and angle observations, bases and Laplace azimuths. This incorporation ultimately resulted in the Deutsches Hauptdreiecksnetz (EPSG: 6314).


The HOUGHTEAM was disbanded in September 1945 after completing a hugely successful operation for the war effort. During its 11-month mission the collection can be summarised as:

  • Obtained complete geodetic data coverage of four provinces of Germany, discovered in the combat area, delivered direct to the artillery and put into an immediate operational use at the front.
  • Selected captured enemy material shipped to Army Map Service:
    • 202 boxes of geodetic data on 900,000 stations in Europe, giving nearly complete coverage of first, second, third, and fourth control in all German and Allied operational World War II areas of the continent
    • 627 boxes of captured maps, covering approximately the same areas noted above (a)
    • Large quantities of photograph prints and dispositives for portions of above areas
    • 371 boxes of various surveying and photogrammetric instruments, including seven Zeiss stereoplanigraphs
    • Geodetic and cartographic library reference books on all countries in Europe.
  • Acquisition of a nucleus of German geodesists and mathematicians and their removal to the United States Area of Occupation for use on scientific projects by U.S. forces.
  • Technical supervision of the adjustment of European first-order triangulation to a common geodetic datum, ED50.
  • The compilation of the magnetic atlas of Europe, epoch 1944-45, published in 1950 by the Army Map Service.

List taken from


Whilst German triangulation and locational work was carrying on, the First International Geodetic Conference on the Adjustment of European Triangulation was held on August 7th 1946 in Paris (Hough, 1948). Here it was discussed and the decision made to examine the triangulation adjustment problem of Europe, as a whole, based on joining work currently being carried out on the Central European Adjustment with the ultimate aim of creating a common European Datum.


Due to the suffering under occupation of most European nations by the Germans contempt lay at the decision to have them involved in the project. As an alternative the United States chose the engineering task to be carried out by the Army Map Service for the first phase of the European-wide adjustment. Each nation taking part reported their…


“observed directions prepared from its latest first-order triangulation observations, its bases, Laplace azimuth, astronomic latitude and longitude observations, descriptions of stations, together with a technical report on the data with recommendations as to its use in the adjustment and relative weights to be accorded” (Hough, 1948)


…in total some 1500 first-order stations were contained in the triangulation adjustment.


The Central European First-Order Triangulation Adjustment was completed in June 1947.


The triangulation arcs can be visualized in Hough, F. W. (1947), The readjustment of European triangulation, Eos Trans. AGU, 28(1), 6266, doi:10.1029/TR028i001p00062.


Expanding the net to create a European Datum

Other blocks were intended for connection to the Central European Net, these included a North-European Net, South-West European Net (Whitten, 1952), South East European Net and East European Net (Weber, 2000). The incorporation of these new blocks into the CEN required large amounts of calculations and processing, a primary place to introduce the use of computers. Charles Whitten, the Chief Geodesist at NOAA, and advocate of using computers to process geodetic computations passed on his methods to incorporate the blocks into a single triangulation network created the European Datum.


International cooperation

The readjustment of the Western European Bloc was completed on June 30th, 1950 along with the combination of additional “blocks” of retriangulation which resulted in the European Datum 1950 (Hough, 1951). This is one of the first examples of true international cooperation, a project that was born out of the combination of national jealousies and war but resulted in a continent-wide standard in cartography, positional science and the study of the shape of the Earth.


Fittingly Floyd Hough wrote appropriate words on the creation of the European datum placing it as one of the major projects of cooperation in European and world history born out of the contrasting chaos of war.


“The term ‘cooperation’ is one of the most satisfying and comprehensive words in the English language. If we were to have complete cooperation in all matters between individuals and nations, the acme of human aspiration would be reached; selfishness would be abandoned; universal peace would be a fact; the millennium would be at hand.” Hough, (1951)


The triangulation was tied to the International Ellipsoid 1924 (Hough, 1948) built upon some 173 astronomic latitudes, 126 astronomic longitudes and 152 azimuths (Barsky, 1971), no one station can be designated as the datum origin rather a fundamental point is designated at the Helmert Tower in Potsdam, Germany (52°22’51.45”n Latitude 13°03’58.74”e longitude). The design of the first-order triangulation network was designed so that any further triangulation and positional calculations were made using this rigid base, as Hough (1948) described:

“Interior triangulation of the area can be adjusted at will to this rigid framework much as the inner portion of a modern steel building is fitted to its network of beams and columns.…” Hough 1948


This was the story about how the European Datum of 1950 was created and has formed the basis of a standard positional framework for the European Continent.



The European Datum 1950


Origin: Potsdam (Helmert Tower). 52°22’51.45”n Latitude 13°03’58.74”e longitude

Ellipsoid: International 1924

Prime Meridian: Greenwich


In Part 1 of this series we saw the setting for the development of a proto European-wide datum by the Germans. This super-National Datum was originally driven from the need of political and military powers in central Europe to comprehensively understand the world around them. Part 2 of the story will concentrate on the Second World War and the Allied military operations that ultimately led to the creation of the European Datum of 1950.


