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HelmertTransform


Unit: SDL_geobasics
Class: none
Declaration: function HelmertTransform (CodeIn: integer; LatIn, LongIn, AltIn: double; CodeOut: integer; var LatOut, LongOut, AltOut: double): integer;

The function HelmertTransform converts coordinates between different geodetic datums specified by the parameters CodeIn and CodeOut. The transformation is a linear combination of a translation, a scaling and a rotation step which is calculated according to the following equation:

The transformation has to be performed in Cartesian space, thus the geodetic coordinates (latitude, longitude, and altitude) have to be converted to Cartesian ones before applying the transformation. All the conversions and the transformation are performed by the function HelmertTransform automatically, so the user only has to specify the initial and the target datum (parameters CodeIn, CodeOut), and the geodetic coordinates in the initial datum (parameters LatIn, LongIn, and AltIn for latitude, longitude, and altitude, respectively). The transformed geodetic coordinates are returned in the variable parameters LatOut, LongOut, and AltOut. The function returns the following error codes:

0 everything OK
-1 invalid CodeIn
-2 invalid CodeOut
-3 invalid LatIn
-4 invalid LongIn

The parameters CodeIn and CodeOut control the type of conversion and may be selected according to the following table:

    ---------------------------------------------------------------------------------------
    Code  Name                                Region                           Ellipsoid
    ---------------------------------------------------------------------------------------
    001   ACCRA                               Ghana                            gelWarOffice
    002   ADINDAN                             Burkina Faso                     gelClrk80
    003   ADINDAN                             Cameroon                         gelClrk80
    004   ADINDAN                             Ethiopa                          gelClrk80
    005   ADINDAN                             Mali                             gelClrk80
    006   ADINDAN                             Mean                             gelClrk80
    007   ADINDAN                             Senegal                          gelClrk80
    008   ADINDAN                             Sudan                            gelClrk80
    009   ANTIGUA ISLAND ASTRO 1943           Antigua                          gelClrk80
    010   AIN EL ABD 1970                     Bahrain                          gelInt24
    011   AIN EL ABD 1970                     Saudi Arabia                     gelInt24
    012   AMERICAN SAMOA 1962                 Samoa Islands                    gelClrk66
    013   RD, AMERSFOORT                      Netherlands                      gelBess41
    014   ANNA 1 ASTRO 1965                   Cocos Islands                    gelAuNat65
    015   ARC 1950                            Southern Africa                  gelClrk80
    016   ARC 1950                            Botswana                         gelClrk80
    017   ARC 1950                            Burundi                          gelClrk80
    018   ARC 1950                            Lesotho                          gelClrk80
    019   ARC 1950                            Malawi                           gelClrk80
    020   ARC 1950                            Swaziland                        gelClrk80
    021   ARC 1950                            Zaire                            gelClrk80
    022   ARC 1950                            Zambia                           gelClrk80
    023   ARC 1950                            Zimbabwe                         gelClrk80
    024   ARC 1960                            Kenya                            gelClrk80
    025   ARC 1960                            Tanzania                         gelClrk80
    026   ASCENSION ISLAND 1958               Ascension                        gelInt24
    027   MONTSERRAT IS. ASTRO 1958           Montserrat                       gelClrk80
    028   ASTRO STATION 1952                  Marcus Islands                   gelInt24
    029   ASTRO BACON E 1845                  Iwo Jima                         gelInt24
    030   AUSTRALIAN GEODETIC 1966            Australia                        gelAuNat65
    031   AUSTRALIAN GEODETIC 1984            Australia                        gelAuNat65
    032   DJAKARTA                            Indonesia                        gelBess41
    033   BEKAA BASE SOUTH END                Lebanon                          gelClrk80IGN
    034   BERMUDA 1957                        Bermuda                          gelClrk66
    035   BISSAU                              Guinea Bissau                    gelInt24
    036   BOGOTA OBSERVATORY                  Colombia                         gelInt24
    037   BERNE (1898),                       Switzerland                      gelBess41
    038   BUKIT RIMPAH                        Indonesia                        gelBess41
    039   CAPE CANAVERAL                      Florida & Bahamas                gelClrk66
    040   CAMPO INCHAUSPE 1969                Argentina                        gelInt24
