T樣條函數(shù)空間的維數(shù)研究.pdf

1、大連理工大學碩士學位論文T樣條函數(shù)空間的維數(shù)研究姓名：李桃申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：羅鐘鉉20070601T樣條函數(shù)空間的維數(shù)研究ResearchonDimensionsofSplineSpacesoverTomeshesAbstractSplinefunctionis821importantapproximationtoolincomputationalgeometrymaditiswidelyusedinmanyen

2、gineeringfieldsInordertobetterunderstandsplinespaceandtoapplyit，thefirstproblemistoexplicititsalgebraicstructureanditsdimensionHowever，thedimensionofmultivariatesplinespacedependsnotonlyitstopologi嘣propertyofitspartition

3、，butalsosometimesheavilyOnthegeometricpropertyofitspartitionTmeshsplinespaceisfirstlypresentedbySederberg，etal[1lin2003，whichisdefinedingeneralTmeshUsingBnetsmethod，JiansongDeng，etal【2]derivedthedimensionOilTmeshsphnespa

4、cewhenthesmoothnessislessthanhalfofthedegreeofthesplinefunctions，whichdependsOnthetopologicalpropertyofTmeshButwhenthesmoothnessisclosetothedegree，thedimensionformulahash’tgottenInthispaper，firstlyageneralformulaofdimens

5、ionofsplinespaceS(rn，札，Q，p，f)overTmeshisgivenbymeansoforderingskilltoinneredgesofTmeshundertheframeofSmoothingCofactorConformalitymethodTheresultofthefirstpartimprovesthecorrespondingresultsin【2]and【17】Secondlybasedonthe