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自由形态B样条曲面网格生成的参数化方法研究(英文).docx

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自由形态B样条曲面网格生成的参数化方法研究(英文) Title:ResearchonParameterizationMethodsforFreeformB-splineSurfaceMeshGeneration Abstract: B-splinesurfaceshavebecomeapopulartoolforrepresentingandmanipulatingfreeformsurfacesinvariousapplicationssuchascomputergraphics,computer-aideddesign,andgeometricmodeling.However,generatingaparameterizationforB-splinesurfacesposessignificantchallengesduetotheircomplexgeometry.ThispaperaimstoexploreandevaluatedifferentmethodsforparameterizingfreeformB-splinesurfacestogeneratehigh-qualitysurfacemesh. 1.Introduction TheintroductionprovidesbackgroundinformationonB-splinesurfacesandtheirsignificanceinvariousfields.Italsohighlightstheimportanceofparameterizationforcreatingsurfacemeshes.Theresearchobjective,scope,andstructureofthepaperareoutlined. 2.B-splineSurfaces:ConceptsandProperties ThissectionbrieflyintroducesthefundamentalconceptsandpropertiesofB-splinesurfaces.ItcoverstheNURBS(Non-UniformRationalB-Spline)representation,controlpoints,knotvectors,andthetensorproductsurfaceconstruction. 3.ChallengesinParameterizationofFreeformB-splineSurfaces Here,thespecificchallengesinvolvedinparameterizingfreeformB-splinesurfacesarediscussed.Topicsincludeirregularknotconfiguration,surfaceself-intersections,geometriccomplexity,andpreservationofsurfacefeatures. 4.LiteratureReview AcomprehensivereviewofexistingliteratureisconductedtoanalyzethedifferentparameterizationmethodsproposedforB-splinesurfaces.Thereviewcoversbothtraditionaltechniquesandmorerecentadvancementsinthefield. 5.ParameterizationMethods ThissectionpresentsadetailedexplanationofvariousparameterizationmethodssuitableforfreeformB-splinesurfaces.Thisincludesmethodsbasedonparameterspaceconstruction,optimization-basedapproaches,andharmonicmappingtechniques.Eachmethodisexplained,alongwithitsadvantagesandlimitations. 6.PerformanceEvaluation Anevaluationframeworkisdevelopedtocomparetheperformanceofdifferentparameterizationmethods.Criteriasuchascomputationtime,distortionmetrics,surfacefeaturepreservation,andmeshqual