“During the war the German Army also connected triangulations of other European nations to [the German national datum]" Hough 1948


Before 1939 the responsibility with Military Survey at the British War Office was vested in the Geographical Section of the General Staff known as MI4. This Section operated under the Director of Operations and Intelligence, was headed by a Royal Engineer Colonel. Typically the Royal Engineer Colonel would be assisted by Royal Artillery and Infantry Officers. This speaks to the principal application of Military Survey, artillery bombardment and infantry navigation. During the inter-war period a Geodetic sub-section was setup to acquire foreign survey and triangulation data. With increasing evidence in the 1930's that Germany was intending and preparing to launch another war a programme to comprehensively map (and update) the whole of north-eastern France and Belgium (at 1:50,000) began. This effort was led by Colonel P. K. Boulnois under War Office control. To see some of these maps have a look at the plates included in the HMSO book. After the Munich Agreement in 1938 and war with Germany becoming inevitable survey officers were assigned to units for mobilisation. To see more detail concerning MI4 and its organisation see HMSO "Maps and Survey" Books from the War Office e.g. Chapter 01.


War was declared on Germany on the 1st September 1939 after the German invasion of Poland.


By June 1940 the German’s had triumphed in the Battle of France which Adolf Hitler coined "the most famous victory in history”. During the Battle of France the defending British Expeditionary Force was trapped along the northern coast of France, forced to scramble an evacuation of over 338,000 troops to England in the Dunkirk evacuation. After Dunkirk, Germany dominated Western Europe. The British Military reported to Prime Minister Winston Churchill on 4th October that even with the help of other Commonwealth countries and the United States, it would not be possible to regain a foothold in continental Europe in the near future.


Through this interlude where Allied forces fought Axis forces outside of Europe a plan for the invasion of Europe was developed.


Born out of war

The decision to undertake a cross-channel invasion within the next year was taken at the Trident Conference in Washington in May 1943.

Operation Overlord (D-Day)

The Allied operation that launched the successful invasion of German-occupied western Europe during World War II.


The U.S Office of the Chief of Engineers was deployed in WW2 and one of its commitments was to produce, with cooperation of the other allied groups, through revisions and new position readings (see here), battle field situation maps such as the Normandy Landings on 6th June 1944.


Millions of maps were produced throughout the war. The Normandy invasion alone required 3,000 different maps with a total of 70 million copies for keeping the military command fully aware of the operational situation on the ground, in the air and at sea. As the war progressed mapping became more small scale covering larger areas for strategic purposes and it quickly became apparent the lack of geodetic control the allies held over Europe. Probably through national jealously as well as security purposes very little geodetic data was publically available.



Army Group, 12th Engineer Section. August 2, 1944, HQ Twelfth Army Group situation map. Library of Congress Geography and Map Division Washington.


HOUGHTEAM (October 1944 to September 1945)

This lack of geodetic data was particularly noticeable when pushing through France and into Germany making artillery bombardment inaccurate particularly so where shelling took place over the horizon and without seeing the target through gun sights. In this situation of shells going awry the Office of the Chief of Engineers formed a secret intelligence unit in 1944 (Hough, 1947), from the Army Mapping Service (AMS), that was allowed to operate throughout the European Theatre without restrictions. This unit was known as the HOUGHTEAM, named after U.S. Army Major Floyd W. Hough (Chief of the Geodesy Division of AMS) the unit consisted of a team of 3 commissioned officers, 10 enlisted men and 4 engineer consultants.


Their task was to move in behind infantry advancements with the aim of gathering as much cartographic and geodetic information as possible from the enemy, calculating the geodetic transformations into the military mapping system and passing the information onto the army and artillerymen in particular (Hough, 1947).


The HOUGHTEAM moved into Europe in September 1944 and set up in Paris to research and identify targets. The team spent time between in Paris as well as on the front typically arriving on the day it was cleared of enemy personnel. By the spring of 1945 the unit was in Germany and working with the 3rd and 7th armies, providing materials to survey and artillerymen greatly assisting in battle performance. During this time the team captured vital geodetic material for the occupation of Baden-Baden, Württemberg and Bavaria.


“…the war in Europe offered a unique opportunity to exploit known targets and thus to procure from enemy sources captured material of this type both for immediate use of artillery units and for preparation of operational maps.”
Hough 1948

Saalfeld, Thuringia

The most famous raid of this unit was made in spring of 1945, when rumour had it that a cache of geodetic data and instrumentation was held in secret including data on parts of the USSR invaded by Germany. On chance when visiting a hospital for wounded Germany soldiers this rumour was confirmed which led to the discovery on April 17th of a huge cache (Bottoms, 1992) in the village of Saalfeld in Thuringia. Interestingly Saalfeld is close (only ~50Km south west) to the town of Jena in the Jena Valley home of Zeiss Optik, the legendary photogrammetry-equipment company that manufactures just the equipment that HOUGHTEAM were hunting, perhaps the team were exploring this area with this knowledge.


