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1、ComputationalGeometry:MethodsandApplicationsJianerChenComputerScienceDepartmentTexasA&MUniversityFebruary19,1996Chapter1IntroductionGeometricobjectssuchaspoints,lines,andpolygonsarethebasisofabroadvarietyofimportantapplicationsandgiverisetoaninterestingsetofproblemsandalgorithms.The
2、namegeometryremindsusofitsearliestuse:forthemeasurementoflandandmaterials.Today,computersarebeingusedmoreandmoretosolvelarger-scalegeometricproblems.Overthepasttwodecades,asetoftoolsandtechniqueshasbeendevelopedthattakesadvantageofthestructureprovidedbygeometry.Thisdisciplineisknown
3、asComputationalGeometry.Thedisciplinewasnamedandlargelystartedaround1975byShamos,whosePh.D.thesisattractedconsiderableattention.Afteradecadeofdevel-opmentthe eldcameintoitsownin1985,whenthreecomponentsofanyhealthydisciplinewererealized:atextbook,aconference,andajournal.PreparataandS
4、hamos'sbookComputationalGeometry:AnIntroduction[23],the rsttextbooksolelydevotedtothetopic,waspublishedataboutthesametimeasthe rstACMSymposiumonComputationalGeometrywasheld,andjustpriortothestartofanewSpringer-VerlagjournalDiscreteandComputationalGeometry.The eldiscurrentlythriving.
5、Since1985,sev-eraltexts,collections,andmonographshaveappeared[1,10,18,20,25,26].Theannualsymposiumhasattracted100papersand200attendeessteadily.Thereisevidencethatthe eldisbroadeningtotouchgeometricmodelingandgeometrictheoremproving.Perhapsmostimportantly,the rststudentswhoobtainedth
6、eirPh.D.sincomputersciencewiththesesincomputationalgeometryhavegraduated,obtainedpositions,andarenowtrainingthenextgenerationofresearchers.ComputationalgeometryisofpracticalimportancebecauseEuclidean12INTRODUCTIONspaceoftwoandthreedimensionsformsthearenainwhichrealphysicalobjectsare
7、arranged.Alargenumberofapplicationsareassuchaspaternrecognition[28],computergraphics[19],imageprocessing[22],operationsresearch,statistics[4,27],computer-aideddesign,robotics[25,26],etc.,havebeentheincubationbedofthedisciplinesincetheyprovideinherentlygeo-metricproblemsforwhichecie
8、ntalgorithmshavetob
