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Thegeometryinsolidmodelingisfullydescribedin3Dspaceobjectscanbeviewedfromanyangle.

SolidmodelingFromWikipedia,thefreeencyclopedia

Solidmodeling(ormodelling)isaconsistentsetofprinciplesformathematicalandcomputermodelingofthreedimensionalsolids.Solidmodelingisdistinguishedfromrelatedareasofgeometricmodelingandcomputergraphicsbyitsemphasisonphysicalfidelity.[1]Together,theprinciplesofgeometricandsolidmodelingformthefoundationofcomputeraideddesignandingeneralsupportthecreation,exchange,visualization,animation,interrogation,andannotationofdigitalmodelsofphysicalobjects.

Contents

1Overview2Mathematicalfoundations3Solidrepresentationschemes

3.1Parameterizedprimitiveinstancing3.2Spatialoccupancyenumeration3.3Celldecomposition3.4Boundaryrepresentation3.5Surfacemeshmodeling3.6Constructivesolidgeometry3.7Sweeping3.8Implicitrepresentation3.9Parametricandfeaturebasedmodeling

4Historyofsolidmodelers5Computeraideddesign

5.1Parametricmodeling5.2Medicalsolidmodeling5.3Engineering

6Seealso7References8Externallinks

Overview

Theuseofsolidmodelingtechniquesallowsfortheautomationofseveraldifficultengineeringcalculationsthatarecarriedoutasapartofthedesignprocess.Simulation,planning,andverificationofprocessessuchasmachiningandassemblywereoneofthemaincatalystsforthedevelopmentofsolid

http://en.wikipedia.org/wiki/Geometric_modelinghttp://en.wikipedia.org/wiki/File:Jack-in-cube_solid_model,_light_background.gifhttp://en.wikipedia.org/wiki/Machininghttp://en.wikipedia.org/wiki/Assembly_linehttp://en.wikipedia.org/wiki/Computer-aided_designhttp://en.wikipedia.org/wiki/Computer_graphics

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Regularizationofa2dsetbytakingtheclosureofitsinterior

modeling.Morerecently,therangeofsupportedmanufacturingapplicationshasbeengreatlyexpandedtoincludesheetmetalmanufacturing,injectionmolding,welding,piperoutingetc.Beyondtraditionalmanufacturing,solidmodelingtechniquesserveasthefoundationforrapidprototyping,digitaldataarchivalandreverseengineeringbyreconstructingsolidsfromsampledpointsonphysicalobjects,mechanicalanalysisusingfiniteelements,motionplanningandNCpathverification,kinematicanddynamicanalysisofmechanisms,andsoon.Acentralprobleminalltheseapplicationsistheabilitytoeffectivelyrepresentandmanipulatethreedimensionalgeometryinafashionthatisconsistentwiththephysicalbehaviorofrealartifacts.Solidmodelingresearchanddevelopmenthaseffectivelyaddressedmanyoftheseissues,andcontinuestobeacentralfocusofcomputeraidedengineering.

Mathematicalfoundations

Thenotionofsolidmodelingaspracticedtodayreliesonthespecificneedforinformationalcompletenessinmechanicalgeometricmodelingsystems,inthesensethatanycomputermodelshouldsupportallgeometricqueriesthatmaybeaskedofitscorrespondingphysicalobject.Therequirementimplicitlyrecognizesthepossibilityofseveralcomputerrepresentationsofthesamephysicalobjectaslongasanytwosuchrepresentationsareconsistent.Itisimpossibletocomputationallyverifyinformationalcompletenessofarepresentationunlessthenotionofaphysicalobjectisdefinedintermsofcomputablemathematicalpropertiesandindependentofanyparticularrepresentation.Suchreasoningledtothedevelopmentofthemodelingparadigmthathasshapedthefieldofsolidmodelingasweknowittoday.[2]

Allmanufacturedcomponentshavefinitesizeandwellbehavedboundaries,soinitiallythefocuswasonmathematicallymodelingrigidpartsmadeofhomogeneousisotropicmaterialthatcouldbeaddedorremoved.ThesepostulatedpropertiescanbetranslatedintopropertiesofsubsetsofthreedimensionalEuclideanspace.Thetwocommonapproachestodefinesolidityrelyonpointsettopologyandalgebraictopologyrespectively.Bothmodelsspecifyhowsolidscanbebuiltfromsimplepiecesorcells.

