简介：ＦａｉｒｉｎｇｏｆＰａｒａｍｅｔｒｉｃＣｕｂｉｃＢｓｐｌｉｎｅＣｕｒｖｅｓａｎｄＢｉｃｕｂｉｃＢｓｐｌｉｎｅＳｕｒｆａｃｅｓＭｕＧｕｏｗａｎｇ，ＺｈｕＸｉｎｘｉｏｎｇ，ＬｅｉＹｉａｎｄＴｕＨｏｕｊｉｅＤｅｐａｒｔｍｅｎｔｏｆＭａｎｕｆａｃｔｕｒｉ...

简介：Thispaperpresentsanewsplinecalledarcspline.Ittakestwoarcsconnectingadjacentpointsamongasampledseries,withknowntangentalofeachsampledpoint.Thecalculationfortheparallel.thecurvelengthandthesegment-ingpointcoordinatesaresimple,thusmakingmapsymbolgenerationsimplified.When'arclet'occurs,somespecialprocessingmustbetaken.

简介：Asaspecialshift-invariantspaces,splinesubspacesyieldmanyadvantagessothattherearemanypracticalapplicationsforsignalorimageprocessing.Inthispaper,wepayattentiontothesamplingandreconstructionprobleminsplinesubspaces.Weimprovelowerboundofsamplingsetconditionsinsplinesubspaces.Basedontheimprovedexplicitlowerbound,aimprovedexplicitconvergenceratioofreconstructionalgorithmisobtained.Theimprovedconvergenceratiooccupiesfasterconvergenceratethanoldone.Attheend,somenumericalexamplesareshowntovalidateourresults.

简介：Forasubdivision△ofaregionind-dimensionalEuclideanspace.weconsidercomputationofdimensionandofbasisfunctioninsplinespaceS((△)consistingofallCpiecewisePolynomialfunc-tionsover△ofdegreeatmostk.AcomputationalschemeispresentedforcomputingthedimensionandbasesofsplinespaceS(△).ThisschemebasedOntheGrobnerbasisalgorithmandthesmoothco-factormethodforcomputingmultivariatespline.Forbivariatesplines,explicitbasisfunctionsofS(△)ageobtainedforanyintegerkandrwhen△isacross-cutpartition.

简介：AnewgeometricmethodtoprovethetotalpositivityofUEsplinebasiswasproposed.UEsplinebasisisakindofbasisdefinedoveralgebraic-trigonometricunifiedspace.UEsplinebasissharesmostpropertiesoftheusualpolynomialB-Splines.Totalpositivityisanimportantpropertyforsplinebasis,itishighlyrelatedwithshapepreservingandvariationdiminishingproperties.Knotinsertedalgorithmisthemostusefulalgorithmforsplinecurvessincemanyotherusefulpropertiesarebasedonit.ItisnecessarytoprovethetotalpositivityofUEsplinebasisusingknotinsertedalgorithmintuitively,notonlyenrichtheUEsplinebasistheory,butalsocanbetreatedassupplementtothetotalpositivityinalgebraicsense.Thisapproachalsocanbeextendedtootheranalogicalbases.

简介：ＢＳｐｌｉｎｅＩｎｔｅｒｐｏｌａｔｉｏｎＢａｓｅｄｏｎＯｐｔｉｍｉｚａｔｉｏｎ①ＤｅｊｕｎＳｏｎｇＸｉｎｘｉｏｎｇＺｈｕＤｅｐａｒｔｍｅｎｔｏｆＭａｎｕｆａｃｔｕｒｉｎｇＥｎｇｉｎｅｅｒｉｎｇＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＡｅｒｏｎａｕｔｉｃ...

简介：Theexplicitformfortheorthonormalperiodictrigonometricsplinewaveletisgiven.Wealsogivethedecompositionandreconstructionequations.Eachofthetwoequationsinvolvesonlytwoterms.WeprovethatthefamilyofperiodictrigonometricsplinewaveletsisdenseinL2([0,2π]).

简介：在这个工作，一条新途径为与紧张构造花键被建议。基本想法在分布理论的使用，它允许我们定义紧张花键在最小化一些精力的合适的Hilbert空格功能。花键的古典直角的条件和描述以一个微分操作符的一个基本解决方案被提供。紧张花键的一个明确的代表被给。紧张花键能被解决一个线性系统计算。一些数字例子被给说明这条途径。

简介：Ageneralprocedureforconstructingmultivariatenon-tensor-productwaveletsthatgen-erateanorthogonaldecompositionofL~2(R~),s≥1,isdescribedandappliedtoyieldexplicitformulasforcompactlysupportedspline-waveletsbasedonthemultiresolutionanalysisofL~2(R~s),1≤s≤3,generatedbyanyboxsplinewhosedirectionsetconstitutesaunimodularmatrix.Inparticular,whenunivariatecardinalB-splinesareconsidered,theminimallysup-portedcardinalspline-waveletsofChuiandWangarerecovered.Arefinedcomputationalschemefortheorthogonalizationofspaceswithcompactlysupportedwaveletsisgiven.Arecursiveapproximationschemefor“truncated”decompositionsequencesisdevelopedandasharperrorboundisincluded.Aconditiononthesymmetryoranti-symmetryofthewaveletsisappliedtoyieldsymmetricbox-splinewavelets.

