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1、0029/09/0415:36PageiGeometryforComputerGraphics0029/09/0415:36PageiiiJohnVinceGeometryforComputerGraphicsFormulae,ExamplesandProofs1230029/09/0415:36PageivJohnVinceMTech,PhD,CEng,FBCSNationalCentreforComputerAnimationBournemouthUniversity,UKBritishLibraryC
2、ataloguinginPublicationDataVince,John(JohnA.)Geometryforcomputergraphics:formulae,examplesandproofs1.Computergraphics2.Geometry–DataprocessingI.Title516′.0028566ISBN1852338342LibraryofCongressCataloging-in-PublicationDataAcatalogrecordforthisbookisavailabl
3、efromtheLibraryofCongressApartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismorreview,aspermittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced,storedortransmitted,inanyformorbyanymeans,withthepriorpermis
4、sioninwritingofthepublishers,orinthecaseofreprographicreproductioninaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesenttothepublishers.ISBN1-85233-834-2Springer-VerlagLondonBerlin
5、HeidelbergSpringerScienceBusinessMediaspringeronline.com©Springer-VerlagLondonLimited2005PrintedintheUnitedStatesofAmericaTheuseofregisterednames,trademarksetc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromthe
6、relevantlawsandregulationsandthereforefreeforgeneraluse.Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyoftheinformationcontainedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrorsoromissionsthatmaybemade.Typese
7、tting:GrayPublishing,TunbridgeWells,UK34/3830-543210Printedonacid-freepaperSPIN109816960029/09/0415:36PagevDedicationThisbookisdedicatedtomyfamily,Annie,Samantha,Anthony,Megan,andMonty,whohavenotseenmuchofmeoverthepasttwoyears.0029/09/0415:36PageviiPreface
8、Anyonewhohaswrittenprogramsforcomputergraphics,CAD,scientificvisualization,computergames,virtualrealityorcomputeranimationwillknowthatmathematicsisextremelyuseful.Topicssuchastransformations,matrixalgebra,vect