Feature ontologies for the explicit representation of shape semantics

Feature ontologies for theexplicit representation ofshape semantics

Gino Brunetti* and Stephan GrimmDepartment of Industrial Applications,Fraunhofer-Institut fuÈ r Graphische Datenverarbeitung, Fraunhoferstrasse 5,64283 Darmstadt, GermanyE-mail: [email protected] E-mail: [email protected]*Corresponding author

Abstract: CAx systems typically encode the semantics of shapes as so-called parametricfeatures on di�erent levels of abstraction. Here we discuss an approach that combinesfeature-based parametric modelling with techniques from the ®eld of knowledgerepresentation and ontological reasoning. Parametric models refer to feature ontologiesthat model feature semantics on several levels of granularity. On higher levels theinterrelation between features and feature interoperability is captured whereas on lowerlevels a feature is described in terms of geometric, topological and parametric entities.Di�erent engineering tasks can utilise feature ontologies as a basis for application-speci®cshape reasoning across several modelling layers.

Keywords: feature ontologies; shape ontologies; shape reasoning; shape semantics.

Reference to this article should be made as follows: Brunetti, G. and Grimm, S. (2005)`Feature ontologies for the explicit representation of shape semantics', Int. J. ComputerApplications in Technology, Vol. 23, Nos. 2/3/4, pp.192±202.

1 INTRODUCTION

The way current CAx systems (Computer-AidedConceptual Design, Manufacturing, Process Planning,Engineering, etc.) allow the capture of semanticinformation on top of raw geometry data is to introducefeatures on di�erent levels of modelling. Features aremodelling entities characterising commonly used shapesand associating them with attributes relevant to anapplication. They are used to reach a higher level ofabstraction in the modelling process. Users of CAxapplications can integrate features as high-level objectscarrying semantics into their geometric models. Thisway the semantic interface to CAx modelling software isimproved. On the other hand the inclusion of featuresemantics provides the possibility of reasoning aboutshapes on di�erent levels of abstraction and potentiallyallows for semantically rich shape retrieval of models inlarge CAx repositories.

Currently the knowledge about what a featureconstitutes is embedded in the underlying applicationtogether with the operations that are applied to featuresin order to combine them or to modify their intrinsic

geometric parameters. We suggest capturing thisknowledge in ontologies that can then be accessed bya CAx system as well as knowledge enhancedapplications like product life cycle management systems(PLM). An ontology is a means of modelling knowledgeabout an arbitrary domain of interest by identifyingbasic domain elements as concepts and interlinkingthem through semantic relationships. With this means ofmodelling knowledge the semantics of the domain canbe made explicit in a declarative way, which makes itaccessible for machines. Explicit knowledge can be usedas input for reasoning algorithms in order to deduceimplicit knowledge, i.e. statements that have not beenexplicitly modelled. In the context of shape modellingthe domain(s) of interest would cover engineeringknowledge on di�erent levels ranging from basicgeometrical and topological relationships to formfeatures and higher-level application-speci®c featuresthat carry semantics. Reasoning would amount toconcluding implicit topological relationships as well ashigher-level relations holding between features and canbe applied to CAx or shape retrieval.

In this paper we present a model of representationlayers for shape data as they are typically used by CAx

Int. J. of Computer Applications in Technology, Vol. 23, Nos. 2/3/4, 2005192

Copyright # 2005 Inderscience Enterprises Ltd.

applications. We exemplify how an ontologicaldescription of shape knowledge can be placed ondi�erent layers of this model by describing reasoningscenarios. Our objective is to show how applicationtasks, such as CAx modelling or shape retrieval, canbene®t from the integration of semantic informationfrom di�erent layers. Examples are chosen in order toprovide readers with a background in CAx with a notionof ontologies and reasoning. Vice versa, readers with abackground in ontology theory should get a briefintroduction to the information and knowledgehandled in CAx. It is not the intention of this articleto introduce a complete ontology for features or shapes,but to illustrate the bene®cial synergy between featuretechnology and ontology-based reasoning.