    041   CANTON ASTRO 1966                   Phoenix Islands                  gelInt24
    042   CAPE                                South Africa                     gelClrk80
    043   CAMP AREA ASTRO                     Antarctica                       gelInt24
    044   S-JTSK                              Czech Republic                   gelBess41
    045   S-JTSK                              Slovakia                         gelBess41
    046   CARTHAGE                            Tunisia                          gelClrk80IGN
    047   CHATHAM ISLAND ASTRO 1971           New Zealand                      gelInt24
    048   CHUA ASTRO                          Paraguay                         gelInt24
    049   CH1903+                             Switzerland                      gelBess41
    050   CORREGO ALEGRE                      Brazil                           gelInt24
    051   OBSERVATOROI                        Mozambique South                 gelClrk66
    052   CYPRUS 1935                         Cyprus                           gelHongKong63
    053   ESTONIA 1937                        Estonia                          gelBess41
    054   DABOLA                              Guinea                           gelClrk80
    055   DECEPTION ISLAND                    Antarctica                       gelClrk80
    056   GUX 1 ASTRO                         Guadalcanal Island               gelInt24
    057   EASTER ISLAND 1967                  Easter Island                    gelInt24
    058   WAKE-ENIWETOK 1960                  Marshall Islands                 gelHough60
    059   EUROPEAN DATUM 1950                 Europe                           gelInt24
    060   EUROPEAN DATUM 1950                 Western Europe                   gelInt24
    061   EUROPEAN DATUM 1950                 Norway & Finland                 gelInt24
    062   EUROPEAN DATUM 1950                 Denmark                          gelInt24
    063   EUROPEAN DATUM 1950                 Channel Islands                  gelInt24
    064   EUROPEAN DATUM 1950                 Portugal and Spain               gelInt24
    065   EUROPEAN DATUM 1950                 Portugal                         gelInt24
    066   EUROPEAN DATUM 1950                 Balearic Islands                 gelInt24
    067   EUROPEAN DATUM 1950                 Spain (except NW),               gelInt24
    068   EUROPEAN DATUM 1950                 Spain NW                         gelInt24
    069   EUROPEAN DATUM 1950                 Gibraltar                        gelInt24
    070   EUROPEAN DATUM 1950                 Italy - Sardinia                 gelInt24
    071   EUROPEAN DATUM 1950                 Italy - Sicily                   gelInt24
    072   EUROPEAN DATUM 1950                 Malta                            gelInt24
    073   EUROPEAN DATUM 1950                 Former Yugoslavia N              gelInt24
    074   EUROPEAN DATUM 1950                 Greece                           gelInt24
    075   EUROPEAN DATUM 1950                 Cyprus                           gelInt24
    076   EUROPEAN DATUM 1950                 Turkey                           gelInt24
    077   EUROPEAN DATUM 1950                 Algeria                          gelInt24
    078   EUROPEAN DATUM 1950                 Tunisia                          gelInt24
    079   EUROPEAN DATUM 1950                 Egypt                            gelInt24
    080   EUROPEAN DATUM 1950                 Lebanon                          gelInt24
    081   EUROPEAN DATUM 1950                 Iran                             gelInt24
    082   EUROPEAN DATUM 1950                 Middle East                      gelInt24
    083   EUROPEAN DATUM 1950                 Oman                             gelInt24
    084   EUROPEAN 1979                       Europe                           gelInt24
    085   EUROPEAN 1979                       Portugal                         gelInt24
    086   ETRF89                              Europe                           gelWGS84
    087   FAHUD                               Oman                             gelClrk80
    088   OBSERVATORIO MET. 1939              Flores                           gelInt24
    089   FORT THOMAS 1955                    St Kitts-Nevis                   gelClrk80
    090   GAN 1970                            Rep. of Maldives                 gelInt24
    091   GEOCENTRIC DATUM AUSTRALIA          Australia                        gelWGS84
    092   GEODETIC DATUM 1949                 New Zealand                      gelInt24
    093   DOS 1968                            Gizo Islands                     gelInt24
    094   GRACIOSA BASE SW 1948               Azores                           gelInt24
    095   GGRS87                              Greece                           gelWGS84
    096   GUNUNG SEGARA                       Indonesia                        gelBess41
    097   GUAM 1963                           Guam                             gelClrk66
    098   HARTEBEESTHOCK 1994                 South Africa                     gelWGS84
    099   HELSINKI, KALLIO CHURCH             Finland                          gelInt24
