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15
WorkingwithCoordinate
SystemsandProjections
Mapsattheirbaseareavisualrepresentationintwodimensionsofasectionof
thethree-dimensionalEarth.Beingabletousemapsinanelectronicformatin
manywaysfreesusfromtheconstrictionsofthetwo-dimensionalmapbecause
wecanusemathematicalformulastocompensateforthecurvatureoftheEarth.
Inthischapter,wecoverthecoordinatesystemsandprojectionsthatarestandard
inMapInfoProfessionalandprovidethetoolswithwhichyoucancreateacustom
projectionstomeetyourorganization'sneeds.Whetheryouarealocalgovernment
tryingtoestablishnewtaxrollsoralargecompanytryingtodefineyoursales
territorymoreprecisely,creatingacustomprojectionmaybeasolutionyouwant
toexplore.
Formoreinformation,seeUsingOceanandGridTablesandFrequentlyAsked
ProjectionFileQuestionsintheHelpSystem.
Inthissection:
• WorkingwithCoordinateSystems . . . . . . . . . . . . . . . . .392
• BuildingBlocksofaCoordinateSystem . . . . . . . . . . . .397
• AddingProjectionstotheMAPINFOW.PRJFile . . . . . .402
• UnderstandingPrecisioninMapInfoProfessional . . . .404
• Understanding Affine Transformations . . . . . . . . . . . . .405
• UsingEarthandNon-EarthMaps . . . . . . . . . . . . . . . . . .407
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WorkingwithCoordinateSystems
Theterms"projection"and"coordinatesystem"areoftenusedinterchangeably,howevertheydonot
meanthesamething.
Projection-Anequationorsetofequationsthatcontainmathematicalparametersforamap.Theexact
numberandnatureoftheparametersdependsuponthetypeofprojection.Youcanthinkofaprojection
asamethodofreducingamap'sdistortioncausedbythecurvatureoftheEarth,ormoreprecisely,a
projectioncompensatesfortheshortcomingsofdepictingmapsintwodimensionswhenthecoordinates
existinthreedimensions.
CoordinateSystem-Whenparametersofaprojectionareassignedspecificvalues,theybecomea
coordinatesystem.Acoordinatesystemisacollectionofparametersthatdescribecoordinates,oneof
whichisaprojection.
DisplayingCoordinates
Therearetwoplaceswherecoordinatesdisplay:
• IntheStatusBarbycursorlocation(setintheMapOptionsdialogboxorbyclickingontheStatus
Bar).
• Indialogboxesthatdisplayareameasurements,suchasaPointObject,RegionObjectetc.
CoordinatescanonlybeenteredintheObjectInfodialogboxeswhenalayeriseditable.
Note:
Youcandisplaycoordinatesinoneofthefollowingformats:
• Decimaldegrees(forexample-97.90052°,42.85732°)
• Degrees,minutes,seconds(forexample-97°54'1.908",42°51'26.28")
• MilitaryGridReference(WGS1984datum)(forexample14TNN8982545555)
• USNationalGridReference(NAD83/WGS84)(forexample14TNN8982545555)
• USNationalGridReference(NAD27)(forexample14TNN8985745342(NAD27))
ThedefaultisDecimaldegrees.
ElementsofaCoordinateSystem
AcoordinatesysteminMapInfoProfessionalismadeupofmanyelementswhichneedtobespecified
inadvance.Oncetheseelementsareinplace,youcanbesurethatyourmapsareasaccurateas
possible.ThesearetheprojectionelementsyouneedtosetintheMAPINFOW.PRJfile:
• ProjectionTypes
• Datums
• Units
• CoordinateSystemOrigin
• StandardParallels(ConicProjections)
• ObliqueAzimuth(HotineObliqueMercator)
• ScaleFactor(TransverseMercator)
• FalseEastingandFalseNorthing
• Range(AzimuthalProjections)
Fordatumandunittables,seeProjectionDatumsandUnits.