The remainder of this paper is organised as follows.In Section 2 we give an overview of current researchareas and activities that are related to feature-basedmodelling and ontology technologies. In Section 3 weintroduce a layer model for shape information in CAxsystems and give examples of how shape knowledge canbe described and reasoned about on di�erent layers.Finally, we mention some realisation issues and give anidea of how the combination of shape retrieval and 3Dmodelling can bene®t from the use of shape and featureontologies.

2 RELATED RESEARCH AREAS

2.1 Feature technology

In CAx, features are the means to incorporate semanticinformation about the form, function and behaviour ofcomputer-generated models representing physicalobjects. Although there are many di�erent de®nitionsof features often related to the application domain inwhich they are used (see Brunetti (2003) and Ovtcharova(1997) for domain dependent and generic featurede®nitions; see also Horva th et al. (1998) for anontology-based approach towards the de®nition ofdesign features) their role in CAx can be seen asmodelling entities that allow the characterisation ofcommonly used shapes and associating them with a setof attributes relevant to an application. In this sense,features may be thought of as information clusters orconcepts. They are intended to provide a natural way ofstoring and using engineering knowledge. In the contextof CAx, entities of a geometric model, e.g. points, curvesand surfaces, provide a micro view to shapecharacteristics that are localised and separated fromthe overall function and behaviour of the physical objectbeing modelled. Features, in turn, provide a high level,or macro view, which can be understood as concepts ofrelated facts and characteristics of the object (Shah andMaÈ ntylaÈ , 1995).

The intention of introducing feature technology is toenrich CAx systems with knowledge structures similar to

those used in human cognition to provide an additionallayer of information, making those systems more usefulfor design and to integrate design with downstreamapplications in the product life cycle, e.g. analysis,assembly, manufacturing, maintenance, recycling (Borgand Giannini, 2003). One goal is to allow designers tocommunicate with the system on a higher abstractionlevel than geometry. The system knows the generalcharacteristics of the used features±feature-based design(e.g. Brunetti (2003)). Furthermore, it is able to use asort of pattern matching in its reasoning ± featurerecognition ± and it is able to discover errors in designspeci®cations ± feature validation (e.g. Bidarra (1999)).However, theories based on cognitive schemata presumethe existence of prede®ned structures, which is thereason that feature-based models must also be limitedwithin a well-bounded application domain (e.g. designfeatures for mechanical engineering or architecture,assembly features, inspection features, ®xturingfeatures, manufacturing features, cost features, etc.),de®ned as an aggregate of more generic features (e.g.form features and tolerance features). Mbang andHaasis (2003), for instance, recently presentedDaimlerChrysler's current state of implementation andvision about design, inspection and manufacturingfeatures as a foundation for integrating productdevelopment, process planning and resourcemanagement in car body engineering.

Early research in feature technology dates back to themid-1970s, using, as for instance Grayer (1976), sectioningmethods on two and a half dimensional geometry todetect manufacturing features for automated NCprogramming in computer-aided process planning. The®rst feature-recognition approach based on reasoningabout topological and geometric relationships andcomparing features of the model to the characteristicsof application features that need to be found has beenintroduced by Kyprianou (1980). Almost all subsequentmethods for feature recognition have been based on thispattern matching idea in some form.

