區(qū)間算法在幾何造型中的應(yīng)用.pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)碩士學(xué)位論文區(qū)間算法在幾何造型中的應(yīng)用姓名：楊霄峰申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：馮玉瑜陳發(fā)來(lái)2001.5.1AbstractThispaperdiscussessomeapplicationsofintervalarithemeticingeom—etrymodelingSpecificiallyweapplyintervalarithemeticinfindingthecom—moilfactorsoftw

2、opolynomials，mergingapairofintervalBeliercurvesanddegreeredcutionofintervalB—splinecurvesTheseproblemshavetheoreticalandpracticalimportanceincomputergraphicsandgeometricmodelingInthefirstchapter，afterabriefviewoftheroleo

3、fsolidmodellersinCADandCAM，weexplaintheimportanceofrobustnessforcurvedorsurfacedsolidmodelsInafloatingcomputingenvironment，therearealwayssomedefectsinthesystemswhencomputingInordertogetridofthiskindofproblem，intervalarit

4、hemeticandroundedintervalarithemeticareintroducedFurthermore，intervalBeiiercurvesandintervalB—splinecurvesandtheirpropertiesarealsodiscussedInthesecondchapter，firstly，weapplytheroundedintervalarithemetictothesolutionofth

5、ecommonfactorsoftwopolynomialsTwodifferentap—proachesareproposedboundedonEuclidalgorithmOneisontheexponentbases，theotherisontheBernsteinbasesAndthevalidityofthealgorithmsareprovedandexamplesarecitedtoillustratethemThethi

6、rdchapterisdevotedtomergeapairofintervalBeliercurvesWepresentedtheprecisemergingconditionoftwoBernsteinpolynomialsBothLlnormand”Discrete”coefficientnorminL2senseareusedtogettwodifferentconstrainedoptimizationmethods，resp

7、ectivelySomeexamplesareprovidedtodemonstratethealgorithmsandcomparethemInthechapterfour，TwodifferentalgorithmicapproachestothedegreereductionofintervalB—splinecurvesarepresentedOneiscalled’’intergralmethod”theotheristhe’

8、’piecewisedegreereductionmethod”ExamplesareprovidedtodemonstratethealgorithmsandcomparethetwodifferentapproachesTheexperimentalresultsshowthatthepiecewisedegreereduc—tionmethodisgenerallymoreefficientandproducestighterbo