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1. and height Latitude Longitude and height with optional input and output formats e ddd ddddd e ddd mm ss s e ddd mm mmm e and conversion between these formats e Lambert Conformal Conic projected coordinates E N and height metric East or West North and height e Universal Transverse Mercator projected UTM coordinates E N and height metric East North and height Coordinate conversions in COCOdat are always strict and apply rigid formulas series expan sion and or iterative algorithms that provide sufficient depth for all spatial extends and thus do not alter the accuracy of the user s genuine input coordinates When choosing a particular coordinate format either on the input or the output side certain default values are preset e g projection parameters cocodat offers the option of any parameter to be customized manually changes are rec ommended only to expert users though b transformation between default or user defined geodetic datum definitions e ISN93 represented by the most recent Icelandic reference network and current official geodetic datum in Iceland e Hj rsey55 ISN93 s predecessor applied for geodetic 1 e surveying pur poses until 1993 still occasionally found as horizontal map datum or geo detic datum of historic surveys Markus Rennen 5 LANDMALINGAR May 1 2004 ISLANDS e Reykjavik 1900 Iceland s oldest nationwide coordinate reference still oc casionally found as horizontal
2. vi atan Es Rs L L0 vi sinBO R Rs Es Q In K R sinBO Iteration for B newsinB exp 2 Q 1 exp 2 Q 1 do oldsinB newsinB f1 0 5 In 1 oldsinB 1 oldsinB e In 1 e oldsinB 1 e oldsinB Q f2 1 1 old sin B e 1 e old sin B newsinB oldsinB f1 f2 j while Math abs newsinB oldsinB gt 0 00000000001 B asin newsinB k 1 e sin2 B R sin BO a cos B 11 3 2 From Geodetic to Lambert Conformal Conic with Two Parallels Coordinates Having the same Datum Input Latitude B in radian Longitude L in radians Output E the east coordinate in meters N the north coordinate in meters Q 0 5 In 1 sin B 1 sin B e In 14e sin B 1 e sin B R K exp Q sinB0 vi LO L sinBO Markus Rennen 24 LANDNUELINGAR E E0 R sin v1 N Rb Nb R cos v1 k l e sin B R sin BO a cos B All formulas from Hooijberg 1 Abbreviation Variable Description a Semi major axis of the ellipsoid f Flattening of the ellipsoid e First eccentricity Bl Latitude of lower parallel Bu Latitude of upper parallel Ql Isometric latitude of lower parallel Qu Isometric latitude of upper parallel BO Central parallel latitude of projection origin K Mapping radius at the equator Q Isometric latitude Bb Latitude of false grid origin in case of 2 parallels latitude of standard parallel in case of 1 parallel RO Mapping radiu
3. False Easting 500000 0 False Northing False Northing gt 500000 0 Standard Parallel 1 Standard Parallel 1 64 25 Standard Parallel 2i Standard Parallel 2i 65 75 2 One Zone 25 telltale He AUD E EA RS M lih ABalb l 669541 3 582285 6 62 8 aeldingur 671050 7 E8207 2 62 9 Figure 15 Output file format If the result is considered satisfying the displayed file can be saved by File Save as in the Browser s main menu A pop up window will be displayed and the local path can be chosen The temporary file name can be overwritten standard output is an ASCII text file Note In HTML Icelandic letters accepted in point number name might not be displayed correctly The stored ASCII file will contain Icelandic letters In case the user does not expect difficulties the file can also be locally stored with out viewing by a right click on the Open button Within the pop up window chose Save target as and proceed as common If Hj rsey55 Lambert projected output is chosen a switch appears underneath the output file field Figure 16 that allows altering between negative or positive East values as output format according to the user s software requirements If marked cocodat will return negative Lambert t proje jected East values Figure 16 Choice of output format for Lambert projected Hj rsey55 coordinates Since a number of software packages e g Arcinfo cannot handle westward positive
4. cocodat Coordinate Converson and Datum Transfomation in Iceland Version 1 3 Online Software Manual and Technical Reference May 1s 2004 Ea LANDM ELINGAR ISLANDS Version 1 3 of cocodati was thoroughly tested and appeared to work flawlessly However as any new release it is expected to reveal inconveniences obstacles and or even malfunction in everyday use Users are encouraged to hand in suggestions and report encountered bugs Thank you in advance Markus Rennen Markus Rennen 2 LANDNUELINGAR 1 General Product Information The online tool cocodat has been developed in its entirety at Landm lingar Islands LM Program author Dalia Prizginiene dalia ilmi is supervision Markus Rennen markus Imi is The mathematics is taken from the sources reported at the end of this manual see References the online tool itself was created using HTML Java Script and Java 2 About this Manual This manual is supposed to guide the user through the operation of cocodat It does NOT intend to contain all necessary information regarding coordinates coordinate formats geodetic datum definitions projections etc For general information the user is referred to the geodetic literature for specifics of Icelandic definitions it 1s recommended to refer to RENNEN M Basics on Coordi nates and their Reference available on the LMI homepage http www lmi is landmaelingar nsf HtmlPages Coordinates in Ice
