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ID:39565417
大小:3.19 MB
页数:241页
时间:2019-07-06
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1、THEMERCATORPROJECTIONSTHENORMALANDTRANSVERSEMERCATORPROJECTIONSONTHESPHEREANDTHEELLIPSOIDWITHFULLDERIVATIONSOFALLFORMULAEPETEROSBORNEEDINBURGH2013ThisarticledescribesthemathematicsofthenormalandtransverseMercatorprojectionsonthesphereandtheellipsoidwithful
2、lderiva-tionsofallformulae.TheTransverseMercatorprojectionisthebasisofmanymapscov-eringindividualcountries,suchasAustraliaandGreatBritain,aswellasthesetofUTMprojectionscoveringthewholeworld(otherthanthepolarregions).Suchmapsareinvariablycoveredbyasetofgrid
3、lines.ItisimportanttoappreciatethefollowingtwofactsabouttheTransverseMercatorprojectionandthegridscoveringit:1.Onlyonegridlinerunstruenorth–south.ThusinBritainonlythegridlinecoincidentwiththecentralmeridianat2Wistrue:allothermeridiansdeviatefromgridlines.
4、TheUTMseriesisasetof60distinctTransverseMercatorprojectionseachcoveringawidthof6inlatitude:thegridlinesruntruenorth–southonlyonthecentralmeridiansat3E,9E,15E,...2.ThescaleonthemapsderivedfromTransverseMercatorpro-jectionsisnotuniform:itisafunctionofpos
5、ition.Forex-ampletheLandrangermapsoftheOrdnanceSurveyofGreatBritainhaveanominalscaleof1:50000:thisvalueisonlyex-actontwoslightlycurvedlinesalmostparalleltothecentralmeridianat2Wanddistantapproximately180kmeastandwestofit.Thescaleonthecentralmeridianiscons
6、tantbutitisslightlylessthanthenominalvalue.Theabovefactsareunknowntothemajorityofmapusers.Theyarethesubjectofthisarticletogetherwiththepresentationofformulaerelatinglatitudeandlongitudetogridcoordinates.PrefaceFormanyyearsIhadbeenintriguedbythethestatement
7、onthe(British)OrdnanceSurveymapspointingoutthatthegridlinesarenotexactlyalignedwithmeridiansandparallels:fourprecisefiguresgivethemagnitudeofthedeviationateachcornerofthemapsheets.Myfirstretirementprojecthasbeentofindoutexactlyhowthesefiguresarecalculatedandth
8、ishasledtoanexplorationofallaspectsoftheTransverseMercatorprojectiononanellipsoidofrevolution(TME).ThisprojectionisalsousedfortheUniversalTransverseMercatorseriesofmapscoveringthewholeoftheEarth,exceptforthep
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