简介:Geometriccomputingisanimportanttoolindesignandmanufacturingandinarts.Conventionally,geometriccomputingistakenbyalgebraiccomputing.Thevividintuitionofobjectsinvisualizationislostinnumericfunctions,whichishoweververyusefultohumancognitionaswellasemotion.Inthispaper,weproposedaconceptandtheoryofgeometricbasis(GB)asthesolvingcellforgeometriccomputing.EachGBrepresentsabasicgeometricoperation.GBworksasbothexpressingandsolvingcelljustliketheconceptofbasisinlinearalgebrabywhicheveryelementofthevectorspacecanbeexpressed.For3Dproblems,withaprocedureofaprojectionsreduction,theproblemcanbereducedtoplaneandthereductionfunctioncanbedesignedasaGB.AsequenceofGBcanconstructahigherlayerGB.Then,bythetraversaloftree,asequenceofGBisgotandthissequenceisjusttheconstructionprocessandalsothesolutionofthisgeometricproblem.
简介:Singularityanalysisinanimportantsubjectofthegeometricconstraintsatisfactionproblem.Inthispaper,threekindsofsingularitiesaredescribedandcorrespondingidentifcationmethodsarepresentedforbothunder0constrainedsystemsandover-constrainedsystems,Anotherspecialbutcommonsingularityforunder-constrainedgeometricsystems,pseudo-singularity,isanalyzed.Pseudo-singularityiscausedbyavarietyofconstraintmathchingofunder-constrainedsystemsandcanberemovedbyimprovingconstraintdistribution.Toavoidpseudo-singularityanddecideredundantconstraintsadaptively,adifferentiaitonalgorithmisproposedinthepaper.Itscorrctnessandeffciencyhavebeenvalidatedthroughitspracticalapplicationsina2D/3DgeometricconstraintsolverCBA.
简介:Inthisnotewecharacterizethegeometricfactureofa(μ,r,k)-FES.Namely,foraC~μtriangularin-terpolationschcmewithC~rvertexdata,anyangleofthemacrotrianglemustbedividedintoatleast(μ+1)/(r+1-μ)parts.
简介:Theemergenceofalargequantityofdigitalresourcesingeometry,variousgeometricautomatedtheoremprovingsystems,andkindsofdynamicgeometrysoftwaresystemshasmadegeometriccomputation,reasoning,drawing,andknowledgemanagementdynamic,automaticorinteractiveoncomputer.Integrationofelectroniccontentsanddifferentsystemsisdesiredtoenhancetheiraccessibilityandexploitability.Thispaperproposesanequivalenttransformationframeworkformanipulatinggeometricstatementsavailableintheliteraturebyusinggeometrysoftwaresystems.Suchaframeworkworksbasedonanewlydesignedgeometrydescriptionlanguage(GDL),inwhichgeometricstatementscanberepresentednaturallyandeasily.TheauthordiscussesandpresentskeyproceduresofautomaticallytransformingGDLstatementsintotargetsystem-nativerepresentationsformanipulation.Theauthoralsodemonstratestheframeworkbyillustratingequivalenttransformationprocessesandinterfacesforcompilingthetransformationresultsintoexecutableformatsthatcanbeinterpretedbythetargetgeometrysoftwaresystemsforautomatedtheoremprovinganddynamicdiagramdrawing.
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简介:YagerpresentedtheOrderedWeightedAveraging(OWA)operatortoprovideamethodforaggregatinginformationofdecision-making.YagerandFilevfurtherpresentedtheInducedOrderedWeightedAveraging(IOWA)operator.Inthispaper,weproposeaGeneralizedInducedOrderedWeightedGeometric(GIOWG)operatorandestablishasimpleobjective-programmingmodeltolearntheassociatedweightingvectorfromobservationaldata.EachobjectprocessedbytheGIOWGoperatorconsistsofthreecomponents,wherethefirstcomponentrepresentstheimportancedegreeorcharacterofthesecondcomponent,andthesecondcomponentisusedtoinduceanordering,throughthefirstcomponent,overthethirdcomponentswhicharethenaggregated.Thedesirableproperties,suchascommutativity,idempotencyandmonotonicity,etc.,associatedwlththeGIOWGoperatorarestudiedindetail,andsomenumericalexamplesaregiventoshowthepracticalityandeffectivenessofthedevelopedoperator.
简介:Polygonalmodelsarepopularrepresentationsof3Dobjects.Theuseofpolygonalmodelsincomputationalapplicationsoftenrequiresamodeltoproperlybounda3Dsolid.Thatis,thepolygonalmodelneedstobeclosed,manifold,andfreeofself-intersections.Thispapersurveysasizeableliteratureforrepairingmodelsthatdonotsatisfythiscriteria,focusingoncategorizingthembytheirmethodologyandcapability.Wehopetoofferpointerstofurtherreadingsforresearchersandpractitioners,andsuggestionsofpromisingdirectionsforfutureresearchendeavors.