5. VX Y 1 2 f f y h 0 01 There is quick convergence for h lt lt N starting at h 0 oldh 0 Iteration for B and h do oldh h N C 41 e cos B B atan Z N X Y 0 2 f f NN Z h 4X Y cos B N j Markus Rennen 26 LANDNUELINGAR May i 2004 ISLANDS while abs h oldh gt 0 0000000000001 2 Variables Description e Second eccentricity squared Flattening of the ellipsoid Semi major axis of the ellipsoid Polar radius of curvature ZaSS r0 The distance to the Z axis along the normal at the point B L 11 6 3D Transformation Input Xold Yold Zold coordinates of old Datum Output Xnew Ynew Znew coordinates of new Datum The middle part of the concatenated transformation from geocentric to geocentric 1s usually described as a simplified 7 parameter Helmert transformation and expressed in matrix form in what 1s known as the Burse Wolf formula Xnew Xold Dx Ynew M R Yold Dy Znew Zold Dz M 1 Ds 0 000001 3 cosRz sinRz OlcosRy O0 sinRy 1 0 0 R sinRz cosRz 0 0 l 0 0 cosRx sinAx 0 0 lAsnRy 0 cosRy A0 sinRx cos Rx For control the following formula was used Xold Xnew Dx Yold Ro Ynew Dy Zold Znew Dz Variable Description M The scale correction to be made to the position vector in the source coordinate system in order to obtain the correct scale in the target coordinate system Markus Rennen 27 LANDNUELIN
6. E3 11 1 1 From Universal Transverse Mercator UTM to Geodetic Coordinates Having the Same Datum Input Easting E in meters Northing N in meters Output Latitude B in radian Longitude L in radian omega N N0 S0 k0 r Bf omega sin omega cos omega V0 V2 cos omega V 4 cos omega V6 cos omega Rf k0 a 41 e sin Bf Q E E0 Rf Markus Rennen 18 LANDNUELINGAR May i 2004 ISLANDS tf tan Bf nif e cos Bf Constants B2 0 5 tf 1 nif B4 5 3 1f e nif 1 9 1 A nif 12 B6 61490 of A5 tf nif 46 252 tf 90 tf 360 B3 142 1f t nif 6 B5 5 28 tf 24 tf nif 6 8 1 2 120 B7 2 614 662 tf 1320 tf 720 1f 5040 B Bf B2 O 1 Q B4 B6 Q L1 Q Q B34 Q B5 B1 Q y LO zone 30 6 3 3 1415926535897932384626433832795 180 L L0 L1 cos Bf D1 tf D3 1 ff nif 2 nif 3 D5 24 5 tf 3 1f 15 G2 0 5 1 nif G4 1 5 nif 12 vi D1 O 1 Q D3 D5 Q k k0 1 G2 Q 1 G4 Q All formulas from Hooijberg 1 11 1 2 From Geodetic to Universal Transverse Mercator UTM Having the Same Datum Input Latitude B in radian Longitude L in radians Output Easting coordinate E in meters Northing N in meters LO zone 30 6 3 L1 L L0 3 14159265358979323846264
7. Hayford 1909 are synonym and refer to exactly the same spheroid For GRS80 resp WGS84 see the WGS84 publication by NIMA 12 References 10 2 Transformation parameters Table 3 Default Transformation Parameters Deby Bi p Rx Ry Rz in Ds in ppm Reykjav k 1900 Hj rsey 55 ISN93 Dx 629 020 Rx 4 154 Dx 5560 20 Rx 4 154 Reykjav k 1900 Dy 214 701 Ry 0 269 Dy 168 701 Ry 0 269 Dz 1028 364 Rz 2 279 Dz 942 364 Rz 2 279 Ds 3 729 Ds 3 729 Dx 629 019 Rx 4 154 Dx 73 Rx 0 Hj rsey 55 Dy 214 730 Ry 0 269 Dy 46 Ry 0 Dz 1028 365 Rz 2 279 Dz 86 Rz 0 Ds 3 729 Ds 0 Dx 5560 19 Rx 4 154 Dx 73 Rx 0 Dy 168 730 Ry 0 269 Dy 46 Ry 0 Dz 942 365 Rz 2 279 Dz 86 Rz 0 Ds 3 729 Ds 0 The transformation parameters between Hj rsey55 and ISN93 are taken from DMA Technical Report Supplement to the Department of Defense World Geodetic System The semi major axis of the Danish ellipsoid is genuiniely defined in the historic unit TOISE 3271883 257 The digits after the comma are derived result from toise meter conversion and DO NOT indicate the accuarcy level Flattening WGS84 1 f 298 257223563 yielding a difference in semi minor axis of 0 1mm millimeter Thus for all practical purposes the GRS80a nd WGS84 spheriod can be considered as equal Markus Rennen 16 LANDMALINGAR May 1 2004 ISLANDS 1984 Part II Parameters Formulas and Graphics for
8. counting direc tions as historically defined for Hj rsey55 or Reykjav k 1900 these tools incorrectly change the false easting to 500000m and in doing so alter the direction of growing East values cCocodat has a feature that allows the user to choose whether input or output East coordinates are provided or shall be obtained with negative index This feature is supposed to make further editing obsolete especially when working with ASCII file import However the user should be confident in knowing what type of coordinate format his her software requires and how it 1s handling it e g file does not contain the format defined in the projection format section coordinates exceed the defined boundaries for instance if Longitude value is not negative 1 e 22 23456 instead of 22 Markus Rennen 15 LANDNALINGAR May i 2004 ISLANDS n dii 10 Default Settings 10 1 Datum definitions Table 2 Spheroid parameters Ellipsoid a m 1 f Reykjavik 1900 Danish Andr 6377019 25666 300 Hj rsey 1955 International 1924 6378388 297 ISN93 GRS80 WGS84 6378137 298 257222101 User Defined No defaults The default datum definitions resp spheroid parameters are taken from the sources stated in the references For details on the derivation of the Danish spheroid s parameters the user is referred to Markus Rennen s report available in pdf format on the LM homepage see Refer ences 12 The spheroid terms International 1924 and
9. definition does NOT require transformation parameters and can therefore be performed without loss of quality In order to perform this operation o A and height East North and height in cocodat the ISN93 datum has to be chosen on both sides i e the input side on the left and the output side on the right Further information for program operation see below A misunderstanding going along with the above mentioned is the presumed scale of the ISN93 The ISN93 does not have a scale The apparent scale detected between true distances and coordinate derived distances alongside practical surveys is not caused by the ISN93 but by the frequently associated Lambert Conformal Conic projec tion ISN93 coordinates in geocentric cartesian X Y Z format do not show any scale except random errors Scale is simply a problem of the chosen projection When using projected coordinates for practical purposes e g construction small scale surveys lt lkm can be corrected by applying the local scale provided by cocodat In larger areas espe cially North South extension for Lambert coordinates resp East West extension for UTM coordinates the scale 1s changing significantly for projected coordinates It is rather difficult to handle this change in practice Thus it is strongly recommended not to use projected coordinates for extended surveys Calculations can be carried out in non scaled coordinate formats such as cartesian If complex soft wa
