B樣條曲線和圓域B樣條曲線數(shù)據(jù)縮減的研究.pdf

1、福建師范大學(xué)碩士學(xué)位論文B樣條曲線和圓域B樣條曲線數(shù)據(jù)縮減的研究姓名：翁彬申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：潘日晶20060401塑壟塹薹奎蘭堡主蘭垡笙蘭AbstractBsplinecurvesandsurfacesarebasicfigurerepresentationt001ofmostoftheComputerAidedDesign(CAD)systemsThedatastorage，errorrepresentatio

2、nanddataexchangeofthemintheCADsystems，areimportantintheresearchareaoftheComputerAidedGeometricDesign(CAGD)ThispaperstudiesindepththedatareductionofB—splinecurves(includesdegree—reductionandknot—removal)anddisk／spherecurv

3、esandsurfacesmodelingtechenologythemainresultsandaresummedupasfollows：1Thispapersummarizesandanalyzestheexisteddegree—reductionalgorithmsandknot—removalalgorithmspointoutoneoftheinsufficienceofthealgorithmsisthat，theycan

4、’tsimultaneouslyreducedegreesandremoveknots，inthepracticewhichthedegree—reductionandknot—removalarebothneeded，thedegreereductionandknot—removalcanonlybeexcutedseparatelythustheaccumulateerrorswillbeincreasedThisPaDercomb

5、inetheB—splinetransitionmatrixandthe1eastsquaretheoryproposeaunifornlmethodtodegree—reductionandknotremovalofBsplinecurvesThismethodcanreducemulti—degreeandremoveseveralknotsoftheB—splinecurvessimultaneouslybysomecomputa

6、tionofmatrixItissimpleandCallbeeasilyrealizedandcanreducetheaccumulateerrorsTheuniforillmethodcanbeusedtosinglyreducethedegreesorsinglyremovetheknotsWhenusedtodegree—reductionitcanreducemultidegreeWhenusedtoknot—removal，

7、itcanremoveseveralknotsatonetimeTheapproximatecurvesoftheunifornlmethodcaninterpolatetheend—pointsoftheoriginalcurvesAlotofexamplesareprovidedtotestifythefeasibilityofthemethod，andcomparewithsometheexisteddegree—reductio

8、nandknot—removaIalgorithmThismethodmaybeusedinthedatareductionofBsplinecurvesandthedataexchangeofdifferentCADsystems2TheresearchofcurvesandsurfacesmodelingtechenologybaseonerrorrepresentationaresummarizedandanalyzedBaseo

9、nthediskarithmetic，thispaperproposesdiskBsplinecurves，anddiscussestheirsomebasicpropertiesandalgorithmsWhenwecomparethediskBsplinecurveswithintervalBsplinescurves，italsoCaBrepresenttheerrorrangeofBsplineCurves，besides，it

10、hastheadvantageofsmallerstorageinformationandtheerrorrangewon’tbechangedundertherotationtransition3Thispaperstudiestheknot—removalproblemofthediskB—splinecurves，thatis，boundingdiskB—splinecurveswithone—knot—removeddiskBs

11、plinecurvesTwomethodsareproposedtosolvetheproblem，bothofthemcangettheanalyticsolutionTheexamplesareprovided，andtheapproximateerroroftwomethodsarecomparedTheknot—removalalgorithmcancarrytheerrorinformationoftheoriginalcur