简介:Theauthorsdefinethesceneryflowofthetorus.Theflowspaceistheunionofallflat2-dimensionaltoriofarea1withamarkeddirection(orequivalently,theunionofalltoriwithaquadraticdifferentialofnorm1).Thisisa5-dimensionalspace,andtheflowactsbyfollowingindividualpointsunderanextremaldeformationofthequadraticdifferential.Theauthorsdefineassociatedhorocycleandtranslationflows;thelatterpreserveeachtorusandarethehorizontalandverticalflowsofthecorrespondingquadraticdifferential.Thesceneryflowprojectstothegeodesicflowonthemodularsurface,andadmits,foreachorientationpreservinghyperbolictoralautomorphism,aninvariant3-dimensionalsubsetonwhichitisthesuspensionflowofthatmap.Theauthorsfirstgiveasimplealgebraicdefinitionintermsofthegroupofaffinemapsoftheplane,andprovethattheflowisAnosov.Theygiveanexplicitformulaforthefirst-returnmapoftheflowonconvenientcross-sections.Then,inthemainpartofthepaper,theauthorsgiveseveraldifferentmodelsfortheflowanditscross-sections,intermsof:●stackingandrescalingperiodictilingsoftheplane;●symbolicdynamics:thenaturalextensionoftherecodingofSturmiansequences,ortheS-adicsystemgeneratedbytwosubstitutions;●zoomingandsubdividingquasi-periodictilingsoftherealline,oraperiodicquasicrystalsofminimalcomplexity;●thenaturalextensionoftwo-dimensionalcontinuedfractions;●inductiononexchangesofthreeintervals;●rescalingonpairsoftransversemeasurefoliationsonthetorus,ortheTeichmiillerflowonthetwice-puncturedtorus.
简介:Hybridmodelsderivedfromrotationalsolidslikecylinders,conesandsphereswereimplementedonCATIAsoftware.Firstly,maketheisoscelestriangularprism,cuboid,cylinder,cone,sphere,andtheprismwithtangentconicandcurvedtriangleends,thecuboidwithtangentcylindricalandcurvedrectangleends,thecylinderwithtangentsphericalandcurvedcircularendsasthebasicBooleandeferenceunitstotheprimarycylinders,conesandspheresonsymmetricalandsomecriticalgeometricconditions,formingaseriesofvariantsolidmodels.Secondly,makethedeferenceunitsaboveasthebasicunionunitstothemaincylinders,cones,andspheresaccordingly,forminganothersetofsolidmodels.Thirdly,makethetangentendsofunionunitsintoobliqueconic,cylindrical,orwithrevolvedtriangularpyramid,quarterlycylinderandannulusendsonsketchbasedfeaturestothemaincylinders,cones,andspheresrepeatedly,thusformingstillanothersetofsolidmodels.Itisexpectedthatthesederivativemodelsbebeneficialbothinthestructuredesign,hybridmodeling,andfiniteelementanalysisofengineeringcomponentsandincomprehensivetrainingofspatialconfigurationofengineeringgraphics.
简介:ThemodeloftheuniversalTeichmullerspacebythederivativesoflogarithmistheunionofinfinitedisconnectedcomponents.Inthispaper,thefactthateachcomponentisnotstarlikewithrespecttoitscenterisproved,andtheouterradiusofthespacewithrespecttoeachcenterisobtained.
简介:BasedonexactGreenstrainofspatialcurvedbeam,thenonlinearstrain-displacementrelationforplanecurvedbeamwithvaryingcurvatureisderived.Insteadofusingthepreviousstraightbeamelements,curvedbeamelementsareusedtoapproximatethecurvedbeamwithvaryingcurvature.Basedonvirtualworkprinciple,rigid-flexiblecouplingdynamicequationsareobtained.Physicalexperimentswerecarriedouttocapturethelargeoverallmotionandthestrainofcurvedbeamtoverifythepresentrigid-flexiblecouplingformulationforcurvedbeambasedoncurvedbeamelement.Numericalresultsobtainedfromsimulationswerecomparedwiththoseresultsfromthephysicalexperiments.Inordertoillustratetheeffectivenessofthecurvedbeamelementmethodology,thesimulationresultsofpresentcurvedbeamelementsarecomparedwiththoseobtainedbypreviousstraightbeamelements.Thedynamicbehaviorofaslider-crankmechanismwithaninitiallycurvedelasticconnectingrodisinvestigated.Theadvantageofemployinggeneralized-αmethodispointedoutandthespecialnonlineardynamiccharacteristicsofthecurvedbeamareconcluded.
简介:Thegeometricshapesofspecimensareimportantinimpacttensiletestsbecausegeometricshapesdeterminethestressstatesofthespecimens,andprecisegeometricshapescanobtainpropermaterialpropertieswithoutnon-materialfactors.Theaimofthisstudywastoinvestigatethe1Dformofthestressbychangingthelength-to-diameter(L/D)ratiosofspecimens.TheexperimentswerecarriedoutonasplitHopkinsontensilebar(SHTB)-rotatingdiskindirectbar-bartensileimpactapparatus.TheL/DratiosoftheLY12CZspecimensusedinthetestrangedfrom1to5.ResultsshowthatthespecimenscanbeusedtoobtainexactparametersofmaterialsundertheproposedconditionswhentheL/Dratioisgreaterthan2.Thisisbecausethelongerlengthwillreduceoreliminatetheeffectsoftheinterfaces.
简介:InthispaperwepresentatransformationpathalgorithmforUnconstrainedSignomialGeometricProgramming(USGP).ThealgorithmisproposedfromanewpointofviewbasedonexploringthecharacteristicsofUSGPproblem.Firstlybysomestabletransformations,aparticularsubproblemisderivedwhichisveryeasytosolve.Secondly,aspecialpathisformedconveniently.Andthenthestepofthealgorithmconsistsinfindinga"good"pointtothecurrentiteratebychoosingitalongthespecialpathandwithinatrustregion.Itisprovedthatthealgorithmisgloballyconvergent.