10. e sin B R sin B0 a cos B 11 2 2 From Geodetic to Lambert Conformal Conic with One Parallel Coordinates Having the same Datum Input Latitude B in radian Longitude L in radian Output East E in meters North N in meters Q 0 5 In 1 sin B 1 sin B e In 14e sin B 1 e sin B R K exp Q sin B0 Markus Rennen 22 LANDNUELINGAR vi L0 L sin BO E E0 R sin v1 N Rb Nb R cos v1 k 2 40 e sin B R sin BO a cos B All formulas from Hooijberg 1 11 3 Lambert Conformal Conic with Two Parallels e 4 Q f f QI 0 5 In 1sin Bl 1 sin Bl e In 1 e sin Bl 1 e sin Bl Qu 0 5 In 14sin Bu 1 sin Bu e In 1 e sin Bu 1 e sin Bu WI 4 0 e sin BD Wu 40 e sin Bu sinB0 In Wu cos Bl Wl cos Bu Qu Ql BO asin sinBO K a cos Bl exp Ql sinBO0 Wl sinBO Qb 0 5 In 1 4sin Bb 1 sin Bb e In 1 e sin Bb 1 e sin Bb Q0 0 5 In 1 sinBO 1 sinBO e In 1 e sinBO 1 e sinBO RO K exp QO0 sinBO Rb K exp Qb sinB0 WO0 41 e sin BO k0 WO tan BO RO a NO Rb Nb RO Markus Rennen 23 LANDNUELINGAR May i 2004 ISLANDS 11 3 1 From Lambert Conformal Conic with Two Parallels to Geodetic Coordinates Having the Same Datum Input E east coordinate N north coordinate Output B Latitude L Longitude Rs Rb N Nb Es E EO
11. grow northwards Table 1 9 2 ASCII File Import cocodatc allows the import and export of ASCII text files c SE o E 4 Je VA Figure 12 File Input In order to indicate that file input is desired the switch in front of the file input line must be market as shown in Figure 12 Pressing the Browse button will open a standard window that enables to select a file from the user s local computer An input file contains of at least one line and three coordinate components sorted in columns separated by a TAB delimiter Optionally cocodat also accepts coordinate files with the first column containing the point number Figure 13 As point numbers all kinds of numeric alphanumeric or combined strings of in principle infinite length are allowed except the point num ber name must not contain a blank white space cocodati recognizes automati cally whether the file contains point numbers names in the first column It is mandatory that all columns contain an entry e g if the height column does not contain any entry the first column containing the point number name will be inter preted as first coordinate component and most probably cocodat will return an er ror message or entirely wrong coordinates Figure 13 ASCII File Format Figure 13 shows a typical ASCII input file Column one contains the point num ber name while the next columns contain the coordinate components In the displayed TAB delimiter was c
12. long period polynomial effects an Iceland specific linear shift is applied subsequently e When choosing one of the projected coordinate formats Universal Trans verse Mercator UTM or Lambert Conformal Conic the coordinate fields to E N h and H a MSL appear 1 e metric East North and height values The definition and handling of the height values is analog to the description above Though not characteristic for any particular datum specific projections are as sociated with specific datum definitions In general that 1s e SN93 Lambert Conformal Conic two parallels e Hj rsey55 Lambert Conformal Conic one parallel e Reykjav k1900 Lambert Conformal Conic one parallel parallel s refers to the number of Standard Parallels for details refer to the recommended lit Markus Rennen 11 LANDNALINGAR May i 2004 ISLANDS LE The default projection parameters are preset in COCOdat Table 1 Be aware that e though the projection common for 7j rsey55 and Reykjavik1900 both feature one standard parallel the projection parameters central merid ian false easting and false northing differ e variations in spheroid parameters do have impact on the result The default parameters of projections used in Iceland are displayed in Table 1 Table 1 Default Projection Parameters used in Iceland Central Latitude of Eis Mae Standard Standard one Meridian Grid Origin 46 8 ud 8 Parallel 1 Parallel
13. the Practical Application of WGS84 DMA TR 8350 2 B 1987 updated 2003 In 1993 the contemporary WGS84 coincided with ITRF93 ISN93 itself was referenced to ITRF93 hence in 1993 WGS84 coordinates and ISN93 can be considered as referring to one and the same da tum The current deviations between WGS84 and ISN93 referenced coordinates is sufficiently ex plained by tectonic plate motion and thus does not exceed a few decimeter Taking into account the accuracy of the Hj rsey55 to WGS84 transformation parameters oX oY c3m resp oZ 6m the difference between ISN93 and WGS84 can be neglected when applying this transformation The transformation parameters between Reykjavik 1900 and Hj rsey55 were derived from the coordinate list published by Gunnar Porbergsson Orkustofnun For details see 12 References b rbergsson transforms the coordinates in several steps using only one identical point No 86 Reykjav k Astronomic Station Thus the derived parameters may prove less representative the more the user departs from this station However the results have been checked against graphic validations car ried out by NIMA available at LM and seem to be sufficient throughout the country for cartographic purposes The accuracy can be estimated below 10m In order to conduct the transformation in several steps Porbergsson s results have been converted into a one step 7 parameter affine transformation Note Transformations involving rotatio