Accordingtothecontinuumpointsetmodelofsolidity,allthepointsofanyX3canbeclassifiedaccordingtotheirneighborhoodswithrespecttoXasinterior,exterior,orboundarypoints.Assuming3isendowedwiththetypicalEuclideanmetric,aneighborhoodofapointpXtakestheformofanopenball.ForXtobeconsideredsolid,everyneighborhoodofanypXmustbeconsistentlythreedimensionalpointswithlowerdimensionalneighborhoodsindicatealackofsolidity.Dimensionalhomogeneityofneighborhoodsisguaranteedfortheclassofclosedregularsets,definedassetsequaltotheclosureoftheirinterior.AnyX3canbeturnedintoaclosedregularsetorregularizedbytakingtheclosureofitsinterior,andthusthemodelingspaceofsolidsismathematicallydefinedtobethespaceofclosedregularsubsetsof3(bytheHeineBoreltheoremitisimpliedthatallsolidsarecompactsets).Inaddition,solidsarerequiredtobeclosedundertheBooleanoperationsofsetunion,intersection,anddifference(toguaranteesolidityaftermaterialadditionandremoval).Applyingthe

http://en.wikipedia.org/wiki/Neighborhood_(topology)http://en.wikipedia.org/wiki/Point-set_topologyhttp://en.wikipedia.org/wiki/Heine%E2%80%93Borel_theoremhttp://en.wikipedia.org/wiki/Algebraic_topologyhttp://en.wikipedia.org/wiki/Weldinghttp://en.wikipedia.org/wiki/Exterior_(topology)http://en.wikipedia.org/wiki/Isotropichttp://en.wikipedia.org/wiki/Boundary_(topology)http://en.wikipedia.org/wiki/Dynamics_(physics)http://en.wikipedia.org/wiki/Ball_(mathematics)http://en.wikipedia.org/wiki/Boundary_(topology)http://en.wikipedia.org/wiki/Reverse_engineeringhttp://en.wikipedia.org/wiki/Manufacturinghttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Motion_planninghttp://en.wikipedia.org/wiki/Mechanism_(engineering)http://en.wikipedia.org/wiki/Compact_spacehttp://en.wikipedia.org/wiki/Injection_moldinghttp://en.wikipedia.org/wiki/Closure_(topology)http://en.wikipedia.org/wiki/Rapid_prototypinghttp://en.wikipedia.org/wiki/Euclidean_metrichttp://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Kinematicshttp://en.wikipedia.org/wiki/Interior_(topology)http://en.wikipedia.org/wiki/Pipinghttp://en.wikipedia.org/wiki/Computer-aided_engineeringhttp://en.wikipedia.org/wiki/File:Regularize1.pnghttp://en.wikipedia.org/wiki/Sheet_metal

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standardBooleanoperationstoclosedregularsetsmaynotproduceaclosedregularset,butthisproblemcanbesolvedbyregularizingtheresultofapplyingthestandardBooleanoperations.[3]Theregularizedsetoperationsaredenoted,,and.

ThecombinatorialcharacterizationofasetX3asasolidinvolvesrepresentingXasanorientablecellcomplexsothatthecellsprovidefinitespatialaddressesforpointsinanotherwiseinnumerablecontinuum.[1]TheclassofsemianalyticboundedsubsetsofEuclideanspaceisclosedunderBooleanoperations(standardandregularized)andexhibitstheadditionalpropertythateverysemianalyticsetcanbestratifiedintoacollectionofdisjointcellsofdimensions0,1,2,3.Atriangulationofasemianalyticsetintoacollectionofpoints,linesegments,triangularfaces,andtetrahedralelementsisanexampleofastratificationthatiscommonlyused.Thecombinatorialmodelofsolidityisthensummarizedbysayingthatinadditiontobeingsemianalyticboundedsubsets,solidsarethreedimensionaltopologicalpolyhedra,specificallythreedimensionalorientablemanifoldswithboundary.[4]InparticularthisimpliestheEulercharacteristicofthecombinatorialboundary[5]ofthepolyhedronis2.ThecombinatorialmanifoldmodelofsolidityalsoguaranteestheboundaryofasolidseparatesspaceintoexactlytwocomponentsasaconsequenceoftheJordanBrouwertheorem,thuseliminatingsetswithnonmanifoldneighborhoodsthataredeemedimpossibletomanufacture.