Note:
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UnderstandingCoordinateSystems
Youcanmakeamapoutofanyglobewithoutdistortingthepointsonthesurfacebyplacingtheglobe
intoanimaginarycylinder.
GlobewithLongitude/LatitudeProjection
Ifyoutransferthetouchpointsfromtheglobesurfaceontothecylinderandrolloutthecylinderonto
graphpaper,theresultisamapasinthefigurebelow.Inthemapthatwouldbecreatedfromthiscylinder,
theEquatoris0degreesallthewayaroundtheglobeandthepointsonthatlinearecompletelyaccurate.
Longitude/LatitudeProjectionMap
Whenyouaddlongitudeandlatitudelinesat15degreeincrementstoeachsideoftheEquatorandthe
PrimeMeridianyoucreateareferencegrid.ThelinesfurthestfromthePrimeMeridianare+180degrees
towardtherightand-180degreestotheleft.Thismapprojectioniscommonlycalledthe
Longitude/Latitudeprojection.
Thisisoftenconsideredthedefaultprojection.ItisthemosteffectivemapforareasnearesttheEquator
butmeasurementsfurtherawaytendtoincreaseindistortion.
BecausemanypeopledonotliveneartheEquator,otherprojectionscameintousetocreatemore
accuratelocalmaps.Accuracydependsuponhowyouprojecttheglobeontothecylinder.Ifyouturn
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thecylindersothatittouchesthePrimeMeridianinstead(oranylineoflongitude,90degreesawayfrom
theEquator)youhaveaTransverseProjection.Thecloseryouaretotheplacethecylindertouchesthe
globe,themoreaccuratethemeasurementsare.
GlobeDemonstratingtheTransverseProjection
TransverseprojectionsallowustomakemapsthataremoreNorth-Southlineaccurate,aslongasyou
compensateforthedistancefromthenew"Equator"whichinthiscaseisthePrimeMeridian.
Figure:TransverseMercatorProjectionMap
Athirdtypeofprojectionattemptstoresolvethedistortionprobleminanotherway.Conicprojections
useaconeshapeinsteadofacylindertocreatethe"touchpoints".
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GlobewithConicProjection
ThistypeofprojectionismuchmoreaccurateforlargeregionsorcountriesthatarewiderintheEast-West
directionthanintheNorth-Southdirection.Thereismuchlessdistortionregionallybecausethetouch
pointsofaconeareclosertothemapsurfacethanthoseofacylinder.
BrazilianPolyconicProjectionMap
Asyoucanseefromthepreviousfigure,theconicmapsarebestforsmallregionalareas.The
smaller-scalemaphastoomuchdistortiontobeuseful.
Afourthtypeofprojection,theAzimuthalprojection,doesnotuseconesorcylindersbutasimplecircle
thatgoesallthewayaroundtheglobeoveraparticularpoint.Thisprojectionprovidesa"viewfrom
space"overaparticularpoint.
GlobewithAzimuthalProjection
Thistypeofprojectionismostusefulwhenyouneedtoworkwithaparticularhemisphere.Ahemisphere
neednotbeNorth-SouthorEast-Westbased.ThenextfigureusestheNorthPoleasthecenterpoint
fortheAzimuthalProjection.
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LambertAzimuthalProjectionMap
YoucanusemorethanoneprojectionthatrotatesacylinderslightlyalongtheEquator.Thisstyleis
usedintheUniversalTransverseMercator(UTM)projection.UTMmapstheEarthwithatransverse
cylinderprojectiontocreatestandard"UTMZones".Byrotatingthecylinderaroundtheglobeinsix
degreeincrements,theUTMassuresthatallspotsontheEartharewithin3degreesofthecenterline.
(TheGauss-KrugersystemisaEuropeansystemakintoUTMthatalsousesatransversecylinder
rotatedinsixdegreesteps).