14. www os is g surveying transformations 6 http earth info nima mil GandG datums dtp CountryEuropeTable html HJO 7 http www posc org Epicentre 2_2 DataModel ExamplesofUsage eu_cs35 ht ml Markus Rennen 28 LANDNUELINGAR ISLANDS May 1 2004
15. zero meridian de fined at the Copenhagen Observatory Note For Reykjavik1900 geographic coordinates West of Copenhagen Observatory is de fault Be aware of the origin of your coordinates A switch that enables to choose the suitable zero meridian is active when the Reykjavik 1900 datum is chosen in the Datum Definition section Figure 11 The output will always refer to the Greenwich zero meridian Sense ess o Bb ooo ooo ooo Figure 11 Greenwich vs Kopenhagen Zero Meridian Geographic coordinates are curvilinear surface coordinates and require the definition of a spheroid in the Datum Definition section Unlike geocentric coordinates they also feature a height The reference surface of this height needs to be known and defined when transforming coordinates 1 e ellipsoidal or MSL heights d cocodatc offers the user to enter heights as ellipsoidal heights A or physi cal heights referenced to Mean Sea Level MSL H a MSL only one of the height fields h or H a MSL alternatively should contain an entry the other one is to leave blank If both fields contain entries only h will be processed by cocodat cocodat can be used to transform h to H a MSL or vice versa In the internal workflow the geoid height interpolation and application to the input height is carried out as final step The geoid used for Icelandic is the Nordic Geodetic Commission s NKG96 In order to eliminate
16. 2 Lambert Conformal Conic 0m 0m f 19 01719 65 65 00 00 65 00 00 Reykjavik1 900 West North Lambert Conformal Conic 18 00 00 65 00 00 PUDE oe 65 00 00 Hj rsey55 West North Lambert Conformal Conic 500000m 500000m E IONOS 19 00 00 65 00 00 North 64 15 00 euer 45 00 Universal Transverse 0 s 0 00 00 500000m 0m zu o Mercator UTM 15900700 Equator East t North f Metric UTM coordinates are hardly in use in Iceland anymore though some map corpuses projected 1n UTM are still in use e g C762 or C761 In order to calculate with metric UTM coordinates the correct zone has to be chosen by the user in the Format Projection Parameter section Iceland is covered by three UTM zones see Table 1 cocodat allows the transformation from one UTM zone into the neighbor ing zone if the coordinates are located within a 0 5 overlapping area for co ordinates outside an error message will appear g When using projected plane coordinates distances are obtained scaled The scale varies with chosen map projection and location cocodat displays the local scale introduced to by the map projection in the Format Projection Parameter Section Thus in order to obtain true distances the calculated projected distance has to be multiplied with the inverse scale true distcance calculated distance scale Note Since the change of scale is a function of location direction and map projection the ap plicati
17. 33832795 180 cos B S0 k0 r B sin B cos B 12 E1 cos B E2 cos B E3 R k0 a Al1 e sin B Markus Rennen 19 LANDNUELINGAR May i 2004 ISLANDS t tan B ni 2 Je cos B Constants Al R A3 2 1 t ni 6 A5 2 5 18 t t o ni 14 58 1 120 AT 61 479 t 179 t 1 5040 A2 0 5 R t AA 5 t ni 9 4 ni 12 A6 61 58 t t ni 270 330 1 360 E E0 A1 L1 14 LI A3 LY 454 A7 L1 y N S S0 N0 A2 LV 12 LY A4 A6 L1 Constants C t C3 123 ni 42 ni 3 C5 2 t 15 F2 2 0 5 12 ni FA 5 4 f e ni 9 24 12 12 k k0 1 F2 LY 1 FA LIPY vi C1 L1 1 L1 C3 C5 L1 All formulas from Hooijberg 1 Abbreviation Variable Description f Flattening of the ellipsoid k0 Grid scale factor assigned to the central meridian e First eccentricity squared e Second eccentricity squared a Semi major axis of ellipsoid n Second flattening r Radius of the rectifying sphere C Constants for meridian arc U0 U2 U4 U6 Constants for meridian arc Markus Rennen 20 LANDM LINGAR May i 2004 ISLANDS V60 V2 VA VO Omega Rectifying latitude R Radius of curvature in the prime vertical zone Zone number k Point grid scale factor LO Central meridian N Northing coordinate on the projection NO False northing constant assigned to the latitude of grid ori gin S0 Merid
18. GAR Mav 1 ISLANDS ay 1 2004 m aii Rx Ry Rz Rotations to be applied to the point s vector in radians Dx Dy Dz Translation vector to be added to the point s position vector in the source coordinate system in order to transform from source system to target system also Ds The scale correction expressed in parts per million 11 7 Geoid s implementation Searching for h ellipsoidal height having H over MSL or searching for H over MSL having h the geoid s height N is required For interpolation Geoid Gravsoft is used H over MSL h N offset offset 1 2733m calculated by Markus Rennen LM for Iceland Geoid Gravsoft geoid interpolation and transformation software version MRR95 lt c gt RF by Kort og Matrikelstyrelsen Denmark 12 l References HOOUBERG Practical Geodesy using computers 1997 Springer Verlag Berlin Heidelberg NIMA DMA Technical Report Supplement to the Department of Defense World Geodetic System 1984 Part II Parameters Formulas and Graphics for the Practical Application of WGS54 DMA TR 8350 2 B 1987 updated 2003 RENNEN M Basics on Coordinates and their Reference February 2002 version 2 3 Febr 25 2004 http www lmi is landmaelingar nsf HtmlPages Coordinates in Iceland Sfile Coordinates in Iceland pdf unpublished STRANG G BORRE K Linear Algebra Geodesy and GPS 1997 Wellesley Cambridge Press PORBERGSSON G http