Thepointsetandcombinatorialmodelsofsolidsareentirelyconsistentwitheachother,canbeusedinterchangeably,relyingoncontinuumorcombinatorialpropertiesasneeded,andcanbeextendedtondimensions.Thekeypropertythatfacilitatesthisconsistencyisthattheclassofclosedregularsubsetsofncoincidespreciselywithhomogeneouslyndimensionaltopologicalpolyhedra.Thereforeeveryndimensionalsolidmaybeunambiguouslyrepresentedbyitsboundaryandtheboundaryhasthecombinatorialstructureofann1dimensionalpolyhedronhavinghomogeneouslyn1dimensionalneighborhoods.

Solidrepresentationschemes

Basedonassumedmathematicalproperties,anyschemeofrepresentingsolidsisamethodforcapturinginformationabouttheclassofsemianalyticsubsetsofEuclideanspace.Thismeansallrepresentationsaredifferentwaysoforganizingthesamegeometricandtopologicaldataintheformofadatastructure.Allrepresentationschemesareorganizedintermsofafinitenumberofoperationsonasetofprimitives.Thereforethemodelingspaceofanyparticularrepresentationisfinite,andanysinglerepresentationschememaynotcompletelysufficetorepresentalltypesofsolids.Forexample,solidsdefinedviacombinationsofregularizedbooleanoperationscannotnecessarilyberepresentedasthesweepofaprimitivemovingaccordingtoaspacetrajectory,exceptinverysimplecases.Thisforcesmoderngeometricmodelingsystemstomaintainseveralrepresentationschemesofsolidsandalsofacilitateefficientconversionbetweenrepresentationschemes.

Belowisalistofcommontechniquesusedtocreateorrepresentsolidmodels.[4]Modernmodelingsoftwaremayuseacombinationoftheseschemestorepresentasolid.

Parameterizedprimitiveinstancing

Thisschemeisbasedonmotionoffamiliesofobjects,eachmemberofafamilydistinguishablefromtheotherbyafewparameters.Eachobjectfamilyiscalledagenericprimitive,andindividualobjectswithinafamilyarecalledprimitiveinstances.Forexampleafamilyofboltsisagenericprimitive,andasingleboltspecifiedbyaparticularsetofparametersisaprimitiveinstance.Thedistinguishingcharacteristicofpureparameterizedinstancingschemesisthelackofmeansforcombininginstancestocreatenew

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structureswhichrepresentnewandmorecomplexobjects.Theothermaindrawbackofthisschemeisthedifficultyofwritingalgorithmsforcomputingpropertiesofrepresentedsolids.Aconsiderableamountoffamilyspecificinformationmustbebuiltintothealgorithmsandthereforeeachgenericprimitivemustbetreatedasaspecialcase,allowingnouniformoveralltreatment.

Spatialoccupancyenumeration

Thisschemeisessentiallyalistofspatialcellsoccupiedbythesolid.Thecells,alsocalledvoxelsarecubesofafixedsizeandarearrangedinafixedspatialgrid(otherpolyhedralarrangementsarealsopossiblebutcubesarethesimplest).Eachcellmayberepresentedbythecoordinatesofasinglepoint,suchasthecell'scentroid.Usuallyaspecificscanningorderisimposedandthecorrespondingorderedsetofcoordinatesiscalledaspatialarray.Spatialarraysareunambiguousanduniquesolidrepresentationsbutaretooverboseforuseas'master'ordefinitionalrepresentations.Theycan,however,representcoarseapproximationsofpartsandcanbeusedtoimprovetheperformanceofgeometricalgorithms,especiallywhenusedinconjunctionwithotherrepresentationssuchasconstructivesolidgeometry.

