计算几何小论文英文.doc

《计算几何小论文英文.doc》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、ComputationalGeometryCollegeofgrudationpostgruduateclass3grade2008computationalmathematics(2008010320)ComputationalgeometryisageometricalbranchofComputationalmathematics,Approximationtheory,Differentialgeometry,AlgebraicgeometryandComputerscience・Ithasveryimportanttheoteticalsig

2、nificancenotonlyingeometrybutalsoinCAD,CAM,Computergraphics,Imageprocessingandotherconcernedfieldhasimportantvalue・ComputationalgeometryisalivelysubfieldinTheoteticalcomputerscience.Theachievementhasbeenuseincomputergraphics,Chemistry,Statisticalanalysis,Patternrecognition,Geogr

3、aphicaldatabaseandsomeotherfields.Howtosupplyallkindsofbasiceffectivealgorithmtheoteticalfoundationisalwaystheresearchdirectionofnativeandabroadscholors・1ThemathematicalbasisofComputationalgeometry.ComputationalgeometryincludesWeierstrastheorem,Theoptimalunifoimapproximation,qua

4、draticapproximation,polynomialinterpolation,splineandmultivariatespline・(1)WeierstrastheoremSupposef(%)eC{a,b],thenforanygiven£〉0,itexistssuchpolynomialp(x),suchthatmaxlp(x)-/(x)

5、<£a

6、Theoptimaluniformapproximation(Tchebyshev)：p(x)istheoptimalunifoimpolynomialofPnwhenf(x)GC[a.b],ifandonlyif:P(x)~fMhasasequencenolessthann+2at[a,b].n+2ItcouldgettoA(p)bytheformofnegativeandpositiveandtheoptimaluniformapproximationissole.(2)PolynomialinterpolationPolyn

7、omialinterpolationincludesLagrangeinterpolation,Newtoninterpolation,Hermiteinterpolationandotherinterpolations.ByLagrangeasanexample:0?（兀）=（兀_首））（兀_兀］）…（兀_£）1Thebasictheoryofcurvedshapeandcurvedsurface.Thebasictheoryofcurvedshapeandcurvedsurfaceinclude:representation,basicterms,

8、geometricaljointandbasicformula.Therepresentationofcurvedshapeandcurvedsurfaceinclude:parametricrepresentationandalgebraicrepresentation.(1)Thefirstbasicformula・S2=p2=p-pT=(uv)(Ph)(ruPvX.)=VuV)F()=pFp•VsmeansthearclengthandF几•仇、C•PjPvPv)(2)Thesecondbasicformula・s?ke•n=pG卩丁G=(e'

9、Puu「An，、2Thesplinescurvedshapeandcurvedsurfaceo