Provided by: gmt_4.5.11-1build1_amd64

**NAME**

mapproject - Forward and Inverse map transformation of 2-D coordinates

**SYNOPSIS**

mapprojectinfiles-Jparameters-Rwest/east/south/north[r] [-Ab|B|f|F[lon0/lat0] ] [-C[dx/dy] ] [-Dc|i|m|p] [-E[datum] ] [-F[k|m|n|i|c|p] ] [-G[x0/y0][+|-][/unit] ] [-H[i][nrec] ] [-I] [-Lline.xy[/unit][+] ] [-Q[d|e] [-S] [-T[h]from[/to] ] [-V] [-:[i|o] ] [-b[i|o][s|S|d|D[ncol]|c[var1/...]] ] [-f[i|o]colinfo] [-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] ] [-m[i|o][flag] ]

**DESCRIPTION**

mapprojectreads (longitude, latitude) positions frominfiles[or standard input] and computes (x,y) coordinates using the specified map projection and scales. Optionally, it can read (x,y) positions and compute (longitude, latitude) values doing the inverse transformation. This can be used to transform linear (x,y) points obtained by digitizing a map of known projection to geographical coordinates. May also calculate distances along track, to a fixed point, or closest approach to a line. Finally, can be used to perform various datum conversions. Additional data fields are permitted after the first 2 columns which must have (longitude,latitude) or (x,y). See option-:on how to read (latitude,longitude) files.infilesData file(s) to be transformed. If not given, standard input is read.-JSelects the map projection. The following character determines the projection. If the character is upper case then the argument(s) supplied as scale(s) is interpreted to be the map width (or axis lengths), else the scale argument(s) is the map scale (see its definition for each projection). UNIT is cm, inch, or m, depending on theMEASURE_UNITsetting in .gmtdefaults4, but this can be overridden on the command line by appendingc,i, ormto thescaleorwidthvalues. Appendh,+, or-to the givenwidthif you instead want to set map height, the maximum dimension, or the minimum dimension, respectively [Default iswfor width]. In case the central meridian is an optional parameter and it is being omitted, then the center of the longitude range given by the-Roption is used. The default standard parallel is the equator. The ellipsoid used in the map projections is user-definable by editing the .gmtdefaults4 file in your home directory. 73 commonly used ellipsoids and spheroids are currently supported, and users may also specify their own custum ellipsoid parameters [Default is WGS-84]. Several GMT parameters can affect the projection:ELLIPSOID,INTERPOLANT,MAP_SCALE_FACTOR, andMEASURE_UNIT; see thegmtdefaultsman page for details. Choose one of the following projections (TheEorCafter projection names stands for Equal-Area and Conformal, respectively):CYLINDRICALPROJECTIONS:-Jclon0/lat0/scaleor-JClon0/lat0/width(Cassini). Give projection centerlon0/lat0andscale(1:xxxxor UNIT/degree).-Jcyl_stere/[lon0/[lat0/]]scaleor-JCyl_stere/[lon0/[lat0/]]width(Cylindrical Stereographic). Give central meridianlon0(optional), standard parallellat0(optional), andscalealong parallel (1:xxxxor UNIT/degree). The standard parallel is typically one of these (but can be any value): 66.159467 - Miller's modified Gall 55 - Kamenetskiy's First 45 - Gall's Stereographic 30 - Bolshoi Sovietskii Atlas Mira or Kamenetskiy's Second 0 - Braun's Cylindrical-Jj[lon0/]scaleor-JJ[lon0/]width(Miller Cylindrical Projection). Give the central meridianlon0(optional) andscale(1:xxxxor UNIT/degree).-Jm[lon0/[lat0/]]scaleor-JM[lon0/[lat0/]]widthGive central meridianlon0(optional), standard parallellat0(optional), andscalealong parallel (1:xxxxor UNIT/degree).-Joparameters(Oblique Mercator[C]). Typically used with-R<...>r, otherwise region is in oblique coordinates. Specify one of:-Jo[a]lon0/lat0/azimuth/scaleor-JO[a]lon0/lat0/azimuth/widthSet projection centerlon0/lat0,azimuthof oblique equator, andscale.-Jo[b]lon0/lat0/lon1/lat1/scaleor-JO[b]lon0/lat0/lon1/lat1/scaleSet projection centerlon0/lat0, another point on the oblique equatorlon1/lat1, andscale.-Joclon0/lat0/lonp/latp/scaleor-JOclon0/lat0/lonp/latp/scaleSet projection centerlon0/lat0, pole of oblique projectionlonp/latp, andscale. Givescalealong oblique equator (1:xxxxor UNIT/degree).