UniversalTransverseMercatorProjectionMap(UTMZone29)
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Almostallprojectionsyouwilluseareoneofthesetypes.Theyareeithercylindrical(regularortransverse),
conic,orazimuthalprojectionsandarecustomizedbyslightlydifferentprojectionparameters.Projection
parametersareoptionsthatdescribehowtheprojectionisarranged.
Youcanfurthercustomizeprojectionsbyspecifyingdifferentparametersfortheprojectionyouwantto
use.Forexample,youcanspecifythelongitudeandlatitudeofanypointontheEarthtocreateyour
ownAzimuthalprojectionofthatpoint.Youcancustomizeconicprojectionsbyspecifyingtheparallel
oflatitudeatwhichtheconeshouldbetangent.
BuildingBlocksofaCoordinateSystem
Inthissection,weprovidethetablesrequiredtocreateyourowncoordinatesystemsusingmap
projections,datums,units,Origins,StandardParallels,Azimuths,ScaleFactors,FalseEastings,False
Northings,andRanges.Youmightwanttocreateyourowncoordinatesystemifaccuracyiscrucialto
understandingyourdataorifyourdataisspecifiedinrelationtoanon-standardpoint,andyouwould
prefertokeepyourdatainthatcustomcoordinatesystem.
CoordinateSystems,Projections,andtheirParameters
Byspecifyingaprojectiontypeandvariousrequiredparameters,youcreateamathematicalalgorithm
forproducingequivalentcoordinatesindegreesfortheprojectedcoordinatesystem.Eachprojection
hasspecificparametersyoucancustomizetomakeyourmapsmoregeographicallyaccurate.The
followingtabledetailseachmajorcoordinatesystemtypeandtheparametersyoucanusetocustomize
thatsystem.Theparametersarelistedintheordertheyappearintherelevantprojectionentriesinthe
MAPINFOW.PRJfile.Tocreateyourowncoordinatesystemusingaparticularprojection,youmustadd
anentryintotheMAPINFOW.PRJfile.
Theparametersofacoordinatesystemare(inthisorder):
• CoordinateSystemName
• ProjectionType
• Datum
• Units
• OriginalLongitude
• OriginalLatitude
• StandardParallel1
• StandardParallel2
• Azimuth
• ScaleFactor
• FalseEasting
• FalseNorthing
• Range
Eachoftheseheadingsisdescribedindetailinthenextfewpages.
Note:
Foracompletelistofcommoncoordinatesystemsandtheirnecessaryparameters,seeProjections
andTheirParameters
ProjectionTypes
Theprojectiontypeistheequationorequationsusedbyacoordinatesystem.Foralistofprojections
MapInfoProfessinaluses,seeProjectionTypesList.
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SpecifyingtheBoundsforCoordinateSystems
YoucanspecifytheboundsforcoordinatesystemsintheMapinfoProfessional.PRJfile.Todoso,add
2000totheprojectionnumberandlisttheboundsaftertheprojectionparameters.Thegeneralformis:
name, projectionnum m + + 2000, , projection parameters, , x1, , y1, x2, y2
Forexample,todefineaUTMZone10coordinatesystemwithboundsof(100000,400000)to(200000,
450000),usethisline:
"UTM Zone 10", 2008, , 74, , 7, -123, 0, , 0.9996, , 500000, 0, , 100000, , 400000,
200000, 450000
TodefineaLongitude/Latitudecoordinatesystemwithboundsof(-50,30)to(-48,35),usethisline:
"Longitude / / Latitude", 2000, 0, -50, 30, , -48, 35
Youcanalsodefineacoordinatesystemwithboundsandanaffinetransformation.Inthatcase,add
3000totheprojectionnumber,andlisttheboundsaftertheaffinetransformationconstants.Thegeneral
formis:
name, projectionnum m + + 3000, , projection parameters, , unitnum, , A, B, , C, , D,
E, F, , x1, , y1, x2, y2
AccountingforAffineTransformationsandExplicitBoundsinProjectionTypes
YoucanmodifyprojectiontypeentriesintheMAPINFOW.PRJtoaddaconstantvaluetoaccountfor
affinetransformationsandexplicitbounds.Validconstantvaluesarelistedinthenexttable:
Parameters
CoordinateSystemhas:
Constant
Affineunitsspecifierandcoefficientsappear
aftertheregularparametersforthesystem.