    100   HERAT NORTH                         Afghanistan                      gelInt24
    101   MGI DATUM/HERMANNSKOGEL             Austria                          gelBess41
    102   HERMANNSKOGEL                       Former Yugoslavia                gelBess41
    103   HITO XVIII 1963                     Chile                            gelInt24
    104   HJORSEY 1955                        Iceland                          gelInt24
    105   HONG KONG 1963                      Hong Kong                        gelInt24
    106   HONG KONG 1980                      Hong Kong                        gelInt24
    107   HU-TZU-SHAN                         Taiwan                           gelInt24
    108   HUNGARIAN DATUM 1972                Hungary                          gelGRS67
    109   BELLEVUE (IGN),                     Efate Island                     gelInt24
    110   INDONESIAN 1974                     Indonesia                        gelIndo74
    111   IRAQ-KUWAIT BOUNDARY 1992           Iraq/ Kuwait                     gelWGS84
    112   INDIAN                              Bangladesh                       gelEver30
    113   INDIAN                              India & Nepal                    gelEver56
    114   INDIAN                              Pakistan                         gelEverPak
    115   INDIAN 1954                         Thailand                         gelEver30
    116   INDIAN 1960                         Con Son Island                   gelEver30
    117   INDIAN 1960                         Vietnam                          gelEver30
    118   1 INDIAN 1975                       Thailand                         gelEver30
    119   IRELAND 1965                        Ireland                          gelModifAiry
    120   ISTS 061 ASTRO 1968                 South Georgia                    gelInt24
    121   ISTS 073 ASTRO 1969                 Diego Garcia                     gelInt24
    122   JOHNSTON ISLAND 1961                Johnston Island                  gelInt24
    123   KANDAWALA JACKSON?                  Sri Lanka                        gelEver30
    124   KERTAU 1948                         Malaysia W & Sing.               gelEver48
    125   KERGUELEN ISLAND 1949               Kerguelen Island                 gelInt24
    126   KOREAN GEODETIC SYSTEM 1995         South Korea                      gelWGS84
    127   KKJ                                 Finland                          gelInt24
    128   KUSAIE ASTRO 1951                   Caroline Island                  gelInt24
    129   LC5 ASTRO 1961                      Cayman Brac                      gelClrk66
    130   LEIGON                              Ghana                            gelClrk80
    131   LIBERIA 1964                        Liberia                          gelClrk80
    132   LISBON (Castelo di S. Jorge), D73   Portugal                         gelInt24
    133   LKS94                               Lithuania                        gelWGS84
    134   LUXEMBOURG NT                       Luxembourg                       gelInt24
    135   LUZON                               Philipines - Mindanao            gelClrk66
    136   LUZON                               Philipines                       gelClrk66
    137   MASSAWA                             Eritrea                          gelBess41
    138   MERCHICH                            Morroco                          gelClrk80
    139   MIDWAY ASTRO 1961                   Midway Islands                   gelInt24
    140   MAHE 1971                           Seychelles - Mahe Is.            gelClrk80
    141   MINNA                               Cameroon                         gelClrk80
    142   MINNA                               Nigeria                          gelClrk80
    143   ROME 1940                           Italy mainland                   gelInt24
    144   ROME 1940                           Italy - Sardinia                 gelInt24
    145   ROME 1940                           Italy - Sicily                   gelInt24
    146   MPORALOKO                           Gabon                            gelClrk80
    147   VITI LEVU 1916                      Fiji - Viti Levu                 gelClrk80
    148   NAHRWAN                             Oman - Masirah Island            gelClrk80
    149   NAHRWAN                             Saudi Arabia                     gelClrk80
    150   NAHRWAN                             United Arab Emirates             gelClrk80
    151   NAPARIMA                            Trinidad & Tobago                gelInt24
    152   NORTH AMERICAN 1983                 US - Alaska                      gelWGS84
    153   NORTH AMERICAN 1983                 US - Aleutian                    gelWGS84
    154   NORTH AMERICAN 1983                 Canada                           gelWGS84
    155   NORTH AMERICAN 1983                 US - CONUS                       gelWGS84
    156   NORTH AMERICAN 1983                 US - Hawaii                      gelWGS84
    157   NORTH AMERICAN 1983                 Mexico                           gelWGS84
    158   NORTH AMERICAN 1927                 US - Alaska                      gelClrk66
