简介：在搜集整理Voronoi相关文献与资料的基础上，首先简要介绍了Voronoi图及其应用领域，然后着重从地图信息识别与提取、地图综合和自动注记等方面总结了它在地图制图学中的应用情况，最后分析并探讨了应用中遇到的问题和今后的发展方向。指出Voronoi图在地图制图中的应用是由其特殊的几何与拓扑性质决定的，加权Voronoi图、广义Voronoi图及3DVoronoi图的引入使得其应用有着更远大的前景。

简介：以石家庄市桥东区为例，选取该地区的七家大型综合超市进行大量实际调查和科学的分析研究，根据各种影响因素构建超市位置和市场面积类型的研究模型，采用高阶Voronoi图对该地区内超市的势力范围进行研究，指出新超市选址的大概轮廓，并根据加权因素给出最佳选址范围和新建超市的规模.

简介：对电子电路进行复杂网络分析时，为了很好地体现有些元器件的重要性，本文引入了节点问连边加权的概念。以具体电子电路原理图为例，找出各个元器件之间的连接关系，建立网络的拓扑结构，生成一个加权网络，得出了网络的统计参数，给出了节点连接度的概率分布函数曲线。结果显示这种加权分析方法能更好地体现出电子电路系统的特点。

简介：探讨了大比例尺跨度下居民地综合特点,对比分析了现阶段点群目标综合算法,结合现有算法在处理大比例尺跨度下居民地综合时存在的不足,提出了一种基于行政区划的Voronoi图构建方法,建立了顾及居民地选取优先级的居民地综合模型,有效地提高了大比例尺跨度下居民地综合的效率和质量。

简介：MostexistingapplicationsofcentroidalVoronoitessellations(CVTs)lackconsiderationofthelengthoftheclusterboundaries.Inthispaperweproposeanewmodelandalgorithmstoproducesegmentationswhichwouldminimizethetotalenergy—asumoftheclassicCVTenergyandtheweightedlengthofclusterboundaries.TodistinguishitwiththeclassicCVTs,wecallitanEdge-WeightedCVT(EWCVT).TheconceptofEWCVTisexpectedtobuildamathematicalbaseforallCVTrelateddataclassificationswithrequirementofsmoothnessoftheclusterboundaries.TheEWCVTmethodiseasyinimplementation,fastincomputation,andnaturalforanynumberofclusters.

简介：CentroidalVoronoitessellations(CVTs)havebecomeausefultoolinmanyapplicationsrangingfromgeometricmodeling,imageanddataanalysis,andnumericalpartialdifferentialequations,toproblemsinphysics,astrophysics,chemistry,andbiology.Inthispaper,webrieflyreviewtheCVTconceptandafewofitsgeneralizationsandwell-knownproperties.WethenpresentanoverviewofrecentadvancesinbothmathematicalandcomputationalstudiesandinpracticalapplicationsofCVTs.Wheneverpossible,wepointoutsomeoutstandingissuesthatstillneedinvestigating.

简介：Wepresentanovelalgorithmforadaptivetriangularmeshcoarsening.Thealgorithmhastwostages.First,theinputtriangularmeshisrefinedbyiterativelyapplyingtheadaptivesubdivisionoperatorthatperformsaso-calledred-greensplit.Second,therefinedmeshissimplifiedbyaclusteringalgorithmbasedoncentroidalVoronoitessellations(CVTs).TheaccuracyandgoodqualityoftheoutputtriangularmeshareachievedbycombiningadaptivesubdivisionandtheCVTstechnique.Testresultsshowedthemeshcoarseningschemetoberobustandeffective.Examplesareshownthatvalidatethemethod.

简介：AnovelconstructionalgorithmispresentedtogenerateaconformingVoronoimeshforanyplanarstraightlinegraph(PSLG).Itisalsoextendedtotesselatemultiple-intersectedPSLGs.Allthealgorithmsareguaranteedtoconverge.Examplesaregiventoillustrateitsefficiency.

简介：Wetackletheproblemofconstructing2DcentroidalVoronoitessellationswithconstraintsthroughanefficientandrobustconstructionofboundedVoronoidiagrams,thepseudo-dualoftheconstrainedDelaunaytriangulation.WeexploitthefactthatthecellsoftheboundedVoronoidiagramcanbeobtainedbyclippingtheordinaryonesagainsttheconstrainedDelaunayedges.Theclippingitselfisefficientlycomputedbyidentifyingforeachconstrainededgethe(connected)setoftriangleswhosedualVoronoiverticesarehiddenbytheconstraint.TheresultingconstructionisamenabletoLloydrelaxationsoastoobtainacentroidaltessellationwithconstraints.

