The Essentials of CAGD_scan

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1、TheEssentialsofCAGDGERALDE.FARINDIANNEHANSFORDAKPetersNatick,MassachusettsEditorial,Sales,andCustomerServiceOfficeAKPeters,Ltd.63SouthAvenueNatick,MA01760Copyright©2000byAKPeters,Ltd.Allrightsreserved.Nopartofthematerialprotectedbythiscopyrightnoticemaybereproducedorutilizedinanyform,electronicormec

2、hanical,includingphotocopying,recording,orbyanyinformationstorageandretrievalsystem,withoutwrittenpermissionfromthecopyrightowner.LibraryofCongressCataloging-in-PublicationDataFarin,GeraldE.TheessentialsofCAGDIGeraldFarin,DianneHansfordp.em.Includesbibliographicalreferencesandindex.ISBN1-56881-123-3

3、1.Computergraphics.2.Computer-aideddesign.I.Hansford,Dianne.II.Title.T385.F382000006.6'9-dc2100-044134PrintedintheUnitedStatesofAmerica040302010010987654321ForBarbara&DavidContentsPrefacexi1TheBareBasics11.1PointsandVectors11.2Operations31.3Products......51.4AffineMaps....71.5TrianglesandTetrahedra8

4、1.6Exercises..112LinesandPlanes132.1LinearInterpolation132.2LineForms.....162.3Planes........182.4LinearPieces:Polygons192.5LinearPieces:Triangulations202.6WorkingwithTriangulations222.7Exercises...........233CubicBezierCurves253.1ParametricCurves253.2CubicBezierCurves273.3Derivatives.....303.4Thede

5、CasteljauAlgorithm323.5Subdivision.........343.6ExploringthePropertiesofBezierCurves363.7TheMatrixFormandMonomials.393.8Exercises..................414BezierCurves:CubicandBeyond434.1BezierCurves.............434.2DerivativesRevisited..........454.3ThedeCasteljauAlgorithmRevisited474.4TheMatrixFormand

6、MonomialsRevisited48viiContents4.5DegreeElevation...........494.6DegreeReduction...........524.7BezierCurvesoverGeneralIntervals544.8FunctionalBezierCurves544.9MoreonBernsteinPolynomials554.10Exercises575PuttingCurvestoWork595.1CubicInterpolation......595.2InterpolationBeyondCubics615.3Aitken'sAlgor

7、ithm.....635.4Approximation........665.5FindingtheRightParameters685.6HermiteInterpolation685.7Exercises706BezierPatches716.1ParametricSurfaces716.2BilinearPatches726.3BezierPatches...756.4Propertieso