    159   NORTH AMERICAN 1927                 Canada                           gelClrk66
    160   NORTH AMERICAN 1927                 Canada-Alberta/British Columbia  gelClrk66
    161   NORTH AMERICAN 1927                 US - Aleutian East               gelClrk66
    162   NORTH AMERICAN 1927                 US - Aleutian West               gelClrk66
    163   NORTH AMERICAN 1927                 Bahamas                          gelClrk66
    164   NORTH AMERICAN 1927                 Canal Zone                       gelClrk66
    165   NORTH AMERICAN 1927                 Caribbean                        gelClrk66
    166   NORTH AMERICAN 1927                 Central America                  gelClrk66
    167   NORTH AMERICAN 1927                 US - CONUS                       gelClrk66
    168   NORTH AMERICAN 1927                 Cuba                             gelClrk66
    169   NORTH AMERICAN 1927                 CanadaEast                       gelClrk66
    170   NORTH AMERICAN 1927                 US - Eastern                     gelClrk66
    171   NORTH AMERICAN 1927                 Greenland                        gelClrk66
    172   NORTH AMERICAN 1927                 Canada - Manitoba/Ontario        gelClrk66
    173   NORTH AMERICAN 1927                 Mexico                           gelClrk66
    174   NORTH AMERICAN 1927                 Canada - NW Territory            gelClrk66
    175   NORTH AMERICAN 1927                 San Salvador                     gelClrk66
    176   NORTH AMERICAN 1927                 US - Western                     gelClrk66
    177   NORTH AMERICAN 1927                 Canada - Yukon                   gelClrk66
    178   NTF                                 France                           gelClrk80IGN
    179   NGO 1948                            Norway                           gelBesselMod
    180   NORTH SAHARA 1959                   Algeria                          gelClrk80
    181   BELGIUM DATUM 1972                  Belgium                          gelInt24
    182   OLD EGYPTIAN 1907                   Egypt                            gelHelm06
    183   ORDNANCE GB 1936                    GB - Great Britain               gelAiry30
    184   OLD HAWAIIAN                        US - Hawaii Mean                 gelClrk66
    185   OLD HAWAIIAN                        US - Hawaii                      gelClrk66
    186   OLD HAWAIIAN                        US - Kauai                       gelClrk66
    187   OLD HAWAIIAN                        US - Maui                        gelClrk66
    188   OLD HAWAIIAN                        US - Oahu                        gelClrk66
    189   OLD HAWAIIAN                        US - Hawaii                      gelInt24
    190   OLD HAWAIIAN                        US - Hawaii                      gelInt24
    191   OLD HAWAIIAN                        US - Kauai                       gelInt24
    192   OLD HAWAIIAN                        US - Maui                        gelInt24
    193   OLD HAWAIIAN                        US - Oahu                        gelInt24
    194   PALESTINE 1928                      Israel                           gelNahrwan29
    195   AYABELLA LIGHTHOUSE                 Djibouti                         gelClrk80
    196   PITCAIRN ASTRO 1967                 Pitcairn Island                  gelInt24
    197   PICO DE LAS NIEVES.                 Spain - Canary Islands           gelInt24
    198   PORTO SANTO 1936.                   Portugal - Maderia               gelInt24
    199   PROV. S AMERICAN 1956               Bolivia                          gelInt24
    200   PROV. S AMERICAN 1956               Colombia                         gelInt24
    201   PROV. S AMERICAN 1956               Ecuador                          gelInt24
    202   PROV. S AMERICAN 1956               Guyana                           gelInt24
    203   PROV. S AMERICAN 1956               Chile North                      gelInt24
    204   PROV. S AMERICAN 1956               Peru                             gelInt24
    205   PROV. S AMERICAN 1956               South America                    gelInt24
    206   PROV. S AMERICAN 1956               Chile South                      gelInt24
    207   PROV. S AMERICAN 1956               Venezuela                        gelInt24
    208   POINT 58                            Burkina Faso & Niger             gelClrk80
    209   POINT NOIRE 1948                    Congo                            gelClrk80
    210   PULKOVO 1942                        Russia                           gelKrass40
    211   PULKOVO 1942                        Germany                          gelKrass40
    212   PULKOVO 1942                        Estonia                          gelKrass40
    213   PUERTO RICO & Virgin Is.            Puerto Rico & Virgin Islands     gelClrk66
    214   QATAR NATIONAL 1974                 Qatar                            gelInt24
    215   QATAR NATIONAL 1995                 Qatar                            gelInt24
    216   QORNOQ                              Greenland South                  gelInt24
    217   DHDN (RAUENBERG),                   Germany                          gelBess41