简介：AssumingthataVoronoidiagramofsliceareaisobtained,topologicalstructuresofallVoronoiedgesandVoronoipolygonsareusedtoacceleratetheoffsettingprocess.OncewalklineintersectswithoneofVoronoiedgesofthestartingVoronoiobject,thenextstartingVoronoiobjectisacquiredthroughthetopologyrelationship.Experimentalresultsshowtheapproachiseffectiveandsimple.

简介：Therearemanyphenomenathatgeneratepolygonaltessellationsonsurfacesof3Dobjects.Oneinterestingexampleisthejackfruit,amultiplefruitfoundinthetropics.Arecentstudyfoundthebest-fitsphericalVoronoidiagramfromaphotoofjackfruitskin,buttheoptimizationwasrelativetotheradiusofthesphereandtheheightofthespikes.Inthisstudy,weproposeamethodforadjustingthepositionofthecenterofthesphereinadditiontotheseparameters.Experimentswereconductedusingbothidealandrealdata.However,convergencewithrealdatahasnotbeenconfirmedduetorelaxationoftheconvergencecondition.

简介：Acontourtreeisagoodgraphicaltoolforrepresentingthespatialrelationsofcontourlinesandhasmanyapplicationsinmapgeneralization,mapannotation,terrainanalysis,etc.AnewmethodforgeneratingcontourtreesbyintroducingaVoronoi-basedinterioradjacencyconceptisproposedinthispaper.Theimmediateinterioradjacencysetisemployedtoidentifyallofthechildrencontoursofeachcontourwithoutcontourelevations.Ithasadvantagesoverexistingmethodssuchasthegeometricmethodandtheregiongrowingbasedmethod.

简介：［1］AbdelmotyAI,WilliamsMH.Advancedgeographicdatamodeling.Spatialdatamodelingandquerylanguagefor2Dand3Dapplications.Delft:TheNetherlands,1994［2］FranzA.Voronoidiagrams——asurveyofafundamentalgeometricdatastructure.ACMComputingSurveying,1991,23(3)［3］ZhengC,ChenJ.Organizingandretrievingcadasatraldatabasedonspatio-temporaltopologybetweenfather-sonparcels.JournalofWuhanTechnicalUniversityofSurveyingandMapping,1997,22(3):216～221(inChinese)［4］ChenJ,GoldCM,CuiBL,YongHU,etal.Extendingordinaryplanar-graph-basedspatialdatamodelwithVoronoiapproach.In:ProceedingsofIEAS&IWGIS'97.Beijing,1997.18～20［5］ChenJ,CuiBL.AddingtopologicalfunctionstoMapInfowithVoronoiapproach.JournalofWuhanTechnicalUniversityofSurveyingandMapping,1997,22(3):195～200(inChinese)［6］Clementini,Elisel,PaolinoDiFelice,PetervanOosterom.Asmallsetofformaltopologicalrelationshipssuitableforend-userinteraction.AdvancesinSpatialDatabases,LectureNotesinComputerScience.Springer-Verlag,1993.277～295［7］EdwardsG,LigozatG,FrylA,etal.AVoronoi-basedPIVOTrepresentationofspatialconceptsanditsapplicationtoroutedescriptionsexpressedinnaturallanguage.SpatialDataHandling'96,1996,7B.1～15［8］EgenhoferMJ.Reasoningaboutbinarytopologicalrelations.In:Proceedingsofthe2ndSymposiumonLargeSpatialDatabases.LectureNotesinComputerScience,Springer-Verlag,1991.143～160［9］EgenhoferMJ,FranzosaRD.Point-settopologicalspatialrelations.INT.J.GeographicalInformationSystems,1991,5(2):161～176［10］EgenhoferMJ,HerringJ.Categorizingbinarytopologicalrelationshipsbetweenregions,lines,andpointsingeographicdatabases.TechnicalReport,DepartmentofSurveyingEngineering,UniversityofMaine,Orono,1991［11］EgenhoferMJ,Al-tahaKK.Reasoningaboutgradualchangesoftopologicalrelations,inTheoriesandMet