The cache, found in a remote warehouse on the outskirts of Saalfeld turned out to include the entire geodetic archives of the German Army! (Mindling and Bolton, 2008)


In true world war two stories of adventure, the discovery of these documents didn’t finish this story, instead the reader noting the location of Saalfeld and the time of discovery little time was left for grabbing the materials (the advancing Red Army was within days of occupying the town), of which there were 90 tons (Mindling and Bolton, 2008), this equated to around 75 truckloads of geodetic data, maps and instruments that needed transport to Bamburg in the American Occupation Zone.


In realising the difficult logistical task ahead for the HOUGHTEAM the Soviets had already began moving in to their zone of occupation.


According to the story in Life Magazine (12th May 1958)...

“Hough hurriedly borrowed trucks from a U.S artillery unit and the last of them loaded with data was just clearing one side of the village, rushing for the U.S zone, when the Soviets moved in with their tanks on the other side”.

The materials were lifted completely by May 28th destined for Bamberg and onto Washington for evaluation and archiving.


Russian troops arrived in the city the next day.


The horde of information was huge including...

“triangulation surveys running from Moscow to Vladivostok carried out by Germans in the 1900’s planning of the Trans-Siberian Railway […] first order surveys done by the German army deep within the Soviet Union on the Eastern Front” [as well as] the inaccessible regions of the Communist Bloc countries” (Mindling and Bolton, 2008).

The importance of this cache, the realisation that the Soviets were also looking for this cache and its closeness to being compromised by the occupying Soviet forces is suggested by a short quote at a meeting of geodesists in Toronto a few years later where leading Russian delegates mentioned that ...“We have heard a lot about you, Mr. Hough".


The data gathered by the HOUGHTEAM throughout the Second World War, data from Spain into Russia formed the beginning of a framework for European wide geodetic datum and framework for ballistic missile target localisation.


Bottoms, D., 1992. Reference paper 79. World War II Cartographic and Architectural Bank of the National Archives Washington, D.C.Mindling, G., and Bolton, R., 2008. U.S. Air Force Tactical Missiles, 1949-1969, The Pioneers.

Hough, F., (1948) The adjustment of the Central European triangulation network. Bulletin géodésique 7(1) pp64-93

Mindling, G., and Bolton, R., 2008. U.S. Air Force Tactical Missiles, 1949-1969, The Pioneers.

ArcGIS 10.4 now supports eight small-scale map projections displayed in an animated gif:

Compact Miller
Natural Earth
Natural Earth II
Wagner IV
Wagner V
Wagner VII


The Eckert-Greifendorff, Wagner IV and Wagner VII are equal-area projections; the remaining five are compromise projections that try to minimize overall distortion. Sample definitions for the first seven projections are available in the Projected Coordinate Systems\World  and Projected Coordinate Systems\World(Sphere-based) folders.


The Eckert-Greifendorff, Wagner IV and Wagner VII also support ellipsoidal equations. Gnomonic, quartic authalic and Hammer projections are now available in ellipsoidal forms too.


With Eckert-Greifendorff, Hammer ellipsoidal, quartic authalic ellipsoidal, Wagner IV, and Wagner VII, one can select a custom central latitude and create oblique aspects of the projections.


ArcGIS 10.4 includes three variants of polar stereographic projection (variant A, B and C – EPSG codes 9810, 9829 and 9830 respectively) and two new variants of Mercator projection (variant A and C – EPSG codes 9804 and 1044 respectively). Mercator variant B (EPSG code 9805) was already included before as Mercator projection.


Mercator variants A and B have origin of northings / Y values at the equator. Variant A uses a scale factor at the equator to reduce overall scale distortion and effectively defines two standard parallels that are symmetric around the equator. Variant B takes a standard parallel and effectively forces the scale factor at the equator to be less than one. Variant C is similar to variant B, but with the addition of a latitude of origin. The origin of northings / Y values occurs at the latitude of origin.


The polar stereographic variant A is centered at a pole. The longitude of origin defines which longitude will be going straight “down” from the North Pole or “up” from the “South Pole” towards the middle of the map. A scale factor reduces the overall scale distortion and effectively defines a standard parallel. The variant B is similar to variant A, only that it takes a standard parallel to reduce the overall scale distortion of the projection and results in a scale factor at the pole of less than one. Variant C is similar to variant B, but with the addition of a latitude of origin. The origin of northings / Y values occurs at the intersection of the latitude of origin and the longitude of origin.


Considering the de facto use of the European datum of 1950 (ED50) throughout the oil industry operating in Northern Europe and the North Sea, I thought it would be interesting to explore this datum’s history and how it came to be the first European continent-wide datum. During the research for this project I uncovered a fasinating story of military intelligence during the Second World War. But first we must set the scene and go back to...


European Geodesy at the Turn of the 20th Century

“The first-order triangulation of Europe [was completed] over the last 200 years” (Hough, 1948)

Prior to World War Two (WW2), Europe was divided into a jumble of independent national and sub-national geodetic datums with their own centre point, triangulation networks and ellipsoids only sometimes connecting to their neighbour’s triangulation effort along the borders.


