两种曲面求交方法的对比分析

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1、I．2Pre!viousWorkResearchersaroundtheworldhaveattemptedtosolvethisproblem；however,noperfectalgorithmhasbeenintroduced．Eachalgorithmhasseveralproblems，Latticeevaluationmethodswereusedtodeterminetheintersectioncurvef53][56]．Reviewsofgeneralintersectionmethodsarenumerous【

2、9】【22】[26】【29】[49】【50]．WilfandManor[57】presentedamethodusingamodificationofLevin’sruled．surfaceparameterizationscheme，guidedbyinvariant-factorsclassificationandfurthermore，byfactorizationofthepammeterizationpolynomials．MarketandMagedsonr441presentedaproceduralmethodto

3、parameterizetheintersectioncurveoftwosur自cesbycomputingexactpointsonthetrueintersectioncurve．Aparallelalgorithmusingthedivide．and—conquermethodwaspresentedbyBurgerandSchaback[12]．Thecomputationalcomplexityofthisalgorithmwasalsoanalyzed．Searchtechniqueswereusedtorefine

4、theintervalprogressively【25]．Anothermethodthatwasapplicdtothesurface．surfaceintersectionproblemisatopologicalanddi虢rential-equationmethodf151．Inthismethod，thevectorfielddefinedasthegradientoftheorienteddistaneefunetionisused幻detectcriticalpointsinthefieldsuchassingula

5、rities．"rensorialdifierentialequationsarethenusedtotraceintersectionsegments．AnothermethodthatusesunidimensionalsearchestodetectintersectionpointswaspresentedbyAomuraandUehamf51．SurfaceintersectionusingparallelismwasaddressedbyChangeta1．n41．Adifferentapproachtohigher．

6、dimemionalformulationincludingoffsets．equaldistaneesurfaces．andvariableradiusblendingsurfaceswasdiscussedbyHoffman【281．Ahigher-dimensiomlformulationwasalsousedbyChuang『161todeterminealocalandglobalapproximanLMarchingmethodshavebeenextensivelyusedbyresearchersinthisfie

7、ld[7]【l5】．Theaccuracyofrmrchingmethodshasbeenimprovedbypropercontrolofthestepsize．SingularitieswerearialyzedbyAbdebMalck，K．，Ha!'n-JouYahandRockwood，A．，bybcallyconstructingasecond．orderapproximanttoeachsurfaco．Parametricsurface．surfaceintersectionhasalsobeenaddressedby

8、Houghtonetat【32]GarrityandWarren【23】andMullenheim【47】．SingularitiesabngtheintersectioncurvehavebeenidentifiedintheworkbyLuka