-Jq[lon0/[lat0/]]scaleor-JQ[lon0/[lat0/]]width(Cylindrical Equidistant). Give the central meridianlon0(optional), standard parallellat0(optional), andscale(1:xxxxor UNIT/degree). The standard parallel is typically one of these (but can be any value): 61.7 - Grafarend and Niermann, minimum linear distortion 50.5 - Ronald Miller Equirectangular 43.5 - Ronald Miller, minimum continental distortion 42 - Grafarend and Niermann 37.5 - Ronald Miller, minimum overall distortion 0 - Plate Carree, Simple Cylindrical, Plain/Plane Chart-Jtlon0/[lat0/]scaleor-JTlon0/[lat0/]widthGive the central meridianlon0, central parallellat0(optional), andscale(1:xxxxor UNIT/degree).-Juzone/scaleor-JUzone/width(UTM - Universal Transverse Mercator[C]). Give the UTM zone (A,B,1-60[C-X],Y,Z)) andscale(1:xxxxor UNIT/degree). Zones: If C-X not given, prepend - or + to enforce southern or northern hemisphere conventions [northern if south > 0].-Jy[lon0/[lat0/]]scaleor-JY[lon0/[lat0/]]width(Cylindrical Equal-Area[E]). Give the central meridianlon0(optional), standard parallellat0(optional), andscale(1:xxxxor UNIT/degree). The standard parallel is typically one of these (but can be any value): 50 - Balthasart 45 - Gall-Peters 37.0666 - Caster 37.4 - Trystan Edwards 37.5 - Hobo-Dyer 30 - Behrman 0 - Lambert (default)CONICPROJECTIONS:-Jblon0/lat0/lat1/lat2/scaleor-JBlon0/lat0/lat1/lat2/width(Albers[E]). Give projection centerlon0/lat0, two standard parallelslat1/lat2, andscale(1:xxxxor UNIT/degree).-Jdlon0/lat0/lat1/lat2/scaleor-JDlon0/lat0/lat1/lat2/width(Conic Equidistant) Give projection centerlon0/lat0, two standard parallelslat1/lat2, andscale(1:xxxxor UNIT/degree).-Jllon0/lat0/lat1/lat2/scaleor-JLlon0/lat0/lat1/lat2/width(Lambert[C]) Give originlon0/lat0, two standard parallelslat1/lat2, andscalealong these (1:xxxxor UNIT/degree).-Jpoly/[lon0/[lat0/]]scaleor-JPoly/[lon0/[lat0/]]width((American) Polyconic). Give the central meridianlon0(optional), reference parallellat0(optional, default = equator), andscalealong central meridian (1:xxxxor UNIT/degree).AZIMUTHALPROJECTIONS:Except for polar aspects,-Rw/e/s/n will be reset to-Rg. Use-R<...>rfor smaller regions.-Jalon0/lat0[/horizon]/scaleor-JAlon0/lat0[/horizon]/width(Lambert[E]).lon0/lat0specifies the projection center.horizonspecifies the max distance from projection center (in degrees, <= 180, default 90). Givescaleas1:xxxxorradius/lat, whereradiusis distance in UNIT from origin to the oblique latitudelat.-Jelon0/lat0[/horizon]/scaleor-JElon0/lat0[/horizon]/width(Azimuthal Equidistant).lon0/lat0specifies the projection center.horizonspecifies the max distance from projection center (in degrees, <= 180, default 180). Givescaleas1:xxxxorradius/lat, whereradiusis distance in UNIT from origin to the oblique latitudelat.-Jflon0/lat0[/horizon]/scaleor-JFlon0/lat0[/horizon]/width(Gnomonic).lon0/lat0specifies the projection center.horizonspecifies the max distance from projection center (in degrees, < 90, default 60). Givescaleas1:xxxxorradius/lat, whereradiusis distance in UNIT from origin to the oblique latitudelat.-Jglon0/lat0[/horizon]/scaleor-JGlon0/lat0[/horizon]/width(Orthographic).lon0/lat0specifies the projection center.horizonspecifies the max distance from projection center (in degrees, <= 90, default 90). Givescaleas1:xxxxorradius/lat, whereradiusis distance in UNIT from origin to the oblique latitudelat.-Jglon0/lat0/altitude/azimuth/tilt/twist/Width/Height/scaleor-JGlon0/lat0/altitude/azimuth/tilt/twist/Width/Height/width(General Perspective).lon0/lat0specifies the projection center.altitudeis the height (in km) of the viewpoint above local sea level. Ifaltitudeis less than 10, then it is the distance from the center of the earth to the viewpoint in earth radii. Ifaltitudehas a suffixrthen it is the radius from the center of the earth in kilometers.azimuthis measured to the east of north of view.tiltis the upward tilt of the plane of projection. Iftiltis negative, then the viewpoint is centered on the horizon. Further, specify the clockwisetwist,Width, andHeightof the viewpoint in degrees. Givescaleas1:xxxxorradius/lat, whereradiusis distance in UNIT from origin to the oblique latitudelat.