Celldecomposition

Thisschemefollowsfromthecombinatoric(algebraictopological)descriptionsofsolidsdetailedabove.Asolidcanberepresentedbyitsdecompositionintoseveralcells.Spatialoccupancyenumerationschemesareaparticularcaseofcelldecompositionswhereallthecellsarecubicalandlieinaregulargrid.Celldecompositionsprovideconvenientwaysforcomputingcertaintopologicalpropertiesofsolidssuchasitsconnectedness(numberofpieces)andgenus(numberofholes).Celldecompositionsintheformoftriangulationsaretherepresentationsusedin3dfiniteelementsforthenumericalsolutionofpartialdifferentialequations.OthercelldecompositionssuchasaWhitneyregularstratificationorMorsedecompositionsmaybeusedforapplicationsinrobotmotionplanning.[6]

Boundaryrepresentation

Inthisschemeasolidisrepresentedbythecellulardecompositionofitsboundary.SincetheboundariesofsolidshavethedistinguishingpropertythattheyseparatespaceintoregionsdefinedbytheinteriorofthesolidandthecomplementaryexterioraccordingtotheJordanBrouwertheoremdiscussedabove,everypointinspacecanunambiguouslybetestedagainstthesolidbytestingthepointagainsttheboundaryofthesolid.Recallthatabilitytotesteverypointinthesolidprovidesaguaranteeofsolidity.Usingraycastingitispossibletocountthenumberofintersectionsofacastrayagainsttheboundaryofthesolid.Evennumberofintersectionscorrespondtoexteriorpoints,andoddnumberofintersectionscorrespondtointeriorpoints.Theassumptionofboundariesasmanifoldcellcomplexesforcesanyboundaryrepresentationtoobeydisjointednessofdistinctprimitives,i.e.therearenoselfintersectionsthatcausenonmanifoldpoints.Inparticular,themanifoldnessconditionimpliesallpairsofverticesaredisjoint,pairsofedgesareeitherdisjointorintersectatonevertex,andpairsoffacesaredisjointorintersectatacommonedge.Severaldatastructuresthatarecombinatorialmapshavebeendevelopedtostoreboundaryrepresentationsofsolids.Inadditiontoplanarfaces,modernsystemsprovidetheabilitytostorequadricsandNURBSsurfacesasapartoftheboundaryrepresentation.Boundaryrepresentationshaveevolvedintoaubiquitousrepresentationschemeofsolidsinmostcommercialgeometricmodelersbecauseoftheirflexibilityinrepresentingsolidsexhibitingahighlevelofgeometriccomplexity.

Surfacemeshmodeling

http://en.wikipedia.org/wiki/Constructive_solid_geometryhttp://en.wikipedia.org/wiki/Connected_spacehttp://en.wikipedia.org/wiki/Voxelhttp://en.wikipedia.org/wiki/Topological_propertieshttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Topologically_stratified_spacehttp://en.wikipedia.org/wiki/Finite_elementshttp://en.wikipedia.org/wiki/Ray_castinghttp://en.wikipedia.org/wiki/Nurbshttp://en.wikipedia.org/wiki/Combinatorial_mapshttp://en.wikipedia.org/wiki/Quadrichttp://en.wikipedia.org/wiki/Genus_(mathematics)

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Similartoboundaryrepresentation,thesurfaceoftheobjectisrepresented.However,ratherthancomplexdatastructuresandNURBS,asimplesurfacemeshofverticiesandedgesisused.Surfacemeshescanbestructured(asintriangularmeshesinSTLfilesorquadmesheswithhorizontalandverticalringsofquadrilaterals),orunstructuredmesheswithrandomlygroupedtrianglesandhigherlevelpolygons.

