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1、December13,2010Time:06:48pmfm.texDiscreteandComputationalGEOMETRYThispageintentionallyleftblankDecember13,2010Time:06:48pmfm.texDiscreteandComputationalGEOMETRYSATYANL.DEVADOSSandJOSEPHO’ROURKEPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDiiiDecember13,2010Time:06:48pmfm.texCopyrightc2011byPrince
2、tonUniversityPressRequestsforpermissiontoreproducematerialfromthisworkshouldbesenttoPermissions,PrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsRes
3、ervedLibraryofCongressCataloging-in-PublicationDataDevadoss,SatyanL.,1973Discreteandcomputationalgeometry/SatyanL.DevadossandJosephORourke.p.cm.Includesindex.ISBN978-0-691-14553-2(hardcover:alk.paper)1.GeometryDataprocessing.I.ORourke,Joseph.II.Title.QA448.D38D482011516.00285dc222010044434Brit
4、ishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinSabonPrincetonUniversityPressbooksareprintedonacid-freepaper,andmeettheguidelinesforpermanenceanddurabilityoftheCommitteeonProductionGuidelinesforBookLongevityoftheCouncilonLibraryResourcesTypesetbySRNovaPvtLtd,Bangalor
5、e,Indiapress.princeton.eduPrintedinChina10987654321ivDecember13,2010Time:06:48pmfm.texSLDDedication.Tomyfamily,fortheirunconditionalloveofthisragamuffin.JORDedication.InmemoryofMichaelAlbertson.vThispageintentionallyleftblankDecember13,2010Time:06:48pmfm.texContentsPrefaceix1POLYGONS1.1Diagonal
6、sandTriangulations11.2BasicCombinatorics71.3TheArtGalleryTheorem131.4ScissorsCongruencein2D201.5ScissorsCongruencein3D262CONVEXHULLS2.1Convexity332.2TheIncrementalAlgorithm362.3AnalysisofAlgorithms392.4GiftWrappingandGrahamScan422.5LowerBound462.6Divide-and-Conquer482.7ConvexHullin3D513TRIANGU
7、LATIONS3.1BasicConstructions593.2TheFlipGraph663.3TheAssociahedron733.4DelaunayTriangulations793.5SpecialTriangulations874VORONOIDIAGRAMS4.1VoronoiGeometry984.2AlgorithmstoConstructtheDiagram1044.3DualityandtheDelaunayTriangulation1074.