-Jslon0/lat0[/horizon]/scaleor-JSlon0/lat0[/horizon]/width(General Stereographic[C]).lon0/lat0specifies the projection center.horizonspecifies the max distance from projection center (in degrees, < 180, default 90). Givescaleas1:xxxx(true at pole) orlat/1:xxxx(true at standard parallellat) orradius/lat(radiusin UNIT from origin to the oblique latitudelat). Note if1:xxxxis used then to specifyhorizonyou must also specify thelatas +-90 to avoid ambiguity.MISCELLANEOUSPROJECTIONS:-Jh[lon0/]scaleor-JH[lon0/]width(Hammer[E]). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Ji[lon0/]scaleor-JI[lon0/]width(Sinusoidal[E]). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jkf[lon0/]scaleor-JKf[lon0/]width(Eckert IV)[E]). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jk[s][lon0/]scaleor-JK[s][lon0/]width(Eckert VI)[E]). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jn[lon0/]scaleor-JN[lon0/]width(Robinson). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jr[lon0/]scale-JR[lon0/]width(Winkel Tripel). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jv[lon0/]scaleor-JV[lon0/]width(Van der Grinten). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).-Jw[lon0/]scaleor-JW[lon0/]width(Mollweide[E]). Give the central meridianlon0(optional) andscalealong equator (1:xxxxor UNIT/degree).NON-GEOGRAPHICALPROJECTIONS:-Jp[a]scale[/origin][r|z] or-JP[a]width[/origin][r|z] (Polar coordinates (theta,r)) Optionally insertaafter-Jp[ or-JP] for azimuths CW from North instead of directions CCW from East [Default]. Optionally append /originin degrees to indicate an angular offset [0]). Finally, appendrif r is elevations in degrees (requires s >= 0 and n <= 90) orzif you want to annotate depth rather than radius [Default]. Givescalein UNIT/r-unit.-Jxx-scale[/y-scale] or-JXwidth[/height] (Linear, log, and power scaling) Givex-scale(1:xxxxor UNIT/x-unit) and/ory-scale(1:xxxxor UNIT/y-unit); or specifywidthand/orheightin UNIT.y-scale=x-scaleif not specified separately and using1:xxxximplies that x-unit and y-unit are in meters. Use negative scale(s) to reverse the direction of an axis (e.g., to have y be positive down). Setheightorwidthto 0 to have it recomputed based on the implied scale of the other axis. Optionally, append tox-scale,y-scale,widthorheightone of the following:dData are geographical coordinates (in degrees).lTake log10 of values before scaling.ppowerRaise values topowerbefore scaling.tInput coordinates are time relative toTIME_EPOCH.TInput coordinates are absolute time. Default axis lengths (seegmtdefaults) can be invoked using-JXh(for landscape);-JXv(for portrait) will swap the x- and y-axis lengths. The default unit for this installation is either cm or inch, as defined in the file share/gmt_setup.conf. However, you may change this by editing your .gmtdefaults4 file(s).-Rxmin,xmax,ymin, andymaxspecify the Region of interest. For geographic regions, these limits correspond towest,east,south,andnorthand you may specify them in decimal degrees or in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Appendrif lower left and upper right map coordinates are given instead of w/e/s/n. The two shorthands-Rgand-Rdstand for global domain (0/360 and -180/+180 in longitude respectively, with -90/+90 in latitude). Alternatively, specify the name of an existing grid file and the-Rsettings (and grid spacing, if applicable) are copied from the grid. For calendar time coordinates you may either give (a) relative time (relative to the selectedTIME_EPOCHand in the selectedTIME_UNIT; appendtto-JX|x), or (b) absolute time of the form [date]T[clock] (appendTto-JX|x). At least one ofdateandclockmust be present; theTis always required. Thedatestring must be of the form [-]yyyy[-mm[-dd]] (Gregorian calendar) or yyyy[-Www[-d]] (ISO week calendar), while theclockstring must be of the form hh:mm:ss[.xxx]. The use of delimiters and their type and positions must be exactly as indicated (however, input, output and plot formats are customizable; seegmtdefaults). Special case for the UTM projection: If-Cis used and-Ris not given then the region is set to coincide with the given UTM zone so as to preserve the full ellipsoidal solution (See RESTRICTIONS for more information).