Affinetransformations
1000
Boundsappearaftertheregularparameters
forthesystem.
Explicitbounds
2000
Affineparametersfollowsystem's
parameters;boundsfollowaffine
parameters.
Bothaffinetransformationsandbounds
3000
Example:
InthisexampleweusetheTransverseMercatorcoordinatesystemwiththeNAD1983datum.Youmight
havethislineinyourMAPINFOW.PRJfile:
"UTM Zone 1 1 (NAD 83)", , 8, , 74, , 7, -177, 0, , 0.9996, , 500000, 0
Ifyouwanttoaccountforanaffinetransformationforthissystem,youwouldaddtheconstanttothe
projectiontypeandappendtheparametersoftheaffinetransformationaslistedbelow:
Units=meters;A=0.5;B=-0.866;C=0;D=0.866;E=0.5;andF=0
Therefore,thenewentrytoappendtheparametersoftheaffinetransformationwouldbe:
"UTM Zone 1 1 (NAD 83) - - rotated d 60 0 degrees", 1008, 74, 7, , -177, , 0,
0.9996, 500000, , 0, , 7, , 0.5, -0.866, , 0, 0.866, 0.5, 0
where:
Description
Entry
Achievedbyaddingtheconstant(1000)tothe
projectiontype(8)
1008
Unitsfortheaffinetransformation(7=meters)
7
Affineparameters.
0.5,-0.866,0,0.866,0.5,0
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Tosupplyexplicitboundstothecoordinatesystem(x1,y1,x2,y2)=(-500000,0,500000,1000000),the
requiredlineentrieswouldbe:
"UTM Zone 1 1 (NAD 83) - - bounded", 2008, 74, 7, , -177, 0, , 0.9996, 500000,
0, -500000, , 0, , 500000, 1000000
where:
Description
Entry
Producedbyaddingtheconstant(2000)tothe
projectiontype(8)
2008
Explicitboundsparameters
-500000,0,500000,1000000
Tocustomizethecoordinatesystemusingboththeaffinetransformationandexplicitbounds,theentry
intheMAPINFOW.PRJwouldbe:
"UTM Zone 1 1 (NAD 83) - - rotated d and d bounded", 3008, , 74, , 7, -177, 0,
0.9996, 500000, , 0, , 7, , 0.5, -0.866, , 0, 0.866, 0.5, 0, -500000, , 0,
500000, 1000000
where:
Description
Entry
Producedbyaddingtheconstant(3000)tothe
projectiontype(8)
3008
Unitsfortheaffinetransformation(7=meters)
7
Affineparameters
0.5,-0.866,0,0.866,0.5,0
Explicitboundsparameters(SeeAccountingfor
AffineTransformationsandExplicitBoundsin
ProjectionTypes.)
-500000,0,500000,1000000
Datums
Adatumisestablishedbytyingareferenceellipsoidtoaparticularpointontheearth.Thefollowing
Datumstableliststhedetailsforeachdatum:
• ThenumberusedtoidentifythedatumintheMAPINFOW.PRJfile.
• Thedatum'sname
• Themapsforwhichthedatumistypicallyused
• Thedatum'sreferenceellipsoid
Foracomprehensivelistofsupportedprojectiondatums,seeProjectionDatums.
Foralistofdatumchangesbyversion,seeCoordinateSystemEnhancementsbyVersionintheMapInfo
ProfessionalHelp.
Tocreateacustomdatum,seeDefiningCustomDatumsintheHelpSystem.