    218   REUNION                             Mascarene Is                     gelInt24
    219   RT90                                Sweden                           gelBess41
    220   SANTO(DOS), 1965                    Vanuatu - Espirito Santo         gelInt24
    221   SOUTH AMERICAN 1969                 Argentina                        gelSAm69
    222   SOUTH AMERICAN 1969                 Galapagos                        gelSAm69
    223   SOUTH AMERICAN 1969                 Bolivia                          gelSAm69
    224   SOUTH AMERICAN 1969                 Brazil                           gelSAm69
    225   SOUTH AMERICAN 1969                 Chile                            gelSAm69
    226   SOUTH AMERICAN 1969                 Colombia                         gelSAm69
    227   SOUTH AMERICAN 1969                 Ecuador                          gelSAm69
    228   SOUTH AMERICAN 1969                 Guyana                           gelSAm69
    229   SOUTH AMERICAN 1969                 Paraguay                         gelSAm69
    230   SOUTH AMERICAN 1969                 Peru                             gelSAm69
    231   SOUTH AMERICAN 1969                 South America                    gelSAm69
    232   SOUTH AMERICAN 1969                 Trinidad                         gelSAm69
    233   SOUTH AMERICAN 1969                 Venezuela                        gelSAm69
    234   SAO BRAZ                            Santa Maria Islands              gelInt24
    235   SAPPER HILL 1943 (2000 adj),        Falkland Islands                 gelInt24
    236   SCHWARZECK                          Namibia                          gelBess41Nam
    237   SOUTH EAST ISLAND                   Seychelles                       gelClrk80
    238   SOVIET GEODETIC SYSTEM 85           Russia                           gelSGS85
    239   PZ90 (GLONASS),                     Russia                           gelPZ90;
    240   SELVAGEM GRANDE 1938                Salvage Island                   gelInt24;
    241   DOS 71/4                            St Helena                        gelInt24;
    242   SIERRA LEONE DATUM 1960             Sierra Leone                     gelClrk80;
    243   SIRGAS                              South America                    gelWGS84;
    244   SOUTH ASIA                          Singapore                        gelModifFish60;
    245   S-42 (PULKOVO 1942),                Albania                          gelKrass40;
    246   S-42 (PK42),                        Czechoslavakia                   gelKrass40;
    247   S-42 (PULKOVO 1942),                Hungary                          gelKrass40;
    248   S-42 (PULKOVO 1942),                Latvia                           gelKrass40;
    249   S-42 (PK 1942),                     Kazakhstan                       gelKrass40;
    250   SYSTEM 1942/58 (PULKOVO 1942),      Poland                           gelKrass40;
    251   S-42 (PULKOVO 1942),                Poland                           gelKrass40;
    252   S-42 (PULKOVO 1942),                Romania                          gelKrass40;
    253   S-42 (PULKOVO 1942),                Romania                          gelKrass40;
    254   S-42 (PULKOVO 1942),                Afghanistan                      gelKrass40;
    255   TANANARIVE OBSERVATORY              Madagascar                       gelInt24;
    256   TRISTAN ASTRO 1968                  Tristan da Cunha                 gelInt24;
    257   TETE                                Mozambique                       gelClrk66;
    258   TIMBALAI 1948 (Everest),            Malaysia E & Brunei              gelEverest;
    259   TIMBALAI 1968,Adj of 1948           Malaysia E & Brunei              gelBess41;
    260   TIMBALAI 1968, Adj of 1948          Malaysia E & Brunei              gelEverest;
    261   TIMBALAI 1948 (Bessel),             Malaysia E & Brunei              gelBess41;
    262   TOKYO                               Japan                            gelBess41;
    263   TOKYO                               South Korea                      gelBess41;
    264   TOKYO                               Japan - Okinawa                  gelBess41;
    265   TERN ISLAND (FRIG), 1961            Antarctica                       gelInt24;
    266   VOIROL 1875                         Algeria                          gelClrk80IGN;
    267   WAKE ISLAND ASTRO 1952              Wake Island                      gelInt24;
    268   WORLD GEODETIC SYSTEM 1972          World                            gelWGS72;
    269   WORLD GEODETIC SYSTEM 1984          World                            gelWGS84;
    270   YACARE                              Uruguay                          gelInt24;
    271   ZANDERIJ                            Suriname                         gelInt24;
    ---------------------------------------------------------------------------------------

Hint: Be careful when adding additional datums, since the Helmert transformation parameters depend on the signs of the rotation matrix. Two different matrix versions can be found in the literature and on the Internet, and sometimes things are mixed up (i.e. the sign of the rotation parameters do not match the equation).



Last Update: 2012-Oct-20