19. e default values represent the parameters com monly associated with the chosen projection in Iceland International 1924 is identical to Hayford 1909 and GRS80 equals for all practical purposes the WGS84 ellipsoid Markus Rennen 9 LANDNMUELINGAR T2 May 1 2004 Th A mouse click on the Change button beside the Projection Format drop down list activates the fields for customized user entries This option is generally meant for user defined projections Customizing parameters is strongly recommended to expert users only Note Changes might not only affect absolute coordinates but also relative coordinates e g distances 9 Coordinate input cocodat is designed for single point input 9 1 as well as import and export of ASCII files 9 2 9 1 Single Point Input Single point input is understood as on screen entries an input file might also contain only one point see ASCTI File import Single point input is the default mode and active when cocodat is launched In or der to select single point input after ASCII file import has been used before the switch in front the single point input line has to be activated Figure 10 Moses OE a Fs 1 gH 0 M ET E Browse d geb ur nl ba fear tet eet oe g etl ate sg Figure 10 Single Point Input Single point input returns a single point output in the output area on the right It is not possible to direct the output i
20. ection parameters bottom section have to be dealt with separately The middle section also contains the parameters for a 7 parameter datum transforma tion For three predefined datum definitions default transformation parameters are preset Spheroid parameters commonly associated with the chosen datum definition are set default A mouse click on the Change button beside the Datum Definition drop down list activates the fields for customized user entries This option is generally meant for user defined datum definitions Customizing parameters is strongly recommended to expert users only Note Changes might not only affect absolute coordinates but also relative coordinates e g distances Mieimm jen o o ooo B T a Figure 9 Logical separation of settings 8 5 FormatlProjection Parameter Section The lower section is dedicated the fundamental coordinate format The available choices contain two unprojected formats cartesian and geographic and two projected UTM and Lambert Conformal Conic coordinate formats The choice of coordinate format in this section determines the units expected as input resp being returned as output in the upper Coordinate Settings section In case of unprojected formats are being chosen the parameters below are without significance and therefore deactivated When one of the two projected coordinate formats 1s chosen projection parameters appear in the fields of this section Th
21. ee 9 1 1 by selecting the switch beside the file entry field Figure 12 Equivalent to single point input the de sired height reference has to by chosen on the output side as well As shown in Table 1 the projected coordinates feature historically constituted positive counting directions that differ in East West Especially with Hj rsey55 Lambert projected coordinates that frequently leads to confusion for most GIS software packages e g ArcInfo do not accept westward positive counting directions In many cases the correct false easting of 500000m is thus often substituted by the formally wrong false easting value of 500000m i e negative East values cocodat recog nizes the automatically whether positive or negative East values are imported and handles them accordingly For output see 9 3 below 9 3 ASCII File Output When the input file and the datum and projection format settings are chosen the trans formation conversion is performed by pressing the Transform button The processing might take a while depending on file size 1 e the number of points Progress is indicated by the Browser s standard progress bar After processing the input screen switches to the output screen and the formerly inac tive Open Button on the right of the output file field 1s activated Figure 14 Figure 14 Output screen in file input mode In order to regard for the users security it is not possible to save the output file directly
22. hosen since software packages such as Microsoft Excel can easily export and pen files with columns separated by TAB As remedy the blank should be repalced by any other ASCII symbol e g an underline as in YTRI STRAKUR Markus Rennen 13 LANDMALINGAR May i 2004 ISLANDS case the Latitude and Longitude values are given in ddd mm ss s format and there fore occupy each wise three columns separated by a TAB delimiter cocodat re cognizes automatically whether the input format of geographic coordinates 1s ddd mm ss s ddd mm mmm or ddd ddddd It is mandatory that Latitude and Longitude values have the same format Decimal separator is a lower dot The order of coordinate components is equivalent to the single point input For geo centric cartesian coordinates that is X Y Z for geographic coordinates Latitude Lon gitude height for all projected coordinates it is East North and height cocodat allows the input file to contain comment lines e g a header A line is con sidered as comment lines and therefore ignored if it is preceded by a see Figure 13 The comment line is not conveyed to the output file As for single point input the ASCII file import requires the definition of datum and projection format on the input side as well as on the output side Additional to the user definitions required in single point the user has to define whether the heights in the file refer to hA or H a MSL s