**OPTIONS**

No space between the option flag and the associated arguments.infile(s)input file(s) with 2 or more columns. If no file(s) is given,mapprojectwill read the standard input.-A[f|b]-Acalculates the (forward) azimuth from fixed pointlon/latto each data point. Use-Abto get back-azimuth from data points to fixed point. Upper caseForBwill convert from geodetic to geocentric latitudes and estimate azimuth of geodesics (assuming the current ellipsoid is not a sphere). If no fixed point is given then we compute the azimuth (or back-azimuth) from the previous point.-CSet center of projected coordinates to be at map projection center [Default is lower left corner]. Optionally, add offsets in the projected units to be added (or subtracted when-Iis set) to (from) the projected coordinates, such as false eastings and northings for particular projection zones [0/0]. The unit used for the offsets is the plot distance unit in effect (seeMEASURE_UNIT) unless-Fis used, in which case the offsets are always in meters.-DTemporarily overrideMEASURE_UNITand usec(cm),i(inch),m(meter), orp(points) instead. Cannot be used with-F.-EConvert from geodetic (lon, lat, height) to Earth Centered Earth Fixed (ECEF) (x,y,z) coordinates (add-Ifor the inverse conversion). Append datum ID (see-Qd) or giveellipsoid:dx,dy,dzwhereellipsoidmay be an ellipsoid ID (see-Qe) or given asa[,inv_f], whereais the semi-major axis andinv_fis the inverse flattening (0 if omitted). Ifdatumis - or not given we assume WGS-84.-FForce 1:1 scaling, i.e., output (or input, see-I) data are in actual projected meters. To specify other units, appendk(km),m(mile),n(nautical mile),i(inch),c(cm), orp(points). Without-F, the output (or input, see-I) are in the units specified byMEASURE_UNIT(but see-D).-GCalculate distances along track OR to the optional point set with-Gx0/y0. Append IT(unit), the distance unit; choose amonge(m),k(km),m(mile),n(nautical mile),d(spherical degree),c(Cartesian distance using input coordinates) orC(Cartesian distance using projected coordinates). The last unit requires-Rand-Jto be set. Upper caseE,K,M,N, orDwill use exact methods for geodesic distances (Rudoe's method for distances in length units and employing geocentric latitudes in degree calculations, assuming the current ellipsoid is not spherical). With no fixed point we calculate cumulate distances along track. To obtain incremental distance between successive points, use-G-. To specify the 2nd point via two extra columns in the input file, choose-G+.-HInput file(s) has header record(s). If used, the default number of header records isN_HEADER_RECS. Use-Hiif only input data should have header records [Default will write out header records if the input data have them]. Blank lines and lines starting with # are always skipped.-IDo the Inverse transformation, i.e., get (longitude,latitude) from (x,y) data.-LDetermine the shortest distance from the input data points to the line(s) given in the ASCII multi-segment fileline.xy. The distance and the coordinates of the nearest point will be appended to the output as three new columns. Append the distance unit; choose amonge(m),k(km),m(mile),n(nautical mile),d(spherical degree),c(Cartesian distance using input coordinates) orC(Cartesian distance using projected coordinates). The last unit requires-Rand-Jto be set. A spherical approximation is used for geographic data. Finally, append+to report the line segment id and the fractional point number instead of lon/lat of the nearest point.-QList all projection parameters. To only list datums, use-Qd. To only list ellipsoids, use-Qe.-SSuppress points that fall outside the region.