Central Europe during the late 19th to early 20th Century is a prime example of this situation. Within the German Confederation and other German States their existed nearly as many datum’s as there were political entities (e.g. Hannover (Gauss, 1821); Bavaria (Soldner, 1808-1828), Prussia (Schreiber, 1975), Württemberg etc). Each of these states contained a survey office directing surveying activities. One of the attempts to connect various datums was during the First German Reich. The Reiehsdreieeksnetz began in Prussia through the Preußische Landesaufnahme (Prussian State Survey) along the Baltic coast as far as Berlin and Lübesk. This triangulation was continued under orders for the survey of Hannover by King George IV (the Hannover triangulation is known as Hannoversche triangle chain).


These networks had their origin normally at a major observatory such as Greenwich in London, Pulkovo near St. Petersburg and the Pantheon in Paris. Additionally these datums referenced a variety of ellipsoids making transformation calculations difficult. However a common more fundamental problem summarised by Hough (1948), on the original triangulation of Germany, was that...

“…no attempt [was made] to minimize the effect of the deflection of the vertical at the initial station” Hough (1948)

...and therefore errors in position were found at the place of joining to other triangulation networks before any transformation had even been started.

The direction of the vertical is defined by a local plumbline, where a survey instrument is set up to measure the horizontal plane that is exactly perpendicular to the vertical. The ellipsoid normal through the same point is perpendicular to the local tangent to the ellipse. However due to variations of gravity, the two are not necessarily coincident. The difference is called deflection-of-the-vertical.

Other technical issues existed for trying to connect existing triangulations. The connection between the New Triangulation of France (NTF) Datum and the Belgian Datum of 1927 is an example where the connecting of triangulation networks was insufficiently calculated. A calculation was conducted to find the difference in longitudinal values between Brussels and Greenwich. However this was result was not  incorporated in the joining of the triangulation networks and hence left large errors for the connection of the networks.


Germany - An example of “first order triangulation”

Since the formation of the First German Reich after unification in 1871, efforts had been made to standardise triangulation across the country beginning to solve some of the issues mentioned above. However, state military survey organisations within the German army produced uncoordinated products throughout the period up to the end of WW1, perhaps indicating disloyalty within the newly unified country. This lack of coordinatation and communication between survey organisations led to some poor quality mapping products being produced during the First World War (see Cruickshank, 2006 for more details).


After the First World War and the Treaty of Versailles in 1919 a reduction in military staff led to the demilitarisation of survey groups and the establishment of Reichsamt für Landesaufnahme (Reich Office for State Survey) who led an overhaul of Germany's mulitiple triangulations. A “Neutriangulation” of Bavaria, Baden, Württenberg, Silesia, Pomerania, Mecklenburg and Schleswig-Holstein took place in 1925. This “Neutriangulation” can been noted as a geodetic manifestation in the balance of power from the German Provinces.


As political tensions rose during the 1920 – 1930’s, driven in part by the dire economic situation throughout Germany and global depression, extremes in the political arena took hold eventually leading to the events that resulted in the rise of Nazism. Adolf Hitler and the Nazi party took hold of the country via emergency decree on 27th February 1933 after the Reichstag fire.


Development of a Military Survey

After the seizing of power by the Nazi’s Germany no longer cooperated according to the Treaty of Versailles, restoring pre-war military institutions and a 9th Division to the General Staff of the Army, known as the Military Survey (Reichsamt Kriegskarten und Vermessungswesen, see details about the organisation in Cruickshank, 2005). In 1936 Lt. Colonel Hemmerich was appointed Department Chief. Under Hemmerich’s leadership the division dealt with the collection, evaluation, cataloguing and co-ordination of foreign maps and geodetic data, which were collated and reported in the ‘Planhefte’. These became major publications of the German Military Survey.

Hemmerich.pngFigure 1 Lt. Colonel Hemmerich (image from


The development of the military survey coincided with early attempts by the Minister of the Interior to create a A Neuordnung des Vermessungswesens (New Order of Survey and Mapping) and by 1936 Survey Commissars were established throughout the regions of the now Third Reich. These commissars were also the local political leaders of individual states.

“In 1936 the German main triangulation network was readjusted. Since considerable portions were introduced into the readjustment without any modification and since others had not yet been observed completely, the readjustment could be carried out in parts only.”
Hough 1948

An attempt by the German's to create an early equivalent of the European Datum was started in preparation for, and developed throughout,  the Second World War. This was due to the failings of the pre-First World War military survey activity that resulted in poor location plots and the use of old data (see Cruickshank, 2006 for a detailed discussion). During the inter-war period lessons were drawn from the experience of the First World War,  in particular about the importance of collecting up-to-date foreign maps and geodetic data.


With war imminent in August 1939, the Military Survey was mobilized and made ready to be attached to the individual commanding authorities within the Germany Army. These geodetic units followed the German army into field of operations that by 1942 occupied the vast majority of Europe and Northern Africa.


World_War_II_in_Europe%2C_1942.svgFigure 2 Maximum Extent of Nazi Germany during World War 2 (image taken from wikipedia)



From this military position work began on the establishment of a single unified geodetic framework for the whole of continental Europe (including Northern Africa). Hemmerich’s division uniquely had control of nearly every geodetic department in Europe and thus controlled the expansion of a wealth of knowledge and equipment that would allow the Germans to accurately survey Europe. It is this work, carried out by Hemmerich’s division during the Second World War, that sowed the seeds for the creation of the European Datum.