23. ian distance from the equator to BO multiplied by the central meridian scale factor Vi Meridian convergence angle E Easting coordinate on the projection E0 False easting constant assigned to the central meridian B2 B3 B4 B5 B6 B7 Constants D1 D3 D5 G2 G4 BO Parallel of geodetic latitude grid origin B Parallel of geodetic latitude positive north L Meridian of geodetic longitude positive east S Meridian distance 11 2 Lambert Conformal Conic with One Parallel e 4 2 f f Qb 0 5 In 14sin Bb 1 sin Bb e In 1 e sin Bb 1 e sin Bb Q0 0 5 In 14sin BO 1 sin BO0 e In 1 e sin BO 1 e sin BO WO 41 e sin B0 k0 1 K a k0 cos B0 exp Q0 sin B0 W0 sin B0 R0 K exp Q0 sin B0 Rb K exp Qb sin B0 Nb N0 Markus Rennen 21 LANDM LINGAR May ikg 2004 ISLANDS 11 2 1 From Lambert Conformal Conic with One Parallel to Geodetic Coordinates Having the Same Datum Input E east coordinate N north coordinate Output B latitude L longitude Rs Rb N Nb Es E E0 vi atan Es Rs L L0 vi sin BO R Rs Es Q In K R sin BO Iteration for B newsinB exp 2 Q 1 exp 2 Q 1 do oldsinB newsinB f1 0 5 In 1 oldsinB 1 oldsinB e In 1 e oldsinB 1 e oldsinB Q f2 1 old sin B e d e old sin B newsinB oldsinB f1 f2 j while Math abs newsinB oldsinB gt 0 00000000001 B asin newsinB k 1
24. kflow using the NKG96 Geoid sup plemented by an Iceland specific linear offset calculated at LMI d On screen input of individual point coordinates and corresponding on screen output or file input with corresponding file output e Online assistance Help T Help Figure 1 Help access The online help or rather online assistance provided by cocodat was designed to support users with answers to simple questions e g entry formats for detailed in formation refer to this manual or the recommended literature Instructions for online assistance access can be found on the top right of the input screen Figure 1 Online assistance is available only for active fields 1 e highlighted white The online assistance appears in pop up windows In order to open the online assistance the field has to be marked by placing the cursor by mouse click in the desired field with the blinking cursor inside the field the as sistance appears after right mouse click inside the active field The top right of the input screen also features a link to download this user manual as pdf document Markus Rennen 6 LANDNALINGAR May i 2004 ISLANDS 8 Structure of cocodat 8 1 Input and Output When opening cocodat with a standard browser the input screen appears see Figure 3 Entries or changes can only be made in the input screen Active entry fields or switches are highlighted white Figure 2 left while non active fields or swi
25. land file Coordinates in Iceland pdf 3 Legal Remark Although thoroughly tested any software might present errors bugs and or malfunc tions The National Land Survey of Iceland LM cannot be held responsible for complica tions caused by software errors faulty use or misinterpretation temporary unavail ability of the online application etc and any emerging implications The same applies for the contents of this manual Except NKG Geoid and subroutine for Geoid height interpolation by Ren Forsberg KMS courtesy of Kort amp Matrikelstyrelsen National Land Survey of Denmark Markus Rennen 3 tne ul ISLANDS WE May 1 2004 4 Practical remark for Iceland A common but nevertheless serious misunderstanding in Iceland is to refer to coordinates given in Latitude g Longitude 4 and height as WGS84 while coordinates in East North and height are labeled as ISN93 This is simply wrong WGSS84 and ISN93 are different datum definitions and due to tectonic plate motion currently showing a difference of a few decimeters or with other words coordinates given in one of these datum definitions need to be shifted a few decimeters to fit into the other However and that is the misunderstanding it is not this difference the users are usually trying to cor rect between WGS84 and ISN93 in general they need to change format from 9 4 and height towards East North and height within the ISN93 This change does NOT change the datum
26. map datum or geodetic datum of historic surveys e Any kind of global or local geodetic datum with user defined transforma tion parameters and if required spheroid parameters cocodati performs a 7 parameter affine transformation in the cartesian coordinate space i e all coordinate formats are first converted to 3D cartesian coordinates then transformed and subsequently converted into the desired format Any kind of lower order transformation e g 3 parameter can be obtained by setting the parameters to be neglected to zero Unlike coordinate conversions see above a transformation is based on empirical 1 e some how surveyed transformation parameters Thus the performance of the transformation is limited by the quality of the parameters and hence can degrade the quality of the transformed coordinates compared to the original input values If coordinate conversion and datum transformation are performed at the same time as possible with cocodati the quality of the obtained coordinates is predefined by the transformation parameters applied and NOT by the simultaneous format conversion or projection Determination of transformation parameters between two user data sets is not yet a feature of cocodati but is planned for future versions c 1D vertical datum transformation linear shift from ellipsoidal heights h to Mean Sea Level heights H a MSL and vice versa The operation is performed at the end of the internal wor
27. ns have to be inverted by also inverting the order of transfor mation steps As a consequence the user either has to use different formulas between back and forth transformation or slightly different transformation parameters if using the same formula back and forth From the programming point of view the software cannot decide whether a transformation is forward or backward and thus only one set of equations was used see 11 6 As consequence the transformation parameters between Reykjavik 1900 and Hj rsey55 resp Hj rsey55 and Reykjavik 1900 differ slightly Table 3 The transformation parameters between ISN93 and Reykjavik 1900 were derived by combining the two sets discussed above Therefore they inherit all of their character istics 10 3 Projection Parameters The provided default projection parameters have already been discussed and are listed in Table 1 Note The conversion between coordinate projections formats is strict and thus does not have any impact on the derived coordinates accuracy i e the coordi nates will inherit the accuracy of the input coordinates If a transformation is applied simultaneously or not with the conversion of projection format the ac curacy of the derived coordinates is limited by the quality of the transformation parameters The default parameters offered in cocoda might therefore not always fulfill the demands In these cases it is mandatory to the user to determine appropriate transfo