简介：Inthispaperwedevelopperiodicquarticsplineinterpolationtheorywhich,ingeneral,givesbetterfustocontinuousfunctionsthandoestheexistingquinticsplineinterpolationtheory.Themaintheoremofthepaperistoestablishthatr=0,1,2,3.Also,thenanperiodiccasescannotbeconstructedempoly-ingthemethodologyofthispaperbecausethatwillinvolveseveralotherendconditionsentirelydifferentthan(1,10).

简介：InthispaperweusethesimplexB-splinerepresentationofpolynomialsorpiecewisepolynomialsintermsoftheirpolarformstoconstructseveraldifferentialordiscretebivariatequasiinterpolantswhichhaveanoptimalapproximationorder.Thismethodprovidesanefficienttoolfordescribingmanyapproximationschemesinvolvingvaluesand(or)derivativesofagivenfunction.

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简介：一个方法为转换被描述在Laguerre多项式使用扩大并且把Mellin变换变换成Laplace变换的Mellin变换，然后，Laplace变换被合适的替换变换成第一个客气的卷绕旋转积分方程。那么获得的不可分的方程是一个提出病的问题，我们使用花键规则化解决它。方法的性能被在文学可得到的测试函数的倒置说明[J。Inst。数学。与Appl。20(1977)，p。73]，[J。数学。Comp。53(1989)，p。589]，[J。Sci。Stat。Comp。4(1983)，p。164]。方法的有效性被获得的结果显示出借助于桌子和图示威了。

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简介：Basicrequirementforapplyingisoparametricelementisthattheelementhastobeconvexandnoviolentdistortionisallowed.Inthispaper,acubicquadrilateralsplineelementwith12nodeshasbeendevelopedusingthetriangularareacoordinatesandtheB-netmethod,whichcanexactlymodelthecubicfieldforquadrilateralelementwithbothconvexandconcaveshapes.Neithermappingnorcoordinatetransformationisrequiredandthesplineelementcanobtainhighaccuracysolutionsandinsensitivetomeshdistortions.

简介：InterpolatingasetofplanarpointsisacommonprobleminCAD.Mostconstructionsofinterpolationfunctionsarebasedontheparametersatthesamplepoints.Assigningparameterstoallsamplepointsisavitalstepbeforeconstructinginterpolationfunctions.Themostwidelyusedparameterizationmethodisaccumulativechordlengthparameterization.Inthispaper,wegiveoutabettermethodbasedontheinterpolationofconics.Basedonthismethod,asequenceoffairerHermitecurvescanbeconstructed.

简介：TheexplicitexpressionoftheG~3basisfunctionispresentedinthispaper.ItisderivedbyconstructingtheconversionmatrixbetweenG~3basisfunctionandBézierrepresentation.Afterthematrixdecomposition,equationsforconstructingG~3splinescanbepresentedindependentlyofgeometricshapeparameters’values.Itmakestheequation’ssolvingeasier.ItisalsoknownthatthegeneralformoftheG~3splinebasisfunctionisgiveninthefirsttime.Itsgeometricconstructionmethodispresented.

简介：Amethodforfairingasurfacecomposedofasetofdiscretedatapointsdistributedinanonrectangulartopologicalmeshispresented.AllcurvesareexpressedbynonuniformcubicB-splinecurves.Thefairingmethodisminimizingtheelasticstrainenergyofmeshcurvesandofspringsat-tachedtothedatapoints.Thefairingsurfacecanbegeneratedbyinterpolatingthroughthemeshcurves.Thegenerationandfairingofashiphullsurfaceisgivenasanexample.

简介：LetιbeatriangulationofapolygonaldomainDR2withverticesV={v1:1≤i≤N,}andRSk（D,τ）={u∈Ck（D）:(T∈τ,u|τisarationalfunction}.Thepurposeofthispaperistostudytheexist-enceandconstructionofC^{μ-rationalsplinefunctionsonanytriangulationτforCAGD.TheHermiteprob-lemHμ（V,U）={findu∈}