Constructivesolidgeometry

Constructivesolidgeometry(CSG)connotesafamilyofschemesforrepresentingrigidsolidsasBooleanconstructionsorcombinationsofprimitivesviatheregularizedsetoperationsdiscussedabove.CSGandboundaryrepresentationsarecurrentlythemostimportantrepresentationschemesforsolids.CSGrepresentationstaketheformoforderedbinarytreeswherenonterminalnodesrepresenteitherrigidtransformations(orientationpreservingisometries)orregularizedsetoperations.Terminalnodesareprimitiveleavesthatrepresentclosedregularsets.ThesemanticsofCSGrepresentationsisclear.Eachsubtreerepresentsasetresultingfromapplyingtheindicatedtransformations/regularizedsetoperationsonthesetrepresentedbytheprimitiveleavesofthesubtree.CSGrepresentationsareparticularlyusefulforcapturingdesignintentintheformoffeaturescorrespondingtomaterialadditionorremoval(bosses,holes,pocketsetc.).TheattractivepropertiesofCSGincludeconciseness,guaranteedvalidityofsolids,computationallyconvenientBooleanalgebraicproperties,andnaturalcontrolofasolid'sshapeintermsofhighlevelparametersdefiningthesolid'sprimitivesandtheirpositionsandorientations.Therelativelysimpledatastructureandelegantrecursivealgorithms[7]havefurthercontributedtothepopularityofCSG.

Sweeping

Thebasicnotionembodiedinsweepingschemesissimple.Asetmovingthroughspacemaytraceorsweepoutvolume(asolid)thatmayberepresentedbythemovingsetanditstrajectory.Sucharepresentationisimportantinthecontextofapplicationssuchasdetectingthematerialremovedfromacutterasitmovesalongaspecifiedtrajectory,computingdynamicinterferenceoftwosolidsundergoingrelativemotion,motionplanning,andevenincomputergraphicsapplicationssuchastracingthemotionsofabrushmovedonacanvas.MostcommercialCADsystemsprovide(limited)functionalityforconstructingsweptsolidsmostlyintheformofatwodimensionalcrosssectionmovingonaspacetrajectorytransversaltothesection.However,currentresearchhasshownseveralapproximationsofthreedimensionalshapesmovingacrossoneparameter,andevenmultiparametermotions.

Implicitrepresentation

AverygeneralmethodofdefiningasetofpointsXistospecifyapredicatethatcanbeevaluatedatanypointinspace.Inotherwords,Xisdefinedimplicitlytoconsistofallthepointsthatsatisfytheconditionspecifiedbythepredicate.Thesimplestformofapredicateistheconditiononthesignofarealvaluedfunctionresultinginthefamiliarrepresentationofsetsbyequalitiesandinequalities.Forexampleif

theconditions , ,and representrespectivelyaplaneandtwoopenlinearhalfspaces.Morecomplexfunctionalprimitivesmaybedefinedbybooleancombinationsofsimplerpredicates.Furthermore,thetheoryofRfunctionsallowconversionsofsuchrepresentationsintoasinglefunctioninequalityforanyclosedsemianalyticset.Sucharepresentationcanbeconvertedtoaboundaryrepresentationusingpolygonizationalgorithms,forexample,themarchingcubesalgorithm.

Parametricandfeaturebasedmodeling

http://en.wikipedia.org/wiki/Half-space_(geometry)http://en.wikipedia.org/wiki/Isometryhttp://en.wikipedia.org/wiki/Node_(computer_science)http://en.wikipedia.org/wiki/Rvachev_functionhttp://en.wikipedia.org/wiki/Orientation_(mathematics)http://en.wikipedia.org/wiki/STL_(file_format)http://en.wikipedia.org/wiki/Predicate_(mathematical_logic)http://en.wikipedia.org/wiki/Marching_cubeshttp://en.wikipedia.org/wiki/Recursionhttp://en.wikipedia.org/wiki/Binary_tree

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Featuresaredefinedtobeparametricshapesassociatedwithattributessuchasintrinsicgeometricparameters(length,width,depthetc.),positionandorientation,geometrictolerances,materialproperties,andreferencestootherfeatures.[8]Featuresalsoprovideaccesstorelatedproductionprocessesandresourcemodels.Thus,featureshaveasemanticallyhigherlevelthanprimitiveclosedregularsets.FeaturesaregenerallyexpectedtoformabasisforlinkingCADwithdownstreammanufacturingapplications,andalsofororganizingdatabasesfordesigndatareuse.Parametricfeaturebasedmodelingisfrequentlycombinedwithconstructivebinarysolidgeometry(CSG)tofullydescribesystemsofcomplexobjectsinengineering.