Hemmerich lost his commanding post on 05th April 1945 where he was resigned to the Führerreserve and later arrested and imprisoned by Allied forces until 04 June 1947.


Next time we shall have a look at the development of the European Datum from the side of the allies and explore the story of the military intelligence division code named the HOUGHTEAM.


[1]This discrepancy was one of the major factors that prompted the recomputation of all geodetic control in Western Europe after the First World War. The Bonne Grid “New Convention” is also referred to as the “Orange Report Net Grid” and was used through WWII until 1950.



Cruickshank, J. L., 2005. “The Reichsamt fur Landesaufnahme and the Ordnance Survey (Part 1)”. Sheetlines, 72, pp.9-22

Cruickshank, J. L., 2006. “Kaiser Bill thought he knew where you lived”. Sheetlines, 77, pp.5-20

Hough, F., (1948) The adjustment of European first-order triangulation. Bulletin géodésique 7(1) pp35-41

Whilst not a blog written out on this site I thought this link was worth sharing. It discusses geodetic integrity and provides some nice insights into geodesy in the Oil and Gas Industry...positional integrity is so important in natural resource exploration and production it forms an essential element of the expensive process of drilling and producing Earth's natural resource.


Managing geodetic risks in E&P - Exprodat Blog -


"Geodetic integrity plays a small but vital part in the success of every E&P venture. It’s basically like Vitamin C: you don’t need much of it, but you can’t live without it. A deficiency in geodetic controls will slowly lead to guaranteed damage: “geo-scurvy”."


The following blog lays out some examples of where positional accuracy has not been good enough outside of the Lake Peigneur Example.





Managing geodetic risks in E&P - Exprodat Blog -

What is an antipode?

Any point on the surface of a sphere, in this case the Earth, that lies diametrically opposite from a given point on the same surface, so that a line drawn between the two points through the center of the sphere forms a true diameter (e.g. through the Poles of a Sphere). The Antipodes islands of New Zealand, in the South Pacific, are named after this phenomenon because of there "closeness" to the antipodes of London.


The image below shows the relative distribution of landmasses on opposite sides of the Earth.


How can you calculate the antipodal point for any point on the Earth's surface?


The method using decimal degrees:

Take the latitude and convert it to the opposite hemisphere. This is done by multiplying by minus 1 (e.g. -x * -1 = x).


The longitude is calculated by taking the maximum possible longitudinal value and subtracting the input longitude value. The if statements allow for "which way round the Earth" the calculation is conducted this is important because the values are bounded to +180 and -180. For example a longitude of -10 has an antipodal location of ((-180) - (-10))*-1 = 170.


# Original latitude and longitude values in Decimal Degrees
Latitude =  33.918861
Longitude = 18.4233

# Convert latitude to opposite hemisphere (e.g. −x* −1 = x)
AntiLatitide = Latitude *-1

print "Antipodal Latitude: " + str(AntiLatitide)

# Convert Longitude to opposite hemisphere (e.g. (180 - x)*-1 = y)
# Note this binds the maximum values to be -180 and 180 degrees
if Longitude > 0:
    AntiLongitude = (180 - Longitude)*-1
elif Longitude < 0:
    AntiLongitude = (-180 - Longitude)*-1

print "Antipodal Longitude: " + str(AntiLongitude)


A result...the Antipodal point of London

Combining the above code with the XY to Line tool allows me to construct a geodesic line joining the two points thus producing this result!



A free map calculating the antipodal point of any location:

An easier place to search for coordinate systems...

If you need a quick and easy to use resource for coordinate systems search try: This is an open source web-service providing a database based on the official EPSG database that is maintained by OGP Geomatics Committee.


You can quickly search for an area, name and type like any other web-search engines.


For Example searching "United Kingdom" and click on the British National Grid result produces the following page:


See below for a British National Grid example:

OSGB 1936 / British National Grid - United Kingdom Ordnance Survey - EPSG:27700


Some of the Key Features:

  • Easy full text search for the complete database of coordinate systems from EPSG
  • Short URLs that reference the EPSG code e.g.
  • Area of use for any CRS referenced on an embedded map
  • Export definitions in various formats


Check it's free

A common question asked when working with Coordinate Reference Systems (CRS) in ArcMap is not only how to transform between different CRS but simply what transformations are available between two CRS in a given area?

There are several ways of finding this information with ArcMap:


PDF resources found in your ArcMap installation:

C:\Program Files (x86)\ArcGIS\Desktop10.2\Documentation\projected_coordinate_systems.pdf

C:\Program Files (x86)\ArcGIS\Desktop10.2\Documentation\geographic_transformations.pdf

C:\Program Files (x86)\ArcGIS\Desktop10.2\Documentation\geographic_coordinate_systems.pdf


Using the OGP EPSG Area Polygons:

OGP's EPSG Area Polygons as Searchable Layers which is available to download from here @exprodat

blog_epsg_areapoly_image1.jpgUsing the ListTransformation and SpatialReference Object

The spatial reference object allows you to interrogate a layer, features class, shapefile, raster or a coordinate reference name to view or manipulate a spatial object's properties. These include spheroidName, datumName, projectionName, scaleFactor and many more.


