空間閉折線所圍的極小網(wǎng)格曲面設(shè)計(jì).pdf

1、浙江大學(xué)數(shù)學(xué)系碩士學(xué)位論文空間閉折線所圍的極小網(wǎng)格曲面設(shè)計(jì)姓名：馮敬真申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王國瑾20080501浙江大學(xué)碩士學(xué)位論文關(guān)鍵詞：極小曲面，PlateauBspfine問題，Dirichlet能量函數(shù)，3次口一B樣條曲線，均勻三角剖分ABSTRACTTobeginwithwebrieflyretrospectthebirthandtheevolutionoftheminimalsurfaceproblem

2、(PlateauProblem)，andwecomprehensivelyintroduceSOftieimportantmethods，usefulsignifieances，andessentiallindrationsofrecentresearchesonB6zierminimalsurfacemodelingandBsplineminimalsurfacemodelinginthefieldofCAGDFurthermorew

3、epointoutthatitisnecessaryandreasonableforUStOstudydesignofminimalmeshsurfacesurroundedgivenspatialclosedbrokenlineAndthenweintroducethegeneralideaandthespecificDirichletapproachoftheplateauB6zierproblemWealsoretrospectt

4、hemodelingandpropertyofthecubic口13splinecurvethatinterpolatesgivendataAfterwards，weexpandaseriesofindepthdiscussionsandresearchesOiltheminimalmeshsurfacemodelingsurroundedgivenspacialclosedbrokenline，includingitsgenerals

5、tatementitstheoreticalmechanismalsobringforwardtheideaofusingtheDirichletsolutionofthePlateau一出叩lineproblemThen，wegetthedesignoftheminimalmeshsurfacemodelingfromtheviewofgeometryapproachFinally，wevalidatethisnewkindofthe

6、oDrandalgorithmbygivingalargevarietyofexamplesofthedoublethreedegreeBsplinesurfaccsThemostimportantcontributionsandinnovationsofthisthesiscanbesummedupasfollows：1Itisthefirsttimethattheminimalmesh娜rfacesmodelingproblemha

7、sbeenproposedandapproachedsuccessfullyinCAGD，whichwillhaveaprofoundinfluenceonsomefieldsofengineering，suchasconstructionandmechanism2WeextendDirichletenergyfunctionmethodintothefieldofdoublethreedegreeBspline鋤rfacesWeu∞t