28. nto a file from single point input use ASCII file import in order to generate an output file 9 1 1 Input Format and Settings The appearance of the Coordinate Settings entry fields changes according to the coordinate format chosen in the Format Projection Parameters section a When choosing cartesian Geocentric X Y Z unprojected coordinates three entry fields titled X Y and Z 1 e metric geocentric earth fixed earth centered coordinates appear b When choosing Geographic 9 4 h or H unprojected the input line shows four fields Latitude Longitude h and H a MSL The entries accepted are Latitude in degrees between 60 N and 70 N Longi tude in degrees between 0 and 90 For the users upmost convenience and in order to avoid confusion cocodat will switch positive longitude values automatically to negative 1 e 21 West to 21 East this apllies as well to file input Markus Rennen 10 May 1 2004 The following entry formats for Latitude or Longitude are accepted and re cognized automatically example for Latitude e 64 9 11 1 degrees minutes decimal seconds ddd mm ss s e 64 9 185 degrees decimal minutes ddd mm mmm e 64 15308 decimal degrees ddd ddddd Degrees Minutes and seconds are separated by a blank white space Geographic longitude values usually refer to the zero meridian at Greenwich However coor dinates referenced to the Reykjavik1900 datum are often referenced to the
29. ocks The two horizontal blocks separate the area for input settings and entries on the left and the area for the output settings and results on the right Figure 8 rsa RAR 32i FAR 75727 fl Figure 8 Input Settings vs Output Settings The vertical separation 8 3 to 8 5 refers to the requirements of user definitions see Figure 9 8 3 Coordinate Settings Section The top section is dedicated to more or less formal definitions of input and output co ordinates such as data source etc 8 4 Datum Definition Section The middle section is dedicated to all parameters referring the datum definition NOT to be confused with projection The datum choice is always to be set first With chosing the user datum the most commonly associated coordinate format will be set as default in the Projec tion Format section These parameters can then be changed subsequently Coordinates showing identical formats 1 e for instance A and height might still be except the New Transformation and the Open button for file export 9 3 Eception When using file input the file shall be chosen first then the datum and so on Markus Rennen 3 LANDNALINGAR May 1 2004 Ei referenced to different datum definitions and vice versa coordinates of the same da tum might be displayed in different formats e g o A4 and height vs metric East North and height both ISN93 Thus datum definition middle section and proj
30. on of a constant scale is only tolerable for limited areas or distances The gradient of scale changes with location and direction and thus indicatory value can be given as rule of thumb a constant scale is not suitable when the area of interest extends more than a few kilo meters 9 1 2 Output Format Before the conversion and or transformation is conducted 1 e before the Transfor mation button is pressed the desired output datum and projection format has to be chosen The settings are equivalent to the input settings see 9 1 1 Positive Counting direction coordinate values grow in direction given in the table e g East indicates that coordinates grow eastwards Markus Rennen 12 LANDNVELINGAR Output coordinates Geographic longitude values are always referred to the Greenwich Zero Meridian even if the input of Reykjav k 1900 coordinates referred to the Copenhagen Zero Meridian For geographic output coordinates the desired Latitude or Longitude format ddd mm ss s ddd mm mmm or ddd ddddd can be chosen by setting the switch below the coor dinate Figure 2 The East value of Lambert projected output coordinates 1s always displayed as genu inely defined for the associated datum With other words the positive counting direc tion corresponds to the historic records In detail that is as displayed 1n Table 1 For change of counting direction according to user software requirements see 9 3 North values in any case
31. re is used it is strongly recommended to make sure that this software takes into account the scale corrections Markus Rennen 4 LANDNUELINGAR 5 Introduction With developing a tool for Coordinate Conversion and Datum Transformation in Iceland abbreviated cocodati LMI intends to enhance its public user service So far every request regarding conversion and transformation of coordinates had to be handled individually leading to unavoidable delays etc The increasing number of re quests at LMI caused increasing costs and bound recourses and hence let it appear mandatory to provide a service that enables every coordinate user to perform the re quired steps himself The format as online application was chosen in to limit LMI s efforts on software maintenance shorten the update cycle and ensure that each user always works with the most recent version For practical reasons 1 e in order to prevent the user from false data entry the per formance of cocodat is currently limited to Iceland and its maritime surroundings covering rather tolerant dimensions The mathematics applied are generally strict though and provide spatially unlimited application 1 e in extend and location Future versions therefore might feature global coverage 6 Features of cocodat cocodat provides a conversion between different coordinate formats and or projections 1 e e Geocentric cartesian X Y Z coordinates metric e Geographic surface coordinates