-TCoordinate conversions between datumsfromandtousing the standard Molodensky transformation. Use-Thif 3rd input column has height above ellipsoid [Default assumes height = 0, i.e., on the ellipsoid]. Specify datums using the datum ID (see-Qd) or giveellipsoid:dx,dy,dzwhereellipsoidmay be an ellipsoid ID (see-Qe) or given asa[,inv_f], whereais the semi-major axis andinv_fis the inverse flattening (0 if omitted). Ifdatumis - or not given we assume WGS-84.-Tmay be used in conjunction with-R-Jto change the datum before coordinate projection (add-Ito apply the datum conversion after the inverse projection). Make sure that theELLIPSOIDsetting is correct for your case.-VSelects verbose mode, which will send progress reports to stderr [Default runs "silently"].-:Toggles between (longitude,latitude) and (latitude,longitude) input and/or output. [Default is (longitude,latitude)]. Appendito select input only oroto select output only. [Default affects both].-biSelects binary input. Appendsfor single precision [Default isd(double)]. UppercaseSorDwill force byte-swapping. Optionally, appendncol, the number of columns in your binary input file if it exceeds the columns needed by the program. Or appendcif the input file is netCDF. Optionally, appendvar1/var2/...to specify the variables to be read. [Default is 2 input columns].-boSelects binary output. Appendsfor single precision [Default isd(double)]. UppercaseSorDwill force byte-swapping. Optionally, appendncol, the number of desired columns in your binary output file. [Default is same as input].-fSpecial formatting of input and/or output columns (time or geographical data). Specifyioroto make this apply only to input or output [Default applies to both]. Give one or more columns (or column ranges) separated by commas. AppendT(absolute calendar time),t(relative time in chosenTIME_UNITsinceTIME_EPOCH),x(longitude),y(latitude), orf(floating point) to each column or column range item. Shorthand-f[i|o]gmeans-f[i|o]0x,1y(geographic coordinates).-gExamine the spacing between consecutive data points in order to impose breaks in the line. Appendx|Xory|Yto define a gap when there is a large enough change in the x or y coordinates, respectively, ord|Dfor distance gaps; use upper case to calculate gaps from projected coordinates. For gap-testing on other columns use [col]z; ifcolis not prepended the it defaults to 2 (i.e., 3rd column). Append [+|-]gapand optionally a unitu. Regarding optional signs: -ve means previous minus current column value must exceed |gapto be a gap, +ve means current minus previous column value must exceedgap, and no sign means the absolute value of the difference must exceedgap. For geographic data (x|y|d), the unitumay be meter [Default],kilometer,miles, ornautical miles. For projected data (X|Y|D), choose frominch,centimeter,meter, orpoints [Default unit set by MEASURE_UNIT]. Note: Forx|y|zwith time data the unit is instead controlled by TIME_UNIT. Repeat the option to specify multiple criteria, of which any can be met to produce a line break. Issue an additional-gato indicate that all criteria must be met instead.-mMultiple segment file(s). Segments are separated by a special record. For ASCII files the first character must beflag[Default is '>']. For binary files all fields must be NaN and-bmust set the number of output columns explicitly. By default the-msetting applies to both input and output. Use-miand-moto give separate settings to input and output.

**ASCII** **FORMAT** **PRECISION**

The ASCII output formats of numerical data are controlled by parameters in your .gmtdefaults4 file. Longitude and latitude are formatted according toOUTPUT_DEGREE_FORMAT, whereas other values are formatted according toD_FORMAT. Be aware that the format in effect can lead to loss of precision in the output, which can lead to various problems downstream. If you find the output is not written with enough precision, consider switching to binary output (-boif available) or specify more decimals using theD_FORMATsetting.

