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Boundaryrepresentation

BRepmodelsrepresentasolidindirectlybyarepresentationofitsboundingsurface.ABRepsolidisrepresentedasavolumecontainedinasetoffacestogetherwithtopologicalinformationwhichdefinestherelationshipsbetweenthefaces.BecauseBRepincludesuchtopologicalinformation,asolidisrepresentedasaclosedspacein3Dspace.Theboundaryofasolidseparatespointsinsidefrompointsoutsideofthesolid.Brepmodelscanrepresentawideclassofobjectsbutdatastructureiscomplex,anditrequiresalargememoryspace.AverysimpleBrepmodelconstructedusing6facesisshowninFigure5.

Figure5:AsimpleBrepmodelconstructedusing6faces

Normallyafaceisaboundedregionofaplanar,quadratic,toroidal,orsculpturedsurface.Theboundedregionofthesurfacethatformsthefaceisrepresentedbyaclosedcurvethatlieonthesurface.AfacecanhaveseveralboundingcurvestorepresentholesinasolidTheboundingcurvesoffacesarerepresentedbyedges.Theportionofthecurvethatformstheedgeisrepresentedbytwovertices.ABRepmodelhastofulfilthefollowingconditions:Thesetoffacesformsacompleteskinofthesolidwithnomissingparts,andfacesdonotintersecteachotherexceptatcommonverticesoredges.Furthermore,theboundariesoffacesdonotintersectthemselves.Theseconditionsdisallowselfintersectingandopenobjects.

Boundaryrepresentationcanbedividedinthreeclasses:facetted,elementary,andadvancedBRep.InfacettedBRep,asolidisboundedbyplanarsurfaces.Onlypoints,planesandplanarpolygonsarenecessaryandareimplicitlyrepresentedbytheirvertexpoints.ThesurfacesincludedinelementaryBRepareplanar,quadric,andtoroidalsurfaces.Theboundingcurvesofthefacesarelines,conics,or4thordercurves.InadvancedBRep,thesurfacesincludesalsosplinesurfaces(BSpline,Bzier,NURBS,etc.)inadditiontoelementaryBRep.Theboundingcurvesaresplinecurves.

Faces,edges,andvertices,andtherelatedgeometricinformationformthebasiccomponentsofBRepmodels.Thegeometricinformationcontainsthefaceandedgeequations(orinformationtocomputethem),andvertexcoordinates.Thetopologycontainstheinformationontherelationofthecomponents,i.e.howthefaces,edgesandverticesareconnectedtogether.InfacettedBRep,alledgesarestraightlinesegments.Thereforefacescanberepresentedaspolygonsandeachpolygonasasetofcoordinatevaluesx,yandz.Thedatastructureinthiscaseissimpleandeasytoimplement.FacettedapproximationofmoresophisticatedBRepmodelsarenormallyusedforgenerationofgraphicaloutputsinceitischeaperintermsofcomputations.

DuetothecomplexityoftheconstructionoftheBRepmodels,itisnottrivialforadesignertobuildcorrectBRepmodelsdirectly.Thedesignerneedsasufficientcollectionofmoreconvenientand

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3/26/2015 Boundaryrepresentation

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efficientsoliddescriptionmethods.ForaBRepmodeller,itisnoteasytoimplementatextualuserinterface.However,itispossibletocreatedescriptionlanguagesthatarebasedonaCSGinput.AcommonsolutionistoconstructBRepmodelsthroughaconversionfromCSGinwhichtheoperationsarelimitedtoBooleanoperations.Forthatpurpose,theBRepmodellermustincludealgorithmsforcreatingBRepmodelsfromtheCSGprimitives,andcomputingBooleanoperationsonthesemodels(i.e.boundaryevaluation).TocomputeBooleanoperationsforBRepmodelsisexpensiveandnumericalproblemsmayoccur.SometimestheboundaryevaluationisnottrivialorevenimpossibletoperformsincesomeCSGmodelshavenoconvenientrepresentationsinBRep.Forexample,aCSGsolidmaybeconstructedasaBooleansubtractionoftwocylinderswherethecylindertobesubtractedisinsidetheothercylinderandtouchesitatoneside.TheresultingBRepmodelwouldhavefoursurfaceedgesatthatpointwhereonlytwoareallowed.

BRepisusedintheautomotiveandaeroplaneindustriessinceitallowstohavedescriptionsofthesurfacestobeused,forexample,inmakingthepresseswhicharetoformthesheetsforthewings,doorsetc.

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