32. rmation parameters by survey These parameters can then be imported into cocoda and processed as explained above 10 4 Geoid The NKG96 geoid represents a gravimetric quasi geoid Thus the derived MSL heights represent Normal heights after M C Molodenski For details refer to the lit 12 erature e g FORSBERG R Development of a cm geoid with basics of geoid determination in HARSSON B G edt Nordic Geodesy Towards the 21st Century Lecture notes for Autumn School Fevik Norway Aug 28 Sept 209 2000 Nordic Geodetic Commission printed by Statens Kartverk Norway 2001 or on normal heights TORGE W Geodesy 3 edition 2001 de Gruyter Berlin New York Markus Rennen 17 LANDNALINGAR May 1 2004 ISLANDS 11 Inside of cocodat The following paragraphs enlist the exact mathematics 1 e the specific equations and algorithms used in cocodat All equations are taken from standard literature 11 1 Universal Transverse Mercator UTM k0 0 9996 n f 2 f e f Q f e e I1 f Constants for meridian arc c al4 01 e r a 1 n 4 u04 nj El n 36 n 45 39 n E3 280 n E2 90 n E3 VO 16384 e7 11025 64 e 175 4 e7 45 16 e 3 4 e V2 20464721 120 e 19413 8 e 1477 32 e 21 32 e V4 4737141 28 e 17121 32 e 151 192 e V6 427211 35 e 1097 1024 e Meridian Arc Formula S0 k0 r B0 sin B0 cos B0 12 E1 cos B0 E2 cos B0
33. s at latitude BO k0 Point scale factor at central parallel Q Isometric latitude of B R Mapping radius at latitude B B Parallel of geodetic latitude positive north vi Convergence angle L Meridian of geodetic longitude positive east LO Longitude of true and grid origin E Easting coordinate E0 False easting constant at grid and projection origin Rb Mapping radius at latitude Bb N Northing coordinate Nb False northing constant for Bb at the reference meridian LO NO Northing constant at intersection of reference meridian LO with central parallel BO k Grid scale factor at a general point 11 4 From Geodetic to Geocentric Coordinates Having the Same Datum Input Latitude B Longitude L Height h Output X Y Z Markus Rennen May 1 2004 25 MEE le m ai e f Q f e f 2 f 0 fy Cu Ja e N 2 C 4l e cos B X N h cos B cos L Y N h cos B sin L Z l e N h sin B 2 Variables Description 2 First eccentricity squared s Second eccentricity squared Flattening of the ellipsoid Semi major axis of the ellipsoid Polar radius of curvature ZaSS o The distance to the Z axis along the normal at the point B L 11 5 From Geocentric to Geographic Coordinates Having the Same Datum Input X Y Z coordinates in meters Output Latitude B in radians Longitude L in radians h height L atan Y X e f Q f fy C a l e B atan Z
34. tches appear grey Figure 2 right and do not allow any entries Figure 2 Switches Figure 5 Input screen Figure 4 Output Screen Active switches can be set on or off by mouse click a switch set to on is indi cated by a dark dot Figure 2 left After all entries are completed and the required switches are set accordingly the soft ware operation is carried out by mouse click on the Transform button on the bottom center of the input screen Figure 5 TRANSFORM Figure 5 Transform Button After data processing the output screen appears Figure 4 or in case of false entries an error message in a pop up window Within the output screen calculated values ap pear blue while predefined values remain in black letters Figure 6 New Transformation button Figure 7 Browser back button Markus Rennen 7 May 1 2004 The output screen is entirely non active and merely designed for display In order to return to the input screen for changes or new operations the New Trans formation button on the bottom of the output screen Figure 6 will return the user to the input screen or the Back button of the browser can be use Figure 7 the input screen appears again and new operations can be conducted or prior operations re newed 8 2 Screen Structure Both cocodat screens and with them the operation structure is separated horizon tally in two blocks and vertically 1n three bl
35. to users local computer Instead the output file is created on the LMI server under a temporary file name displayed in the output file field Markus Rennen 14 May 1 2004 A mouse click on the Open Button will display an HTML page with the obtained file contents In case non valid entries have been processed the concerned line will return a NaN not a number value For valid values the transformation conversion will return a list of coordinates preceded by a header that contains all definitions Figure 15 The coordinate columns are separated by a TAB delimiter If the resulting output is unsatisfying pressing the Browser s Back button Figure 7 will return first to the output screen another back will return to the input screen and enable the user to ao settings accordingly LE LE Terre Ter s en LE Men n Terre n LEX LESE ESL ILES ILES E ESL ESI ESI EX EDS LESE ILES E ES LESS ILES ILES 1 EXER EE ESI EX E ES LESER ILES EDS FEX LESE ILES ILES EFE ILES EDS LESER ILES EE G1 LI File E SEE IER o i a ere Islands 5 From To ti Datum Hjoarsey 1955 6378388 0 Iyf 297 0 Datum ISH93 6378137 0 l1 fi 238 257222101 95 Trans formation Parameters 0 73 0 Dy 46 0 Dz 86 0 Rx n 0 Ry D n R2 0 0 Ds n n 25 Proajection Geodetic Cunprajected Projection Lambert Conformal Conic two parallels 25 Central Meridian Central Meridian P 155 0 Original Latitude Original Latitude 65 0 False Easting
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