In the below example the code interrogates the names of two projections systems, prints their spheroid name, geodetic datum and a list of transformations that are valid between the two projection systems within the specified extent.


# Define from and to Spatial Reference names
fromSpatRef = arcpy.SpatialReference('European Datum 1950 UTM Zone 31N')
toSpatRef = arcpy.SpatialReference('WGS 1984 UTM Zone 31N')

# Print the spheroid name for fromSpatRef and toSpatRef
print("from SpatRef spheroid: " + fromSpatRef.GCS.spheroidName)
print("to SpatRef spheroid: " + toSpatRef.GCS.spheroidName)

# Print the datum name for for fromSpatRef and toSpatRef
print("from SpatRef datum: " + fromSpatRef.GCS.datumName)
print("to SpatRef datum: " + toSpatRef.GCS.datumName)

# Extent for Central North Sea (values can be found in the data frame)
extent = arcpy.Extent(533553, 6469886, 993268, 6179505)

# list transformations valid for Central North Sea region
outlist = arcpy.ListTransformations(fromSpatRef , toSpatRef, extent)
print str(outlist)


This prints the following information:

from SpatRef spheroid: International_1924

to SpatRef spheroid: WGS_1984


from SpatRef datum: D_European_1950

to SpatRef datum: D_WGS_1984


[u'ED_1950_To_WGS_1984_1', u'ED_1950_To_WGS_1984_NGA_7PAR', u'ED_1950_To_WGS_1984_18', u'ED_1950_To_WGS_1984_2', u'ED_1950_To_WGS_1984_24', u'ED_1950_To_WGS_1984_25', u'ED_1950_To_ETRS_1989_4 + ETRS_1989_To_WGS_1984', u'ED_1950_To_WGS_1984_7', u'ED_1950_To_WGS_1984_36', u'ED_1950_To_WGS_1984_32_incorrect_DS', u'ED_1950_To_WGS_1984_32']



The ListTransformations function provides access to the list of transformations for a given area between any projection systems.


With this information it is possible to see a cut down list of what transformations are appropriate between any two CRS for a given area and investigate which of these is the appropriate method.


Further to this the syntax for a transformation method can be easily copy and pasted into other tools such as the Project Tool and can be used within a script such as the below.


# Set variables XY values can be presented as a list
x = 309905
y = 6320846
srIn = 'European Datum 1950 UTM Zone 31N'
srOut = 'WGS 1984 UTM Zone 31N'
Transform = 'ED_1950_To_WGS_1984_18'

# Create point geometry from xy variables and project to   srOut with Tranform method
pointGeometry = arcpy.PointGeometry(arcpy.Point(x,y),srIn,False, False)
projectedPoint = pointGeometry.projectAs(srOut, Transform)

# Copy the reprojected points to a shapefile

What are Geodesic distances?


A geodesic line is the shortest path between two points on a curved surface, like the Earth. They are the analogue of a straight line on a plane surface or whose sectioning plane at all points along the line remains normal to the surface. It is a way of showing distance on an ellipsoid whilst that distance is being projected onto a flat surface.


However there are several types of lines that have different definitions which are listed at the bottom of this blog.

Here's a video example of a geodesic line, the longest geodesic line possible without touching land.


The below image shows a planar distance in orange and the geodesic distance of that planar distance in blue. The maximum deviation of the geodesic from the planar line is near 2,000 Km and the difference in length is 644 Km.


What this image represents is the actual path taken (geodesic line) if I travel in a straight line, relative to me with no turns, from London to Singapore along the International 1924 ellipsoid (this is what I displayed the map in ArcGIS in EPSG:4022).GeodesicCurve.jpg


This type of measurement forms part of a series of geodetic features whose measurements account for the distortion of projected space. The distortion of a sphere into 2D space is nicely visualized in the video below:

Jarke J. van Wijk | Mathematical Art Galleries


Why is this important?

Apart from what can be very large differences between geodetic and planar measurements, see the above example, in the real world these differences can have a legal consequence such as those seen in constructing license areas for oil and gas exploration and production, international boundaries and exclusive economic zones.

An example of geodesic line constructions having a political role is seen in the Beaufort Sea International Border dispute between Canada (Canadian Yukon) and The United States (Alaska). The maritime boundary between the two countries has been defined differently. Canada claims the boundary to be along the 141st meridian west out to a distance of 200 nautical miles, following the Alaska-Yukon land border (this is derived from the 1825 boundary treaty between Great Britain and Russia). The United States on the other hand define the boundary line as stretching out to 200 nautical miles perpendicular to the coast whilst being equidistant from the coast.


Red line is the Canadian boundary, Blue line the USA boundary and the stippled area is claimed by both parties.

Building Geodetic distances in ArcGIS

The features you draw in a normal ArcMap edit session are not geodetic (they are planar) unless you create them using either the Advanced Editor Construct Geodetic tool or one of the following geoprocessing tools: Bearing Distance To Line, Table To Ellipse, or XY To Line. Geodetic features do not account for changes in terrain, this is a topic for another blog.