Historyofsolidmodelers

ThehistoricaldevelopmentofsolidmodelershastobeseenincontextofthewholehistoryofCAD,thekeymilestonesbeingthedevelopmentoftheresearchsystemBUILDfollowedbyitscommercialspinoffRomuluswhichwentontoinfluencethedevelopmentofParasolid,ACISandSolidModelingSolutions.OneofthefirstCADdevelopersintheCommonwealthofIndependentStates(CIS),ASCONbeganinternaldevelopmentofitsownsolidmodelerinthe1990's.[9]InNovember2012,themathematicaldivisionofASCONbecameaseparatecompany,andwasnamedC3DLabs.ItwasassignedthetaskofdevelopingtheC3Dgeometricmodelingkernelasastandaloneproducttheonlycommercial3DmodelingkernelfromRussia.[10]OthercontributionscamefromMntyl,withhisGWBandfromtheGPMprojectwhichcontributed,amongotherthings,hybridmodelingtechniquesatthebeginningofthe1980's.ThisisalsowhentheProgrammingLanguageofSolidModelingPLaSMwasconceivedattheUniversityofRome.

Computeraideddesign

ThemodelingofsolidsisonlytheminimumrequirementofaCADsystemscapabilities.Solidmodelershavebecomecommonplaceinengineeringdepartmentsinthelasttenyearsduetofastercomputersandcompetitivesoftwarepricing.Solidmodelingsoftwarecreatesavirtual3Drepresentationofcomponentsformachinedesignandanalysis.[11]Atypicalgraphicaluserinterfaceincludesprogrammablemacros,keyboardshortcutsanddynamicmodelmanipulation.Theabilitytodynamicallyreorientthemodel,inrealtimeshaded3D,isemphasizedandhelpsthedesignermaintainamental3Dimage.

Asolidpartmodelgenerallyconsistsofagroupoffeatures,addedoneatatime,untilthemodeliscomplete.Engineeringsolidmodelsarebuiltmostlywithsketcherbasedfeatures2Dsketchesthataresweptalongapathtobecome3D.Thesemaybecuts,orextrusionsforexample.Designworkoncomponentsisusuallydonewithinthecontextofthewholeproductusingassemblymodelingmethods.Anassemblymodelincorporatesreferencestoindividualpartmodelsthatcomprisetheproduct.[12]

Anothertypeofmodelingtechniqueis'surfacing'(Freeformsurfacemodeling).Here,surfacesaredefined,trimmedandmerged,andfilledtomakesolid.Thesurfacesareusuallydefinedwithdatumcurvesinspaceandavarietyofcomplexcommands.Surfacingismoredifficult,butbetterapplicabletosomemanufacturingtechniques,likeinjectionmolding.Solidmodelsforinjectionmoldedpartsusuallyhavebothsurfacingandsketcherbasedfeatures.

Engineeringdrawingscanbecreatedsemiautomaticallyandreferencethesolidmodels.

Parametricmodeling

http://en.wikipedia.org/wiki/Material_propertieshttp://en.wikipedia.org/wiki/GUIhttp://en.wikipedia.org/wiki/ACIShttp://en.wikipedia.org/wiki/Freeform_surface_modelinghttp://en.wikipedia.org/wiki/Computer-aided_design#Capabilitieshttp://en.wikipedia.org/wiki/C3Dhttp://en.wikipedia.org/wiki/Parasolidhttp://en.wikipedia.org/wiki/Romulus_(b-rep_solid_modeler)http://en.wikipedia.org/wiki/Engineering_drawinghttp://en.wikipedia.org/wiki/Databasehttp://en.wikipedia.org/wiki/PLaSMhttp://en.wikipedia.org/wiki/Geometric_tolerancehttp://en.wikipedia.org/wiki/Commonwealth_of_Independent_Stateshttp://en.wikipedia.org/wiki/Solid_Modeling_Solutionshttp://en.wikipedia.org/wiki/CAD#Historyhttp://en.wikipedia.org/wiki/Assembly_modellinghttp://en.wikipedia.org/wiki/Geometric_modeling_kernelhttp://en.wikipedia.org/wiki/C3D

