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1、NicholasM.PatrikalakisTakashiMaekawaShapeInterrogationforComputerAidedDesignandManufacturingSPINSpringer'sinternalprojectnumber,ifknownMathematics{Monograph(English)June26,2001Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestPrefaceObjectivesan
2、dFeaturesShapeinterrogationistheprocessofextractionofinformationfromageo-metricmodel.ShapeinterrogationisafundamentalcomponentofComputerAidedDesignandManufacturing(CAD/CAM)systemsandwas rstusedinsuchcontextbyM.Sabin,oneofthepioneersofCAD/CAM,inthelatesix-ties.Thetermsurface
3、interrogationhasbeenusedbyI.BraidandA.Geisowinthesamecontext.Analternatetermnearlyequivalenttoshapeinterro-gationisgeometryprocessing rstusedbyR.E.Barnhill,anotherpioneerofthis eld.Inthisbookwefocusonshapeinterrogationofgeometricmodelsboundedbyfree-formsurfaces.Free-formsur
4、faces,alsocalledsculpturedsur-faces,arewidelyusedinscienti candengineeringapplications.Forexample,thehydrodynamicshapeofpropellerbladeshasanimportantroleinmarineapplications,andtheaerodynamicshapeofturbinebladesdeterminestheperformanceofaircraftengines.Free-formsurfacesaris
5、ealsointhebodiesofships,automobilesandaircraft,whichhavebothfunctionalityandattractiveshaperequirements.Manyelectronicdevicesaswellasconsumerproductsaredesignedwithaestheticshapes,whichinvolvefree-formsurfaces.Whenengineersorstylistsdesigngeometricmodelsboundedbyfree-formsu
6、rfaces,theyneedtoolsforshapeinterrogationtocheckwhetherthede-signedobjectsatis esthefunctionalityandaestheticshaperequirements.Thisbookprovidesthemathematicalfundamentalsaswellasalgorithmsforvariousshapeinterrogationmethodsincludingnonlinearpolynomialsolvers,intersectionpro
7、blems,di erentialgeometryofintersectioncurves,distancefunctions,curveandsurfaceinterrogation,umbilicsandlinesofcurvature,geodesics,ando setcurvesandsurfaces.Thebookcanserveasatextbookforteachingadvancedtopicsofgeomet-ricmodelingforgraduatestudentsaswellasprofessionalsinindu
8、stry.IthasbeenusedasoneofthetextbooksforthegraduatecourseComputationalGeometry"at
