The mercator projections

《The mercator projections》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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