ConvertingCoordinatesfromOneDatumtoAnother
Whenconvertingcoordinatesfromonedatumtoanother,MapInfoProfessionalhasusedtheMolodensky
(3-parameter)andBursa-Wolfe(7-parameter)methods.Thesearegeneral-purposemethodsthatcan
convertcoordinatesfromanydatumtoanyotherdatum.
AftertheNAD83datumwasintroduced,NOAAdevelopedaprogramcalledNADCON,whichstands
forNorthAmericanDatumCONversion.Thisisaveryspecializedprogramthatconvertscoordinates
onlyfromNAD27toNAD83andviceversa.Forthisspecializedtask,itismuchmoreaccuratethan
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theMolodenskygeneral-purposemethod;NADCONisaccuratetoabout0.1meter,andMolodenskyis
accuratetoonly10-30meters.MostU.S.governmentagencies,includingtheCensusBureau,have
standardizedonNADCONforconvertingbetweenNAD27andNAD83.
TheNADCONalgorithmisusedtoconvertcoordinatesbetweenNAD27andNAD83ifthosecoordinates
liewithintheareascoveredbyNADCON(UnitedStates,PuertoRico,andtheVirginIslands).Ifthe
coordinateslieoutsidethoseareas,oriftheyusedatumsotherthanNAD27orNAD83,MapInfo
ProfessionalusestheMolodenskyorBursa-Wolfeconversionmethods.
Duetothefileaccessrequired,theNADCONconversionmethodcanbeslightlyslowerthanthe
Molodenskymethod.IfyouwanttoturnofftheNADCONconversion,adda"NADCON"entrytothe
registry.Theregistryentryshouldhavethispath:
HKEY_LOCAL_MACHINE\Software\MapInfo\MapInfo\Common\NADCON
Ifthisentryissettozero,thentheMolodenskyconversionmethodwillbeusedinsteadofNADCON.
NADCON=0
Units
Theunitsindicatethemeasurementthattheprojectionusestokeeptrackofspace.Tofindacomplete
listofunitsandtheircorrespondingprojectionentries,seeUnits.
CoordinateSystemOrigin
ThecoordinatesystemoriginisthepointontheEarth(specifiedaslongitudeandlatitudedegrees)from
whichallcoordinatedistancesaretobemeasured.X=0andY=0attheoriginpoint,unlessafalse
eastingand/orfalsenorthingisused(seebelow).Itischosentooptimizetheaccuracyofaparticular
coordinatesystem.Aswemovenorthfromtheorigin,Yincreases;Xincreasesaswemoveeast.These
coordinatevaluesaregenerallycallednorthingsandeastings.
FortheTransverseMercatorprojection,theorigin'slongitudedefinesthecentralmeridian.Inconstructing
theTransverseMercatorprojectionacylinderispositionedtangenttotheearth.Thecentralmeridianis
thelineoftangency.Thescaleoftheprojectedmapistruealongthecentralmeridian.
IncreatingaHotineObliqueMercatorprojectionitisnecessarytospecifyagreatcirclethatisnotthe
equatornorameridian.MapInfoProfessionaldoesthisbyspecifyingonepointontheellipsoidandan
azimuthfromthatpoint.Thatpointistheoriginofthecoordinatesystem.
StandardParallels(ConicProjections)
Inconicprojectionsaconeispassedthroughtheearthintersectingitalongtwoparallelsoflatitude.
Thesearethestandardparallels.Oneistothenorthandoneistothesouthoftheprojectionzone.To
useasinglestandardparallelspecifythatlatitudetwice.Bothareexpressedindegreesoflatitude.
ObliqueAzimuth(HotineObliqueMercator)
Whenspecifyingagreatcircle(suchastheHotineObliqueMercator)usingapointandanazimuth(arc),
theazimuthiscalledtheObliqueAzimuthandisexpressedindegrees.
ScaleFactor(TransverseMercator)
Ascalefactorisappliedtocylindricalcoordinatestoaveragescaleerroroverthecentralareaofthe
mapwhilereducingtheerroralongtheeastandwestboundaries.Thescalefactorhastheeffectof
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