The Construct Geodetic tool is found in the "Advanced Editing" toolbar.

AdvancedEditor.jpgHere I shall make the Canadian border line which is defined as 200 nautical miles offshore along the Canadian-US border following the 141st Meridian Line.

  • First I specify the line type (note the other types defined below)
  • Use the snapping tool to add my start vertex to the end of the border
  • Change the segment type to Distance - Direction and specify the distance covered (changing it to Nautical Miles)
  • Specify the direction of the line

CanadianLineConstruct.jpgNow the line is constructed according to the chosen ellipsoid and is saved as a new feature upon saving edits.


Some terms used in ArcGIS:

Taken from About geodetic features

  • Geodesic line—The shortest line between any two points on the Earth's surface on a spheroid (ellipsoid). One sample use for a geodesic line is when you want to determine the shortest distance between two cities for an airplane's flight path. Another example is the creation of the path between the point of impact and the point of origin of a missile. This is also known as a great circle line if based on a sphere, rather than an ellipsoid. The geodesic line type allows you to create lines only. In addition, you can create a multi-segment line which is a series of geodesic lines that make up a single line feature. You can use a multi-segment line when you want to create an airplane's flight path with waypoints, such as an air route with multiple stops that make up a full route.
  • Geodesic circle—A shape whose edge is defined as a particular geodetic distance from a fixed point. Depending on the coordinate system in which it is displayed, it may not appear to be a circle. You might use this if you are creating a range ring of a weapon system, such as to show a weapon's effective range. Geodesic circles can be used to create either lines or polygons.
  • Geodesic ellipse—A shape whose sum of geodetic distances from a fixed pair of points is a constant. You could use this to create a signal error ellipse. This is also known as a geodesic circle when the major and minor axes are the same length. The geodesic ellipse type allows you to create lines or polygons.
  • Great elliptic—The line on a spheroid (ellipsoid) defined by the intersection at the surface by a plane that passes through the center of the spheroid and the start and end points of a segment. This is also known as a great circle when a sphere is used. The great elliptic type allows you to create lines only.
  • Loxodrome—A loxodrome is not the shortest distance between two points, but instead defines the line of constant bearing, or azimuth. Great circle routes are often broken into a series of loxodromes, which simplifies navigation. This is also known as a rhumb line. The loxodrome type allows you to create lines only.

Something extra to try:

A cool app to see the effect of the project on a straightline:

Shortest Distance on Earth

Courtesy of The Magiscian | DIY maps, geoapps, discoveries … and magic in geography

There are two tools in ArcGIS Desktop associated with using coordinate reference systems that often cause confusion. I believe these confusions are mainly sourced from the semantics surrounding projections and the tools in question.


The tools are the Define Projection and Project tools.


In a nut shell...

Define Projection: This tool overwrites the coordinate system information in a dataset

This means only use the Define Projection tool on a dataset that has no coordinate system applied or to a dataset you know for certain has the wrong projection.


Project: This tool projects a dataset from one coordinate system to another through transformation or conversion

Use the Project tool when you want to convert a dataset from one coordinate system to another. For example when converting from ED_50_UTM_31N to ED_50_UTM_30N or when transforming between ED_50_UTM_31N and WGS84_UTM_31N


For more information check out these resources...

Exprodat Blog !@

ArcGIS Help

Support Services Blog

GIS Geek



Have a look at a related course to learn more on managing and working with coordinate reference systems with ArcGIS:

ArcGIS Coordinate Reference Systems for Petroleum | CRS Spatial Reference Petroleum Oil Gas Industry ArcGIS ArcView Trai…

What is a Vertical Datum?

The Geodetic Glossary (2009) defines height as ‘distance, measured along a perpendicular, between a point and a reference surface’. This definition is concise and direct but leaves a vagueness concerning the reference surface. This reference surface is the Vertical Datum. A datum is required to reach accurate and reliable measures of height above a surface.


The EPSG dataset currently lists 128 vertical datums worldwide. There are various types of height including:


  • Ellipsoidal (The difference between the topographic elevation and the ellipsoid)
  • Orthometric (The difference between the topographic elevation and the geoid)
  • Geoid (The difference between the ellipsoidal height and the geoid surface Note this can be negative)


Heights are categorized into two types, those with reference to the Earth's gravity field and those defined on geometry alone. It is important to note that the two categories of height are not directly interchangeable as they are completely different. Where the gravity field heights are based on the geoid that is defined by a eqipotential surface compared to, for example, the height of a tree using right angle geometry where ground level is defined as 0 height.



Figure 1 Difference between the Geoid and Spheroid/Ellipsoid based surfaces and real topography (adapted from ESRI 2012) where h = Ellipsoidal height, N = Orthomatric height and H = Geoid height.


In my experience height is colloquially referred to as X units above or below Mean Seal Level (MSL). Sea level comes from the Earth' gravity field, therefore gravity is studied to understand height.


So, what is mean sea level?

In its simplest form MSL is the average location for the surface of the ocean measured over time to minimise random and periodic variation, such as tides and storm surges. The period of time to measure these variations in the ocean surface was set at 19 years by the U.S. National Ocean Surface, these measurements can be brought together to form a tidal datum.


