細分曲線的形狀控制及應用.pdf

1、西北工業(yè)大學碩士學位論文細分曲線的形狀控制及應用姓名：丁永勝申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：蔣大為20050101細分曲線的形狀控制及應用AbstractThisthesisstudiesmodellingandapplicationofsubdivisioncurvesSubdivisionmethodhasbecomeanimportanttootincomputergraphicsrecently.Toextendapp

2、licationareas(especiallyintheareaofCAD)morewidelyhowevermanyproblemshavetobesolved.TheproblemsincludemodifyingthelocalshapeforsubdivisioncurvesandsurfacesthesubdivisionschemesforNURBSetc.Thethesisinvestigatessomeeffectiv

3、emodellingapproachesforenhancingmodellingabilityofthesubdivisionmethods.especiallymodifyingthelocalshapeforsubdivisioncurves.ThefirstlyweintroduceasubdivisionschemefortheuniformBsplinescurvesthroughtherelationbetweenthes

4、ubdivisionmarkforBsplinesandpascaltriangle.ThenanothersubdivisionschemeforuniformBsplinescurvesofodddegreewithinterpolatoryrestrictionisconstructedandwecanadjustitspartshape.Wecanfinditsefectivemodelinginmodifyingtheloca

5、lshapethroughtheexampleforthesubdivisionscheme.ThesecondlyNURBShavebeenidentifiedasbeingasensiblestandardforparametricsurfacedescriptionsbutthesubdivisionschemesforNURBSarestillfew.AnalgorithmforNURBSsubdivisioncurvesisf

6、irstgiven.Thealgorithmbasedonthesubdivisionforthediferenceoperator.Itisveryefectivethatweappliedthealgorithminthefreecurvefitingandshapecontrolling.ThepropertiesofthecurvesbythismethodarethesameaswhichoftheparameterNURBS

7、curves.Theexamplesofgeneratingcirculararcsandcirclearegiveninthelastpartofthethirdchapter.Thethirdlyweintroduceaninterpolatorysubdivisionschemewithmodifyinglocalshaperestriction.Becausewhentheparametric、ofDynfourpointbin