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1、ComputationalGeometry:MethodsandApplicationsJianerChenComputerScienceDepartmentTexasA&MUniversityFebruary19,1996Chapter1IntroductionGeometricobjectssuchaspoints,lines,andpolygonsarethebasisofabroadvarietyofimportantapplicationsandgiverisetoaninterestingsetofprobl
2、emsandalgorithms.Thenamegeometryremindsusofitsearliestuse:forthemeasurementoflandandmaterials.Today,computersarebeingusedmoreandmoretosolvelarger-scalegeometricproblems.Overthepasttwodecades,asetoftoolsandtechniqueshasbeendevelopedthattakesadvantageofthestructure
3、providedbygeometry.ThisdisciplineisknownasComputationalGeometry.Thedisciplinewasnamedandlargelystartedaround1975byShamos,whosePh.D.thesisattractedconsiderableattention.Afteradecadeofdevel-opmentthe eldcameintoitsownin1985,whenthreecomponentsofanyhealthydiscipline
4、wererealized:atextbook,aconference,andajournal.PreparataandShamos'sbookComputationalGeometry:AnIntroduction[23],the rsttextbooksolelydevotedtothetopic,waspublishedataboutthesametimeasthe rstACMSymposiumonComputationalGeometrywasheld,andjustpriortothestartofanewSp
5、ringer-VerlagjournalDiscreteandComputationalGeometry.The eldiscurrentlythriving.Since1985,sev-eraltexts,collections,andmonographshaveappeared[1,10,18,20,25,26].Theannualsymposiumhasattracted100papersand200attendeessteadily.Thereisevidencethatthe eldisbroadeningto
6、touchgeometricmodelingandgeometrictheoremproving.Perhapsmostimportantly,the rststudentswhoobtainedtheirPh.D.sincomputersciencewiththesesincomputationalgeometryhavegraduated,obtainedpositions,andarenowtrainingthenextgenerationofresearchers.Computationalgeometryiso
7、fpracticalimportancebecauseEuclidean12INTRODUCTIONspaceoftwoandthreedimensionsformsthearenainwhichrealphysicalobjectsarearranged.Alargenumberofapplicationsareassuchaspaternrecognition[28],computergraphics[19],imageprocessing[22],operationsresearch,statistics[4,27
8、],computer-aideddesign,robotics[25,26],etc.,havebeentheincubationbedofthedisciplinesincetheyprovideinherentlygeo-metricproblemsforwhichecientalgorithmshavetob
