離散三角網格上的法向量和曲率估計.pdf

1、大連理工大學碩士學位論文離散三角網格上的法向量和曲率估計姓名：羅良峰申請學位級別：碩士專業(yè)：計算數學指導教師：劉秀平20070622大連理工大學碩士學位論文格式規(guī)范NormalvectorsandcurvaturesestimationOntriangularmeshAbstractCurvatureis趾importantgeometricattributeOilsulfateTheimpfieitorparametricsurfac

2、ehasbeendefinedverywellindifferentialgeometrynetriangularmeshisdefinedbypointscloudandtopologierelationamongthepoints111e∞formulasofthefirstandsecondorderdifferentialpropertiesindifferentialgeomeuy鋤notbeusedOnalaiangular

3、meshandmanyeslimationmethodsappearAtthesametime，Cu／vmturesestimationisthefoundationofmanyapplicationsatarbilraryvertices011atriangularmeshsuchascharacteristicdeteetiagOnapolyhedralsllrffltce，smoothing，simplificationdisto

4、rtionandlegiondecompositionTaubinpresentedasimplemethodtoestimateculvature$whielaislinearintimeandspaceTheydescribedamethodtOesdmatethefallSOl“ofcllrvatttreofasurfaceattheverticesofatriangularmeshPrincipalc：ulvatllresand

5、principaldirectionsa地obtainedbycomputingindosedformtheeigenvaluesandeigenveetorsofcertain3x3symmetricmatricesdefinedbyintegralformulas，andcloselyrelatedtOthemallixrepresentationofthetensorofcuavatureHoweverwefoundoutthat

6、Taubinestimatednormalwithareaweights，whichne西eetedtheeffectsoftriangularshapeSlaengGwoChertpresentedthemethodofnormalvectorsandcurvatureswitheentroidweightsTaubinusedcirculararcstoapproximatethenormalcurvatureandChertShi

7、DongdescribedamoleaccuratemethodwlaieheslJll3砒edthenormalcurvaturewithnormalinformationofnei曲borhoodpointsInthispaperweuseeentroidweightstOapproximatethenormalvectorsandne、^，normalcurvaturesle$1illlationmethodtoimproveTa

8、ubinsmethodin1995WeprovirleparticulareompariSOnresultsofatror011趾implicitandparametricSul“faceNormalvcctotsGamsianandmeancurvaturesestimation黜obtainedbydifferentcurvaturesestimationmethodsandtheeITOriscomputedbycomparing

9、estilllationresultswithrealOnesOnthesphereoftraitradiusandtOmsComparedwi也oldTaubinsmethodtheimprovedTaubinsmethodhasitsadvantageinstabilizationandexactitudeWealsocomparetheresultsofourmethodwithMeyers，andgetbetterresults