二元對(duì)角向量值有理插值和曲線的奇拐點(diǎn)分布的研究.pdf

1、合肥工業(yè)大學(xué)碩士學(xué)位論文二元對(duì)角向量值有理插值和曲線的奇拐點(diǎn)分布的研究姓名：陳歡歡申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：朱曉臨20080501ResearchonBivariateDiagonalVectorValuedRationalInterpolationandDistributionofSingularitiesandInflectionPointsonCurvesABSTRACTThisthesismainlymakess

2、omeresearchonalgorithmsforbivariatediagonalvectorvaluedrationalinterpolationandtheinflectionandsingularpointsonFB。splinecurvesItincludestwokindsofalgorithmsforthebivariatevectorvaluedrationalinterpolationoverleadingdiago

3、nalandsubdiagonalrespectively，thematrixalgorithmforcomputingbivariatediagonalvectorvaluedrationalinterpolationwithpreassignedpoles，distributionofsingularities，inflectionpoints。loopsandcuspsonFBsplinecurvesInthefirstparto

4、fthisthesis，wevectorvaluedrationalinterpolation，reviewthebasictheoryandmethodofthethedevelopmentofcurveandsurfacemodeling，thedevelopmentofanalysisofinflectionandsingularpointsonsoreekindsofcurves，andbrieflyintroducetheal

5、gorithmforthebivariatethieletypevectorvaluedbranchedcontinuedfractionrationalinterpolation，thealgorithmforbivariatevectorvaluedrationalinterpolationoverrectanglegridswhichislackofdatum，thedefinitionofC—Bsplinecufves，H—Bs

6、plinecurvesandFBsplinecurvesanalysisofinflectionandsingularpointsonplanarCB6ziercurvesanalysisofsingularitiesonrationalB6ziercurvesInthesecondpartofthisthesis，wefirstlygivetwomethodsforcomputingbivariatediagonalvectorval

7、uedrationalinterpolation，oneiScomputing反，directly，anotherisakindofmatrixmethodwhichisgivenbydefiningaspecialelementaryoperationinthesenseofSamelsoninverseInadditionweconstructsamatrixalgorithmforcomputingbivariatediagona

8、lvectorvaluedrationalinterpolationwithpreassignedpoles，thensomeexamplesaregiventoillustratethevalidityoftheabovealgorithmsWediscussessingularities，inflectionpointsandconvexityofFB。splinecurvesintermsoftheircontrolpolygon

9、s，andgivesthenecessaryandsufficientconditionsfortestingwhenFBsplinecurveshaveoneortwoinflectionpoints，oracusp，oraloop，ornoneoftheabovepointsbytheenvelopetheoriesandtopologicalmappingmethodAtlast，allkindsofdistributionofs