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1 GeomaticsandInformationScienceofWuhanUniversity Vol.40No.8 Aug.2015 DOI: /j.whugis : (2015) , , , : difusionbasedmethod 100m, : ; ; :P208 :A [1-3] 1, 1.1, (cartogram) [4],, [5], (areacartogram) [7] GIS [6] [8-17] : 1) GDP ;2) [18-19], Gastner- Newman difusionbased method, [14] 1.2 Gastner-Newman : : (O88RA900KA) : zhangxun@lreis.ac.cn : zhangxiaohu@njau.edu.cn.

2 40 8 : 1101, T:g T(g) ρ ( g) : (T x,t y ) T y T y (x,y) Tx x y - Tx y x =ρ( g) 珋 ρ (1), ρ珋 ( 1) 2 Gastner-Newman Gastner Newman 2.1 Fick : J =v(g,t) ρ (g,t) (2),v(g,t) ; ρ, : J =- # ρ (3) (3) ;, : # 2 J+ ρ t =0 (4) (2)~(4) : # 2 ρ- ρ t =0 (5) 1) (ratio) (interval) ρ (cyclic), (5) ρ ( g,t) v(g,t) ρ ( 6)g(t) (7): S : v(g,t)=- # ρ ρ (6) g(t)=g(0)+ t 0v(g,t )dt (7) difusionbased method (restrictionefect) (rep- resentationefect) S : grid high,ij ~S(grid low,kn,l),grid low,kn grid low,ij,l S (grid low,kn -grid high,ij ) 2 kn S = (8) l 2 2) (nominal) (ordinal) (7) t,, (5) ρ S : S = pknlogpkn (9) difusionbased method l,pkn (grid low,kn,grid high,ij ) pkn=1 l 2.2,, (1) Gastner-Newman ScapeToad

1102 2015 8, Gastner-Newman, 100m Gastner-Newman 1: ρ ( g,0): lev x 100m lev x-1 ρ ( g,0,lev x ) ρ Gastner-Newman (g,0,lev x-1 ) ρ ( g,0,lev x ) ρ ( g,0); 100m 1 2: ρ (g,0) : lev x lev x-1 1 S ij S

3 , Gastner-Newman, 100m Gastner-Newman 1: ρ ( g,0): lev x 100m lev x-1 ρ ( g,0,lev x ) ρ Gastner-Newman (g,0,lev x-1 ) ρ ( g,0,lev x ) ρ ( g,0); 100m 1 2: ρ (g,0) : lev x lev x-1 1 S ij S ij>thres 100m ρ ( g,0,lev x ) ρ ij( g,0,lev x-1 )(i,j) ρ ( ij g,0) lev x-1 ρ ij( g,0,lev x-1 ) lev x ρ ( ij g,0,lev x-1 ) ρ ( g, ij 0); 3: ρ (g,0) lev x-1 : lev x-1 lev x-2, lev x-2 Step2 ρ (g, 0) ; 4: : ρ (g,0), # 2 ρ- ρ t =0 v(g,t)=-# ρ / ρ ; 5: : v(g, 1 (2010) t) g(t)=g(0)+ 0v(g,t )dt t Fig.1 GriddedPopulationAreaCartogramofSome DistrictsinBeijing(2010), ρ ( g,0), 4 Gastner- Newman Gastner-Newman, 3, Gastner-Newman difusionbased method 2010 [1] Wang Hailong,Chen Yufen.ResearchonCartog- raphicvisualizationforstatisticaldata[j].science 100 m of Surveying and Mapping,2009,32(6): m (.

