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CoachworkexamplegeneratedusingtheBRepmodel.Noticethatthesurfaceareasarestitchedtogether.

Insolidmodelingandcomputeraideddesign,boundaryrepresentationoftenabbreviatedasBreporBREPisamethodforrepresentingshapesusingthelimits.Asolidisrepresentedasacollectionofconnectedsurfaceelements,theboundarybetweensolidandnonsolid.

Contents

1Overview2History3Standardization4Furtherreading5Seealso6Externallinks

Overview[edit]

Boundaryrepresentationmodelsarecomposedoftwoparts:topologyandgeometry(surfaces,curvesandpoints).Themaintopologicalitemsare:faces,edgesandvertices.Afaceisaboundedportionofasurfaceanedgeisaboundedpieceofacurveandavertexliesatapoint.Otherelementsaretheshell(asetofconnectedfaces),theloop(acircuitofedgesboundingaface)andloopedgelinks(alsoknownaswingededgelinksorhalfedges)whichareusedtocreatetheedgecircuits.Theedgesareliketheedgesofatable,boundingasurfaceportion.[clarificationneeded]

History[edit]

ThebasicmethodforBREPwasdevelopedindependentlyintheearly1970sbybothIanC.BraidinCambridge(forCAD)andBruceG.BaumgartatStanford(forcomputervision).BraidcontinuedhisworkwiththeresearchsolidmodellerBUILDwhichwastheforerunnerofmanyresearchandcommercialsolidmodellingsystems.BraidworkedonthecommercialsystemsROMULUS,the

http://en.wikipedia.org/wiki/Stanfordhttp://en.wikipedia.org/w/index.php?title=Boundary_representation&action=edit&section=1http://en.wikipedia.org/wiki/Computer_visionhttp://en.wikipedia.org/wiki/Face_(geometry)http://en.wikipedia.org/wiki/Romulus_(b-rep_solid_modeler)http://en.wikipedia.org/wiki/Winged_edgehttp://en.wikipedia.org/wiki/File:WEAZER0.jpghttp://en.wikipedia.org/wiki/Wikipedia:Please_clarifyhttp://en.wikipedia.org/wiki/Computer-aided_designhttp://en.wikipedia.org/wiki/Parasolidhttp://en.wikipedia.org/wiki/Topologyhttp://en.wikipedia.org/wiki/Vertex_(geometry)http://en.wikipedia.org/wiki/Computer_representation_of_surfaceshttp://en.wikipedia.org/wiki/University_of_Cambridgehttp://en.wikipedia.org/w/index.php?title=Boundary_representation&action=edit&section=2http://en.wikipedia.org/wiki/Edge_(geometry)http://en.wikipedia.org/wiki/Solid_modelinghttp://en.wikipedia.org/wiki/ACIS

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forerunnerofParasolid,andonACIS.ParasolidandACISarethebasisformanyoftoday'scommercialCADsystems.

FollowingBraid'sworkforsolids,aSwedishteamledbyProfessorTorstenKjellberg,developedthephilosophyandmethodsforworkingwithhybridmodels,wireframes,sheetobjectsandvolumetricmodelsduringtheearly1980s.InFinland,MarttiMntylproducedasolidmodellingsystemcalledGWB.IntheUSAEastmanandWeilerwerealsoworkingonBoundaryRepresentationandinJapanProfessorFumihikoKimuraandhisteamatTokyoUniversityalsoproducedtheirownBrepmodellingsystem.

Comparedtotheconstructivesolidgeometry(CSG)representation,whichusesonlyprimitiveobjectsandBooleanoperationstocombinethem,boundaryrepresentationismoreflexibleandhasamuchricheroperationset.ThismakesboundaryrepresentationamoreappropriatechoiceforCADsystems.[citationneeded]CSGwasusedinitiallybyseveralcommercialsystemsbecauseitwaseasiertoimplement.TheadventofreliablecommercialBrepkernelsystemslikeParasolidandACIS,mentionedabove,hasledtowidespreadadoptionofBrepforCAD.AswellastheBooleanoperations,Brephasextrusion(orsweeping),chamfer,blending,drafting,shelling,tweakingandotheroperationswhichmakeuseofthese.