However in this form MSL is not adequate as a global vertical datum as this mean calculation only exists at the station of measurement and its immediate vicinity, plus the ocean has a dynamic topography that is nicely summarised in this MinutePhysics video.


What is Sea Level? - YouTube


Why is a Vertical Datum important?

I work in the Oil and Gas industry and the application of a correct vertical datum is important in exploration, when defining a height or depth to a geological surface, and also when designing and implementing infrastructure projects such as pipelines, ports and other coastal infrastructure as well as when considering the environmental impacts that spills and other developments may have on coastlines and rivers. For example misunderstanding the vertical datum can impact planning for a storm surge that may have been measured on a different surface when compared to the height of a constructed LNG plant.


In essence there are 2 types of datums used in Vertical Coordinate Reference Systems:


Geoid-based versus Spheroid/Ellipsoid-based

The Geoid is a reference surface of the Earth and is based on the relationship between gravitational force and gravitational potential that produces a surface where all points are perpendicular to the force of gravity. Meyer (2010) provides an extensive review on the Geoid and the physics behind its construction. This surface is considered the proper surface to create geodetic heights and will nominally correspond to mean sea-level (see the previous video).


Recently there has been a move to see if data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) ESA project is able to be used with calculating heights and connecting height systems (see here). This will create a very high resolution Geoid for calculating heights across the globe.



Some examples of Geoid surfaces include:

  • EGM2008 Geoid
  • EGM84 Geoid
  • EGM96 Geoid


Spheroid/Ellipsoid-based surfaces use geometric calculations to define  the local datum and a spheroid.


It is important to note that it is impossible to transform between the geoid and Spheroid/Ellipsoid-based datums. This is because there are no common elements between the two reference systems and  no site-specific gravity measurements in a spheroid/ellipsoid system so no mathematical transformation can be applied.


Some examples of Spheroidal/Ellipsoid-based surfaces found in ArcGIS 10.2 include:

  • D_Cyprus_Geodetic_Reference_System_1993
  • D_Kuwait_Oil_Company
  • D_St_Lucia_1955


Figure 2 Example of the difference parts that make up a Vertical Datum as presented in ArcGIS.


The Geoid has a more complex surface than a Spheroid/Ellipsoid-based surface where the Spheroid/Ellipsoid-based surface shows a constant rate between chosen parameters of calculation whilst the geoid is ‘bumpy’ indicating the changing gravity measurements that represent the ‘real’ topography of the Earth (Figure 3).



Figure 3 The EGM96 Geoid. Taken from Wikipedia.


How do you set a vertical coordinate system in ArcGIS

When creating a new feature class tick the “Coordinates include Z values” option. This will enable the 3D measure of the feature class (Figure 4).



Figure 4 New Feature Class: Select Z values to enable 3D use


Click ‘Next’ to select the Geographic/Projected Coordinate System you want to use and then select the Vertical Coordinate System you would like to use.


Selecting a Vertical Datum.png

Figure 5. Choose the correct vertical coordinate system for you area of interest. Note that local Vertical CRS have been calculated from locally derived measurements and that MSL (Depth) and MSL (Height) use the EGM96 Geoid.


Summary and How to transform between Vertical Coordinate Reference Systems in ArcGIS?

Geoid-based vertical coordinate reference systems are lightly connected to their geographic coordinate system (GCS) and therefore almost any Geoid-based vertical coordinate reference system may be used with any GCS since they include a vertical datum as part of their definition.


Spheroid/Ellipsoid-based coordinate reference system defines heights that are referenced to the spheroid of a geographic coordinate system. A geographic coordinate system’s spheroid may fall above or below the actual earth surface due to the mathematic parameters used in calculating the surface.



A Spheroid/Ellipsoid-based coordinate reference includes a datum, rather than a vertical datum definition and hence will follow those transformations used when switching between different GCS and PCS (Project Coordinate Reference Systems).



Meyer, T. H., 2010. Introduction to Geometrical and Physical Geodesy: Foundations of Geomatics. ESRI Press pp. 246

"It is vitally important to understand the difference between changing the coordinate reference system (CRS) property of a geographic dataset and converting the feature coordinates of a geographic dataset to a different CRS.  Confusing them can lead to incorrectly located data and potentially some gross errors in the position of the features in your geographic data."


Follow these links to some useful blog articles on how to manage CRS in ArcGIS courtesy of @exprodat


Tip 12: Coordinates and ArcGIS - Blogs -


Correctly Aligning Features in ArcMap: 1 - Blogs -


Correctly Aligning Features in ArcMap: 2 - Blogs -


Correctly Aligning Features in ArcMap: 3 - Blogs -




Using OGP's EPSG Area Polygons

Posted by spk578 Jul 18, 2014

The International Association of Oil and Gas Producers (OGP) released EPSG Area Polygons in 2012 as a freely available spatial dataset that accurately defines the applicable extent of the CRSs and transformations in the EPSG Geodetic Parameter Dataset (EPSG Dataset). 


Check out the @Exprodat Blog on using OGP's EPSG Area Polygons



Download the OGP's EPSG Area Polygons as Searchable Layers