4 40 8 : 1103 [J].,2009,32(6):66-68) [2] Liao Ke.Modern Cartography[M].Beijing:Sci- [M]. :,2004) [4] DorlingD.AreaCartograms:TheirUseandCrea- tion[m].westsussex:john Wiley & Sons,2011 [5] ZhangXiaohu,Zhong Ershun,Zhang Xun,etal. The UncertaintyofPolygon-based StatisticalData SpatialAnalysis:CaseofCensus Dataof Haidian District[J].Journalof Geo-information Science, 2013,15(03): (. MethodforProducingDensity-equalizing Maps[C]. [J]. The National AcademyofSciencesofthe United,2013,15(03): ) StatesofAmerica,USA,2004 [6] DuGuoming.MethodsandPracticesofSpatializa- [15]HeilmannR,Keim D A,PanseC,etal.Recmap: tionforstatisticalpopulation[m].beijing:china Rectangular Map Approximations in Information AgriculturalPress,2008(. Visualization[C].INFOVIS 2004,Austin,TX, [M]. :,2008) 2004 [7] AiTinghua.MapsAdaptabletoRepresentSpatial- [16]Keim D A,PanseC,NorthSC.Medial-axis-based cognition[j].journalof RemoteSensing,2008,12 Cartograms[J].Computer Graphicsand Applica- grams[j].the ProfesionalGeographer,1985,37 (1):75-81 (2): (. tions,2005,25(3):60-68 [J].,2008,12(2): ) [17]Kreveld M,SpeckmannB.OnRectangularCarto- [8] DougenikJA,ChrismanN R,NiemeyerD R.An grams[j].computationalgeometry,2007,37(3): Algorithm to Construct Continuous Area Carto [9] Gusein-ZadeS M,TikunovVS.A New Technique forconstructingcontinuouscartograms[j].car- tography and Geographic Information Science, 1993,20(3): [10]HouseD H,KocmoudCJ.ContinuousCartogram Construction[C]. Visualization 98, NC, USA, 1998 todraw[j].information Visualization,2003,2 (1):58-67 [13]Keim D A,PanseC,SchaferM,etal.Histoscale: encepress,2003(. [M]. :,2003) [11]Tobler W R.Pseudo-cartograms[J].Cartography and Geographic Information Science,1986,13 [3] Ma Yaofeng.ThePrincipleofCartography[M]. (1):43-50 Beijing:SciencePress,2004(. [12]Keim D A,PanseC,SchneidewindJ,etal.Visual- izinggeographicinformation:visualpointsvscar- AnEficientApproachforComputingPseudoCar- tograms[c].the14thieee Visualization 2003 (VIS'03),Washington,USA,2003 [14] Gastner M T,Newman M E J.Difusion-based [18]SeemannJ.TheAtlasoftheRealWorld:Mapping the Way WeLive[J].Cartographic Perspectives, 2012,67(4):77-80 [19]HennigBD.Rediscoveringthe World:MapTrans- formationsofhumanandphysicalspace[m].new York:Springer,2003 A ModifiedAlgorithmtoConstructGriddedAreaCartograms byscaleeffectindex ZHANG Xun 1 ZHONG Ershun 2 ZHANG Xiaohu 3 WANG Shaohua 2 LI Shaojun 2 1 ColegeofComputerandInformationEngineering,BeijingTechnologyandBusinessUniversity,Beijing100048,China 2 InstituteofGeographicSciencesandNaturalResourcesResearch,ChineseAcademyofSciences,Beijing100101,China 3 NationalEngineeringandTechnologyCenterforInformationAgriculture,JiangsuKeyLaboratoryforInformationAgriculture, NanjingAgriculturalUniversity,Nanjing210095,China Abstract:Cartogramsisanewapproachforstatisticaldatavisualization.However,drasticdiversityof localdataleadstofailureswhenweapplyexistingcartogram-makingalgorithmsongridstatisticdata withinurbanscale.toaddressthisproblem,wedesignanindexformeasuringthescaleefectofgrid statisticdata.thescaleefectindex weldescribestherestrictionefectandrepresentationefectof

5 multi-scalegriddata.moreover,basedonthescaleefectindex,wemodifythedifusion-basedmeth- oddevelopedbygastnerandnewmanin2004.themodifiedalgorithmisnotsensitivetolocaldiversi- tiesofgridstatisticdata,andareacartogramsachievedbythisalgorithm welkeepthedensity-equali- zingcondition.weapplythisalgorithminmakinggriddedpopulationcartogramsfrom100mgridbei- jingcensusdata,andresultsshowthereliabilityofthealgorithm,whichcanbeusedforproducingar- eacartogramsofstatisticdata. Keywords:griddedcensusdata;areacartograms;scaleefectindex;mappingalgorithm Firstauthor:ZHANG Xun,PhD.specializesinthetheoriesandmethodsofGISSoftware. zhangxun@lreis.ac.cn Correspondingauthor:ZHANG Xiaohu,PhD. zhangxiaohu@njau.edu.cn neseacademyofsciences, No.O88RA900KA 檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪 ( 1099 ) ADEM GeneralizationbyCatchmentAreaCombination LI Jingzhong 1 LI Donglin 1 1 SchoolofResourceandEnvironmentalScience,WuhanUniversity,Wuhan430079,China Abstract:ThispaperpresentsastructuredDEM generalizationbycatchmentareacombination.the valeycatchmentareasareusedasthelinkbetweentheabstractconceptionofvaleyandconcrete DEM gridpoints.theminorvaleybranchesaredeletedbythet pferlawandthevaleycatchment areasarecombinedbasedonthedeletedvaleynetwork.thentheresultingdemisinterpolatedbased onthecatchmentboundaryline (containingthreetypesofbasicterrainskeletoninformation:ridge, mountainandsaddle)andthevaleyline.experimentsshowthatademreconstructedbythismethod candeleteminorterraincharacteristicswhilepreservingmaincharacteristics. Keywords:structuralgeneralization;DEM;catchmentarea;valeyline Foundationsupport:KeyProjectfortheStrategicSciencePlaninInstituteofGeographicSciencesandNaturalResourcesResearch,Chi- Firstauthor:LIJingzhong,PhD,associateprofessor,specializesintheDEM analysisand multiplerepresentationsofspatialdata. lilideyx@126.com Foundationsupport:TheNationalNaturalScienceFoundationofChina,No ;theNationalHighTechnologyResearchandDe- velopmentprogramofchina(863program),no.2012aa12a404;statekeylaboratoryofinformationengineeringinsurveying,map- pingandremotesensingfoundation,no.11i03;virtualgeographicenvironment,ministryofeducation KeyLaboratoryofFunded Projects,No.2012VGE03;NationalScienceTalentsFund GeographicalSciences,WuhanUniversityofScienceBase ResearchCapaci- tytrainingprogram,no.j

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