**EXAMPLES**

To transform a file with (longitude,latitude) into (x,y) positions in cm on a Mercator grid for a given scale of 0.5 cm per degree, runmapprojectlonlatfile-R20/50/12/25-Jm0.5c> xyfile To transform several 2-column, binary, double precision files with (latitude,longitude) into (x,y) positions in inch on a Transverse Mercator grid (central longitude 75W) for scale = 1:500000 and suppress those points that would fall outside the map area, runmapprojecttracks.*-R-80/-70/20/40-Jt-75/1:500000-:-S-Di-bo-bi2 > tmfile.b To convert the geodetic coordinates (lon, lat, height) in the file old.dat from the NAD27 CONUS datum (Datum ID 131 which uses the Clarke-1866 ellipsoid) to WGS 84, runmapprojectold.dat-Th131 > new.dat To compute the closest distance (in km) between each point in the input file quakes.dat and the line segments given in the multi-segment ASCII file coastline.xy, runmapprojectquakes.dat-Lcoastline.xy/k > quake_dist.dat

**RESTRICTIONS**

The rectangular input region set with-Rwill in general be mapped into a non-rectangular grid. Unless-Cis set, the leftmost point on this grid has xvalue = 0.0, and the lowermost point will have yvalue = 0.0. Thus, before you digitize a map, run the extreme map coordinates throughmapprojectusing the appropriate scale and see what (x,y) values they are mapped onto. Use these values when setting up for digitizing in order to have the inverse transformation work correctly, or alternatively, useawkto scale and shift the (x,y) values before transforming. For some projections, a spherical solution may be used despite the user having selected an ellipsoid. This occurs when the users-Rsetting implies a region that exceeds the domain in which the ellipsoidal series expansions are valid. These are the conditions: (1) Lambert Conformal Conic (-JL) and Albers Equal-Area (-JB) will use the spherical solution when the map scale exceeds 1.0E7. (2) Transverse Mercator (-JT) and UTM (-JU) will will use the spherical solution when either the west or east boundary given in-Ris more than 10 degrees from the central meridian, and (3) same for Cassini (-JC) but with a limit of only 4 degrees.

**ELLIPSOIDS** **AND** **SPHEROIDS**

GMTwill use ellipsoidal formulae if they are implemented and the user have selected an ellipsoid as the reference shape (seeELLIPSOIDingmtdefaults). The user needs to be aware of a few potential pitfalls: (1) For some projections, such as Transverse Mercator, Albers, and Lamberts conformal conic we use the ellipsoidal expressions when the areas mapped are small, and switch to the spherical expressions (and substituting the appropriate auxiliary latitudes) for larger maps. The ellipsoidal formulae are used as follows: (a) Transverse Mercator: When all points are within 10 degrees of central meridian, (b) Conic projections when longitudinal range is less than 90 degrees, (c) Cassini projection when all points are within 4 degrees of central meridian. (2) When you are trying to match some historical data (e.g., coordinates obtained with a certain projection and a certain reference ellipsoid) you may find thatGMTgives results that are slightly different. One likely source of this mismatch is that older calculations often used less significant digits. For instance, Snyder's examples often use the Clarke 1866 ellipsoid (defined by him as having a flattening f = 1/294.98). From f we get the eccentricity squared to be 0.00676862818 (this is whatGMTuses), while Snyder rounds off and uses 0.00676866. This difference can give discrepancies of several tens of cm. If you need to reproduce coordinates projected with this slightly different eccentricity, you should specify your own ellipsoid with the same parameters as Clarke 1866, but with f = 1/294.97861076. Also, be aware that older data may be referenced to different datums, and unless you know which datum was used and convert all data to a common datum you may experience mismatches of tens to hundreds of meters. (3) Finally, be aware thatMAP_SCALE_FACTORhave certain default values for some projections so you may have to override the setting in order to match results produced with other settings.

**SEE** **ALSO**

gmtdefaults(1),GMT(1),project(1)

**REFERENCES**

Bomford, G., 1952, Geodesy, Oxford U. Press. Snyder, J. P., 1987, Map Projections - A Working Manual, U.S. Geological Survey Prof. Paper 1395. Vanicek, P. and Krakiwsky, E, 1982, Geodesy - The Concepts, North-Holland Publ., ISBN: 0 444 86149 1.