网格曲面造型技术研究

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1、浙江大学博士学位论文网格曲面造型技术研究姓名：赵向军申请学位级别：博士专业：计算机科学与技术指导教师：鲍虎军20060601浙江大学博士学位论文：同格曲面造型技术研究重建．综上所述，本文对网格曲面的构造、编辑和重构等关键问题提出了新方法t大量实例证明了这些方法具有很好的应用前景．关键词计算机辅助几何设计，网格曲面编辑，曲面分片重建，半静态细分，Box-spline，Loop细分，频谱编辑，数字几何处理，小波分析，自适应采样，特征对齐，无网格法，T-splines，T-splines迭代插值，变分逼近浙江大学博士论文Abstr

2、actRecently,followlngtherapiddevelopmentof3Ddataaequisitiontechniques，itisconvenienttoobtain3DmodelswithfinedetailsForthesimplicityandsuit-abilityofthepolygonmeshes，theyhavebecomethemostappropriaterepresen—tationofthosemodels．However,thepieeewiselinearcharacteristi

3、cofmeshsar-facecausesmillionsofpolygons据representthecomplexgeometrydetails，whichwilIresultjnmoredi脯curiesforthesubsequenctprocessing．Thisdissertationisconcernedwiththeabovepromisingissues，andsomenoveltechniquesofmeshmodelingareextensivelyinvestigated．Thesetechnique

4、sarc，the岛rwardtransformationproblemfromdiscretemeshtocontinuousSnrface．thatis，thesubdivisionmethodofmeshmodel；meshediting；andtheinversefit-tingproblemfromthemeshsurfacetotheparametricsurface，thatis，surfacere-construction．Detailedspeaking，themaincontributionsofourwo

5、rkcontainthreeiSSUeSasfollows．Firstly，combinedwiththelatestdevelopmentofC-B-Spline，anewtypeofparametricsurfaceisproposed，namelyforth—orderandcubicdirectionC*Box-Spline，whichisdefinedonthetriangularmesh，Itsanalyticalformulationisderivedanditsgeometricpropertiesarcal

6、sodiscussed．Moreover,weinvestl—gatethediscreterepresentationofC-Box—Spline．asemi-stationaryloopsubdivi-sionscheme，Wepointoutthatthesubdivisionprocedureisconvergent，andthesubdivisionsurfacehastheproperty．oftangentplanecontinuity．Inaddition，weextendthemethodtotheanis

7、otropieversionandtheonecapableofrepresentingsharpfeatures．Secondly,toaddressthekeyissueofmeshmodeling，anovelmeshspectrumeditingmethodisproposedinthisthesis，whichintegratesthetechniquesofflee。formdeformationandgeometrysignalprocessing．Wetakethedeformationofproxyasge

8、ometrysignal，andimposeitsspectrumuponthegeometrymodel

9、obedeformed，弧eresultantsignalisinversely打aflsformedintothespacedo—main，andthentheeditedmesh