Discrete and Computational Geometry

Papers in this volume cover topics such as: polygons and polyhedrons, divisible dissections, convex polygon packings, symmetric subsets, convex decompositions, graph drawing, graph computations, point sets, approximation, Delauny diagrams, triangulations and chromatic numbers. TheJapanConferenceonDiscreteandComputationalGeometry(JCDCG)has beenheldannuallysince1997. Oneofthegoalsofthisconferenceseriesistobring togetherJapaneseresearchersfrombothacademiaandindustrywithresearchers inthese?eldsfromabroadtosharetheirrecentresults. JCDCG2000washeld22-25November2000atTokaiUniversityinTokyo inconjunctionwiththecelebrationofWorldMathematicsYear2000. Atotalof 120participantsfrom20countriesattended. Thisvolumeconsistsofthepapers presentedatJCDCG2000,whichhavebeenrefereedandrevised. Somepapers whichappearinshortforminthisvolumealsoappearinfullerexpandedversions injournalsdedicatedtocomputationalgeometry. Theorganizersoftheconferencethanktheprincipalspeakersfortheir- terestandsupport:ImreBarany,ErikD. Demaine,GregN. Fredrickson,Gyula Karolyi,NaokiKatoh,DavidKirkpatrick,JosephO'Rourke,JanosPach,Jozsef Solymosi,WilliamSteiger,JorgeUrrutia,andAllanWilks. Theythankthe- jorsponsorsfortheirgenerouscontribution:TheResearchInstituteofEdu- tionalDevelopmentofTokaiUniversity,theMinistryofEducationofJapan(for thegrant-in-aidtoA. Saito(A):10304008),andTokaiEducationInstruments Co. ,Ltd. April2001 TheEditors, JinAkiyama MikioKano MasatsuguUrabe OrganizingCommittee Chairs:JinAkiyamaandMikioKano Members: TetsuoAsano,DavidAvis,VasekChvatal,KiyoshiHosono,HiroshiImai, TakakoKodate,JosephO'Rourke,ToshinoriSakai,XuehouTan,Morimasa Tsuchiya,MasatsuguUrabe,andJorgeUrrutia. TableofContents Papers DudeneyDissectionsofPolygonsandPolyhedrons-ASurvey-...1 J. AkiyamaandG. Nakamura UniversalMeasuringDeviceswithoutGradations...31 J. Akiyama, H. Fukuda,G. Nakamura, T. Sakai, J. Urrutia, andC. Zamora-Cura ANoteonthePurelyRecursiveDissectionforaSequentially n-Divisible Square ...41 J. Akiyama, G. Nakamura, A. Nozaki, and K. Ozawa SequentiallyDivisibleDissectionsofSimplePolygons ...53 J. Akiyama, T. Sakai, andJ. Urrutia PackingConvexPolygonsintoRectangulerBoxes ...67 H. AltandF. Hurtado OntheNumberofViewsofPolyhedralScenes ...81 B. Aronov, H. Br. onnimann,D. Halperin,andR. Schi?enbauer ProblemsandResultsAroundtheErdos-Szek ? eresConvex PolygonTheorem ...91 I. Bar ' an ' y andG. Kar ' olyi OnFindingMaximum-CardinalitySymmetricSubsets ...106 P. Brass FoldingandUnfoldingLinkages,Paper,andPolyhedra ...113 E. D. Demaine OntheSkeletonoftheMetricPolytope ...125 A. Deza,K. Fukuda,D. Pasechnik, andM. Sato GeometricDissectionsThatSwingandTwist ...137 G. N. Frederickson OnConvexDecompositionsofPoints ...149 K. Hosono, D. Rappaport, andM. Urabe VolumeQueriesinPolyhedra ...156 J. IaconoandS. Langerman VIII Table ofContents SumofEdgeLengthsofaGraphDrawnonaConvexPolygon ...160 H. Ito,H. Uehara, andM. Yokoyama OnDoubleBoundGraphswithRespecttoGraphOperations ...167 S. Iwai,K. Ogawa,andM. Tsuchiya GeneralizedBalancedPartitionsofTwoSetsofPointsinthePlane ...176 A. KanekoandM. Kano OnPathsinaCompleteBipartiteGeometricGraph ...187 A. KanekoandM. Kano ApproximatingUniformTriangularMeshesforSpheres ...192 N. Katoh,H. Kojima, andR. Taniguchi TheConstructionofDelaunayDiagramsbyLobReduction ...205 P. Kau?mannand J. C. Spehner GeometricTransformationsinPlaneTriangulations ...217 K. Kawarabayashi, A. Nakamoto, Y. Oda, andM. Watanabe SeparationSensitiveKineticSeparationStructuresforConvexPolygons . . 222 D. Kirkpatrick andB. Speckmann OnAcuteTriangulationsofQuadrilaterals ...237 H. Maehara IntersectingRedandBlueLineSegmentsinOptimalTimeandPrecision . 244 A. MantlerandJ. Snoeyink TightErrorBoundsofGeometricProblemsonConvexObjectswith ImpreciseCoordinates ...252 T. NagaiandN. Tokura TriangleContactSystems,OrthogonalPlanePartitionsandtheirHitGraphs 264 A. Nakamoto NoteonDiagonalFlipsandChromaticNumbersofQuadrangulationson ClosedSurfaces ...274 A. NakamotoandS. Negami AnExtensionofCauchy'sArmLemmawithApplicationtoCurve Development ...280 J. O'Rourke OntheComplexityoftheUnionofGeometricObjects ...292 J. Pach Table of Contents IX StructureTheoremsforSystemsofSegments ...308 J. Pach andJ. Solymosi 3-dimensionalSingleActiveLayerRouting ...