Boundaryrepresentationisessentiallyalocalrepresentationconnectingfaces,edgesandvertices.Anextensionofthiswastogroupsubelementsoftheshapeintologicalunitscalledgeometricfeatures,orsimplyfeatures.PioneeringworkwasdonebyKyprianouinCambridgealsousingtheBUILDsystemandcontinuedandextendedbyJaredandothers.Featuresarethebasisofmanyotherdevelopments,allowinghighlevel"geometricreasoning"aboutshapeforcomparison,processplanning,manufacturing,etc.

Boundaryrepresentationhasalsobeenextendedtoallowspecial,nonsolidmodeltypescallednonmanifoldmodels.AsdescribedbyBraid,normalsolidsfoundinnaturehavethepropertythat,ateverypointontheboundary,asmallenoughspherearoundthepointisdividedintotwopieces,oneinsideandoneoutsidetheobject.[citationneeded]Nonmanifoldmodelsbreakthisrule.Animportantsubclassofnonmanifoldmodelsaresheetobjectswhichareusedtorepresentthinplateobjectsandintegratesurfacemodellingintoasolidmodellingenvironment.

Standardization[edit]

Intheworldofdataexchange,STEP,theStandardfortheExchangeofProductModeldataalsodefinessomedatamodelsforboundaryrepresentations.ThecommongenerictopologicalandgeometricmodelsaredefinedinISO1030342Geometricandtopologicalrepresentation.ThefollowingApplicationIntegratedResources(AICs)defineboundarymodelsthatareconstraintsofthegenericgeometricandtopologicalcapabilities:

ISO10303511Topologicallyboundedsurface,definitionofanadvancedface,thatisaboundedsurfacewherethesurfaceisoftypeelementary(plane,cylindrical,conical,sphericalortoroidal),orasweptsurface,orbsplinesurface.Theboundariesaredefinedbylines,conics,polylines,surfacecurves,orbsplinecurvesISO10303514Advancedboundaryrepresentation,asoliddefiningavolumewithpossiblevoidsthatiscomposedbyadvancedfacesISO10303509Manifoldsurface,anonintersectingareain3DthatiscomposedbyadvancedfacesISO10303521Manifoldsubsurface,asubareaoutofamanifoldsurfaceISO10303508Nonmanifoldsurface,anykindofadvancedfacearrangementISO10303513ElementaryboundaryrepresentationsimilartoISO10303514,butrestrictedtotheelementarysurfacesonly

http://en.wikipedia.org/wiki/Spline_(mathematics)http://en.wikipedia.org/wiki/ISO_10303http://en.wikipedia.org/wiki/Chamferinghttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Boolean_logichttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Boundary_representation&action=edit&section=3http://en.wikipedia.org/wiki/Parasolidhttp://en.wikipedia.org/wiki/Extrusionhttp://en.wikipedia.org/wiki/ACIShttp://en.wikipedia.org/wiki/Constructive_solid_geometry

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ISO10303512Facetedboundaryrepresentationasimplifiedsurfacemodelconstructedbyplanarsurfacesonly

Furtherreading[edit]

FurtherinformationaboutBoundaryRepresentationcanbefoundinavarietyofpapersandthefollowingbooks:

MarttiMntyl:"AnIntroductiontoSolidModeling",ComputerSciencePress,ISBN0881751081,1988.

H.Chiyokura:"SolidModellingwithDESIGNBASE",AddisonWesleyPublishingCompany,ISBN0201192454,1988.

IanStroud:"BoundaryRepresentationModellingTechniques,Springer,ISBN1846283124,2006

Seealso[edit]

WingededgeSplineCoonssurfaceBeziercurveBeziersurfaceBspline

NURBSSolidmodelingConstructivesolidgeometry(CSG)FunctionrepresentationCombinatorialmaps

Externallinks[edit]OpenCascadeanopensourcelibraryforBRepsolidmodelingActualexampleofsourceboundaryrepresentationinSTEPformatSimpleGeoaBrep/CSGhybridmodelingsystemforMonteCarloparticletransportsimulationsFreeREPOpensourcegeometrykerneldevelopmentBrepAboundaryrepresentationbasedmodeler

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