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1、QuaternionsforComputerGraphicsJohnVinceQuaternionsforComputerGraphicsProfessorJohnVince,MTech,PhD,DSc,CEng,FBCSBournemouthUniversity,Bournemouth,UKurl:www.johnvince.co.ukISBN978-0-85729-759-4e-ISBN978-0-85729-760-0DOI10.1007/978-0-85729-760-0SpringerLondonDor
2、drechtHeidelbergNewYorkBritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressControlNumber:2011931282©Springer-VerlagLondonLimited2011Apartfromanyfairdealingforthepurposesofresearchorprivatestudy
3、,orcriticismorreview,asper-mittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced,storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublish-ers,orinthecaseofreprographicreproductioninaccordancewiththete
4、rmsoflicensesissuedbytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesenttothepublishers.Theuseofregisterednames,trademarks,etc.,inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromth
5、erelevantlawsandregulationsandthereforefreeforgeneraluse.Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyoftheinformationcontainedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrorsoromissionsthatmaybemade.Coverdes
6、ign:VTeXUAB,LithuaniaPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)ThisbookisdedicatedtoHeidiPrefaceMorethan50yearsagowhenIwasstudyingtobecomeanelectricalengineer,Icameacrosscomplexnumbers,whichwereusedtorepresentout-of
7、-phasevolt-agesandcurrentsusingthejoperator.Ibelievethattheletterjwasused,ratherthani,becausethelatterstoodforelectricalcurrent.SofromtheverystartofmystudiesIhadaclearmentalpictureoftheimaginaryunitasarotationaloperatorwhichcouldadvanceorretardelectricalquant
8、itiesintime.WheneventsdictatedthatIwouldpursueacareerincomputerprogramming—ratherthanelectricalengineering—Ihadnoneedforcomplexnumbers,untilMan-dlebrot’sworkonfractalsemerged.Butthatwasat
