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1、ComputationalGeometry:MethodsandApplicationsJianerChenComputerScienceDepartmentTexasA&MUniversityFebruary19,1996Chapter1IntroductionGeometricobjectssuchaspoints,lines,andpolygonsarethebasisofabroadvarietyofimportantapplicationsandgiverisetoaninterestingsetofproblemsand
2、algorithms.Thenamegeometryremindsusofitsearliestuse:forthemeasurementoflandandmaterials.Today,computersarebeingusedmoreandmoretosolvelarger-scalegeometricproblems.Overthepasttwodecades,asetoftoolsandtechniqueshasbeendevelopedthattakesadvantageofthestructureprovidedbyge
3、ometry.ThisdisciplineisknownasComputationalGeometry.Thedisciplinewasnamedandlargelystartedaround1975byShamos,whosePh.D.thesisattractedconsiderableattention.Afteradecadeofdevel-opmentthe eldcameintoitsownin1985,whenthreecomponentsofanyhealthydisciplinewererealized:atext
4、book,aconference,andajournal.PreparataandShamos'sbookComputationalGeometry:AnIntroduction[23],the rsttextbooksolelydevotedtothetopic,waspublishedataboutthesametimeasthe rstACMSymposiumonComputationalGeometrywasheld,andjustpriortothestartofanewSpringer-VerlagjournalDisc
5、reteandComputationalGeometry.The eldiscurrentlythriving.Since1985,sev-eraltexts,collections,andmonographshaveappeared[1,10,18,20,25,26].Theannualsymposiumhasattracted100papersand200attendeessteadily.Thereisevidencethatthe eldisbroadeningtotouchgeometricmodelingandgeome
6、trictheoremproving.Perhapsmostimportantly,the rststudentswhoobtainedtheirPh.D.sincomputersciencewiththesesincomputationalgeometryhavegraduated,obtainedpositions,andarenowtrainingthenextgenerationofresearchers.ComputationalgeometryisofpracticalimportancebecauseEuclidean
7、12INTRODUCTIONspaceoftwoandthreedimensionsformsthearenainwhichrealphysicalobjectsarearranged.Alargenumberofapplicationsareassuchaspaternrecognition[28],computergraphics[19],imageprocessing[22],operationsresearch,statistics[4,27],computer-aideddesign,robotics[25,26],etc
8、.,havebeentheincubationbedofthedisciplinesincetheyprovideinherentlygeo-metricproblemsforwhichecientalgorithmshavetob