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Parametricmodelingusesparameterstodefineamodel(dimensions,forexample).Examplesofparametersare:dimensionsusedtocreatemodelfeatures,materialdensity,formulastodescribesweptfeatures,importeddata(thatdescribeareferencesurface,forexample).Theparametermaybemodifiedlater,andthemodelwillupdatetoreflectthemodification.Typically,thereisarelationshipbetweenparts,assemblies,anddrawings.Apartconsistsofmultiplefeatures,andanassemblyconsistsofmultipleparts.Drawingscanbemadefromeitherpartsorassemblies.

Example:Ashaftiscreatedbyextrudingacircle100mm.Ahubisassembledtotheendoftheshaft.Later,theshaftismodifiedtobe200mmlong(clickontheshaft,selectthelengthdimension,modifyto200).Whenthemodelisupdatedtheshaftwillbe200mmlong,thehubwillrelocatetotheendoftheshafttowhichitwasassembled,andtheengineeringdrawingsandmasspropertieswillreflectallchangesautomatically.

Relatedtoparameters,butslightlydifferentareconstraints.Constraintsarerelationshipsbetweenentitiesthatmakeupaparticularshape.Forawindow,thesidesmightbedefinedasbeingparallel,andofthesamelength.Parametricmodelingisobviousandintuitive.ButforthefirstthreedecadesofCADthiswasnotthecase.Modificationmeantredraw,oraddanewcutorprotrusionontopofoldones.Dimensionsonengineeringdrawingswerecreated,insteadofshown.Parametricmodelingisverypowerful,butrequiresmoreskillinmodelcreation.Acomplicatedmodelforaninjectionmoldedpartmayhaveathousandfeatures,andmodifyinganearlyfeaturemaycauselaterfeaturestofail.Skillfullycreatedparametricmodelsareeasiertomaintainandmodify.Parametricmodelingalsolendsitselftodatareuse.Awholefamilyofcapscrewscanbecontainedinonemodel,forexample.

Medicalsolidmodeling

Moderncomputedaxialtomographyandmagneticresonanceimagingscannerscanbeusedtocreatesolidmodelsofinternalbodyfeatures,socalledvolumerendering.Optical3Dscannerscanbeusedtocreatepointcloudsorpolygonmeshmodelsofexternalbodyfeatures.

Usesofmedicalsolidmodeling

VisualizationVisualizationofspecificbodytissues(justbloodvesselsandtumor,forexample)Designingprosthetics,orthotics,andothermedicalanddentaldevices(thisissometimescalledmasscustomization)Creatingpolygonmeshmodelsforrapidprototyping(toaidsurgeonspreparingfordifficultsurgeries,forexample)CombiningpolygonmeshmodelswithCADsolidmodeling(designofhipreplacementparts,forexample)Computationalanalysisofcomplexbiologicalprocesses,e.g.airflow,bloodflowComputationalsimulationofnewmedicaldevicesandimplantsinvivo

Iftheusegoesbeyondvisualizationofthescandata,processeslikeimagesegmentationandimagebasedmeshingwillbenecessarytogenerateanaccurateandrealisticgeometricaldescriptionofthescandata.

Engineering

http://en.wikipedia.org/wiki/3D_scannershttp://en.wikipedia.org/wiki/Constraint_(computer-aided_design)http://en.wikipedia.org/wiki/Prostheticshttp://en.wikipedia.org/wiki/Magnetic_resonance_imaginghttp://en.wikipedia.org/wiki/Segmentation_(image_processing)http://en.wikipedia.org/wiki/Orthoticshttp://en.wikipedia.org/wiki/Injection_moldinghttp://en.wikipedia.org/wiki/Polygon_meshhttp://en.wikipedia.org/wiki/Volume_renderinghttp://en.wikipedia.org/wiki/Image-based_meshinghttp://en.wikipedia.org/wiki/Computed_axial_tomographyhttp://en.wikipedia.org/wiki/Mass_customizationhttp://en.wikipedia.org/wiki/CADhttp://en.wikipedia.org/wiki/Rapid_prototyping

