用雙三次混合孔斯曲面填充n邊域

1、遼寧師范大學碩士學位論文用雙三次混合孔斯曲面填充N邊域姓名：昝志聞申請學位級別：碩士專業(yè)：計算數學指導教師：彭興璇；崔利宏201204用雙三次混合孔斯曲面填充N邊域FillingNsidedregionswithBicubicallyblendedCoonspatchesAbstractFillingNsidedregionsisanessentialoperationinshapeandsurfacemodeling，whichisw

2、idelyusedinvertexblending，fillingsurfacegenerationandothermodelingphasesItaimstoprovideatrimmedsurfaceorsurfacepatchesinpolynomialorrationalB—splineform，whichinterpolatethehole’Sboundaryandcrossboundaryderivativecurves，f

3、ulfillinggeometriccontinuityconditionsontheboundaryPositionalandtangentialcontinuitiesarehighlyrequiredindesigningandmanufacturingSinceBsplinehasbecomeapopularandstandardrepresentationfor3DmodelsinCAD／CAMsystems，fillingN

4、sidedholesusingBsplinesurfacesiswidelydiscussedinthepasttwodecadesThispaperpresentsanalgorithmtofillannsidedregionwithNURBSpatchesthatinterpolateboundarycurvesandapproximategivencross—boundaryderivativesThealgorithmfirst

5、computesacentralpoint，acentralnormal，thecentral，andthecornerderivativevectorsThentheregionissplitintonquadrilateralpatchesbyconnectingacentralvertexoftheregiontothemiddlepointofeachboundarycurve。TheNURBSsurfacesjoiningal

6、onginnerorboundarycHiveshavenormalvectorsthatdonotdeviatemorethantheuserspecifiedangulartolerancesThemethodisgeneral!inthattherearenestrictionsonthenumberofboundaryCHIVES，andthecrossboundaryderivativescanbespecifiedindep

7、endentlyAlso，thevariationalapproachtosolvingsuchproblemshasreceivedconsiderableattentioninthepastfewyears，duetotheirefficiencyandusefulnessinthefittinganddesignofcurvesandsurfacesKeyWords：Nsidedregions；CoonssurfacesBspli