简介：Thispaperconsidershowtouseagroupofrobotstosenseandcontroladiffusionprocess.Thediffusionprocessismodeledbyapartialdifferentialequation(PDE),whichisabothspatiallyandtemporallyvariantsystem.Therobotscanserveasmobilesensors,actuators,orboth.CentroidalVoronoiTessellationsbasedcoveragecontrolalgorithmisproposedforthecooperativesensingtask.Forthediffusioncontrolproblem,thispaperconsiderssprayingcontrolviaagroupofnetworkedmobilerobotsequippedwithchemicalneutralizers,knownassmartmobilesprayersoractuators,inadomainofinteresthavingstaticmeshsensornetworkforconcentrationsensing.ThispaperalsointroducestheinformationsharingandconsensusstrategywhenusingcentroidalVoronoitessellationsalgorithmtocontroladiffusionprocess.Theinformationissharednotonlyonwheretospraybutalsoonhowmuchtosprayamongthemobileactuators.BenefitsfromusingCVTandinformationconsensusseekingforsensingandcontrolofadiffusionprocessaredemonstratedinsimulationresults.

简介：给出了单位圆盘上不同加权B日舯锄空间之间的加权复合算子有界性及紧性刻划.

简介：摘要3D打印技术逐步走入我们日常生活，市场对于3D打印机的要求及需求愈来愈高，但是成本高还是3D打印进一步普遍推广的绊脚石。3D打印中的支撑结构是必需的，而一般切片软件添加支撑都是很规整的，支撑方法比较单一，不仅会浪费很多打印耗材还会增加很多打印时间，从而严重降低了打印效率。将Voronoi方法应用到支撑结构中，改进支撑的方法，在切片时每一层填充生成Voronoi形状，打印出的模型又轻又坚固，并且可以节约耗材，降低成本。

简介：InordertoquantitativelyevaluatethespuriousdianeutralmixinginaglobaloceanmodelMPAS-Ocean(ModelforPredictionAcrossScales)usingasphericalcentroidalvoronoitessellationsdevelopedjointlybytheNationalCenterforAtmosphericResearchandtheLosAlamosNationalLaboratoryintheUnitedStates,wechoosez*verticalcoordinatesysteminMPAS-Ocean,inwhichallphysicalmixingprocesses,suchasconvectionadjustmentandexplicitdiffusionparameterschemes,areomitted,usingalinearequationofstate.BycalculatingtheReferencePotentialEnergy(RPE),frontrevolutionposition,timerateofRPEchange,probabilitydensityfunctiondistributionanddimensionlessparameterχ,fromtheperspectivesofresolution,viscosity,HorizontalGridReynoldsNumber(HGRN),Re?,andmomentumtransmissionscheme,usingtwoidealcases,overflowandbarocliniceddychannel,wequalitativelyanalyzethesimulationresultsbycomparisonwiththethreenon-isopycnalmodelsinIlicaketal.(2012),i.e.,MITGCM,MOM,andROMS.TheresultsshowthatthespuriousdianeutralmixingintheMPAS-Oceanincreasesovertime.ThespuriousdianeutraltransportisproportionaltotheHGRNdirectlyandisreducedbyincreasingthelateralviscosityorusingafinerresolutiontocontrolHGRN.WhentheHGRNislessthan10,spurioustransportisreducedsignificantly.Whenusingtheproperviscosityclosure,MPAS-OceanperformsbetterthanMITGCMandMOM,closelytoROMS,inthe2Dcasewithoutrotation,andmuchbetterthantheabove-mentionedthreeoceanmodelsundertheconditionof3Dspacewithrotationduetothecellareadifferencebetweenthehexagoncellandthequadrilateralcellwiththesameresolution.BoththeZalesak(1979)fluxcorrectedtransportschemeandLeithclosureinMPAS-Oceanplayanexcellentroleinreducingspuriousdianeutralmixing.TheperformanceofLeithschemeispreferabletotheconditionofthree-dimensionalbarocliniceddy.

简介：利用上极限，给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．

简介：设函数φ和Ф是复平面单位圆盘D上的解析函数且φ(D)■D,则将加权复合算子定义为Wφ,Ф:f→Фf°φ.当1

简介：小聪、小颖、小华三个同学正在为谁的成绩最好争论不休……