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MasspropertieswindowofamodelinCobalt

BecauseCADprogramsrunningoncomputersunderstandthetruegeometrycomprisingcomplexshapes,manyattributesof/fora3Dsolid,suchasitscenterofgravity,volume,andmass,canbequicklycalculated.Forinstance,thecubeshownatthetopofthisarticlemeasures8.4mmfromflattoflat.Despiteitsmanyradiiandtheshallowpyramidoneachofitssixfaces,itspropertiesarereadilycalculatedforthedesigner,asshowninthescreenshotatright.

Seealso

PLaSMProgrammingLanguageofSolidModeling.ComputergraphicsComputationalgeometryEulerboundaryrepresentationEngineeringdrawingTechnicaldrawingListofCADcompanies

References

1. Shapiro,Vadim(2001).SolidModeling(http://salcnc.me.wisc.edu/index.php?option=com_remository&Itemid=143&func=fileinfo&id=53).Elsevier.Retrieved20April2010.

2. Requicha,A.A.GandVoelcker,H.(1983).SolidModeling:CurrentStatusandResearchDirections(http://www.computer.org/portal/web/csdl/doi/10.1109/MCG.1983.263271).IEEEComputerGraphics.Retrieved20April2010.

3. Tilove,R.B.andRequicha,A.A.G(1980).ClosureofBooleanoperationsongeometricentities(http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYR481DX38P3&_user=443835&_coverDate=09/30/1980&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1307947802&_rerunOrigin=scholar.google&_acct=C000020958&_version=1&_urlVersion=0&_userid=443835&md5=746253db42dc581e1d64d396ed605799).ComputerAidedDesign.Retrieved20April2010.

4. Requicha,A.A.G.(1980).RepresentationsforRigidSolids:Theory,Methods,andSystems(http://portal.acm.org/citation.cfm?id=356833&dl=).ACMComputingSurveys.Retrieved20April2010.

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5. Hatcher,A.(2002).AlgebraicTopology(http://www.math.cornell.edu/~hatcher/AT/ATpage.html).CambridgeUniversityPress.Retrieved20April2010.

6. Canny,JohnF.(1987).TheComplexityofRobotMotionPlanning(http://mitpress.mit.edu/catalog/item/default.asp?tid=4749&ttype=2).MITpress,ACMdoctoraldissertationaward.Retrieved20April2010.

7. Ziegler,M.(2004)."ComputableOperatorsonRegularSets".Wiley.doi:10.1002/malq.200310107(https://dx.doi.org/10.1002%2Fmalq.200310107).

8. Mantyla,M.,Nau,D.,andShah,J.(1996).Challengesinfeaturebasedmanufacturingresearch(http://portal.acm.org/citation.cfm?id=230808).CommunicationsoftheACM.Retrieved20April2010.

9. Yares,Evan(April2013)."RussianCAD"(http://www.designworlddigital.com/designworld/april_2013#pg61).DesignWorld(WTWHMedia,LLC)8(4).ISSN19417217(https://www.worldcat.org/issn/19417217).

10. Golovanov,Nikolay(2014).GeometricModeling:Themathematicsofshapes(http://www.amazon.com/GeometricModelingThemathematicsshapes/dp/1497473195).CreateSpaceIndependentPublishingPlatform(December24,2014).p.Backcover.ISBN9781497473195.

11. LaCourse,Donald(1995)."2".HandbookofSolidModeling.McGrawHill.p.2.5.ISBN0070357889.12. LaCourse,Donald(1995)."11".HandbookofSolidModeling.McGrawHill.p.111.2.ISBN0070357889.

Externallinks

sgCoreC++/C#library(http://www.geometros.com)TheSolidModelingAssociation(http://solidmodeling.org/)

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Categories: 3Dcomputergraphics Computeraideddesign Euclideansolidgeometry

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