The idea of feature-based design was ®rst proposed inthe mid-1980s by Pratt and Wilson (1987). Ever since thefurther development of feature technology has beenclosely related to the progress in parametric andvariational design, where relationships between designparameters can be expressed in the form of declarativegeometric constraints, allowing the control of variationsof design applying modi®cations to the designparameters. Today, form features are typically de®nedas parametric models specifying the geometric andtopological characteristics of the feature as well as itsinterrelationship to other features in the model(Brunetti, 2003). Form features, e.g. holes, pockets,slots, steps, blendings, etc., provided by currentcommercial CAD systems typically use parametricde®nitions of form features. Some systems allowdesigners to introduce user-de®ned features as acombination of such basic features. In Mbang and

193FEATURE ONTOLOGIES FOR THE EXPLICIT REPRESENTATION OF SHAPE SEMANTICS

Haasis (2003), for instance, the set of user-de®nedfeatures for car body design at DaimlerChrysler arepresented. Prede®ned application speci®c design featuresare typically provided only by specialised CAD systems.Examples are catalogues of prede®ned piping elementsand valves for plant design or a set of joints for assemblymodelling and for analysis of kinematic mechanisms. Infeature recognition, research still concentrates onmanufacturing, where reasoning methods typically areimplemented in the form of algorithmic knowledgededicated to special application domains.

Di�erent research prototypes use an integration offeature-based design and feature recognition to improvethe integration of design with other downstreamapplications of the product life cycle. The aim of thosesystems is to provide di�erent views of the product data,which share a common geometric, topologic, andparametric model, but with di�erent feature models assemantic abstractions according to the di�erent phasesof the product life cycle. Examples of such integratedsystems that also use reasoning on the parametric layerfor feature mappings between di�erent applicationcontexts are given in Bronsvoort et al. (2003) and DeMartino et al. (1998). An example from the automotiveindustry is presented in Mbang and Haasis (2003).

2.2 Ontologies and reasoning

An ontology is a means to model knowledge about acertain domain of interest mostly associated with asemantic network structure. Concepts out of the domainof interest are linked to each other by relationships thatcarry a semantic meaning. The fact that `every carcontains an engine as part' could, for example, bemodelled in an ontology that covers the domain ofautomobiles. In the context of shape modelling facts like`the sum of any triangle's angles amounts to 180�' or`the parallelism relationship is transitive' could occuras basic geometric knowledge. Most knowledgerepresentations distinguish in some way betweenterminological and assertional knowledge. In this sensean ontology would be concerned with terminologicalknowledge since its concepts and relations can be seen asthe terminology which is used to propose statements, asin the above example. Assertional knowledge, on theother hand, binds objects of an interpretation domain toconcepts and relations as their instances. A concrete carwith a certain serial number would, for example, be aninstance of the concept `car' in an ontology aboutautomobiles. Instances of concepts in a shape ontologycould be the concrete occurrences of geometrical objectsas curves and surfaces. With this means of modellingknowledge, semantics can be made explicit in adeclarative way, which makes it accessible to machines.Based on a knowledge representation mechanism likeontologies, an information system can performreasoning on the knowledge that has been madeexplicit. New facts can be derived from already known

facts by reasoning algorithms that take the intrinsicsemantics of the ontology language into account. Thiskind of reasoning can be applied to a wide range ofapplication tasks and to arbitrary domains of interest.

Ontologies, declarative semantics and reasoning areubiquitous in current semantic web research, whereontology description languages have emerged and arecurrently being further speci®ed and standardised. Themost signi®cant among them is the RDF (ResourceDescription Framework) standard together with itsextension RDFS (RDF Schema) both introduced bythe W3C consortium (Lassila and Swick, 1999). On topof RDF(S) several other standards have been introducedlike DAML�OIL (2001) (www.daml.org) or OWL(Dean et al., 2002) which extend RDF(S) by a richermodel-theoretic semantics imposing certain implicationsand constraints on prede®ned language constructs.

Currently used ontology description languages arebased on logic formalisms that have been and are beingstudied in the area of arti®cial intelligence. Building abasis, ®rst order predicate logic is widely used to expressthe semantics of knowledge representation formalismconstructs. However, reasoning procedures in full ®rstorder logic are problematic in terms of decidability andcomputability. There are, therefore, attempts to reducethe expressiveness of knowledge representationformalisms in order to make reasoning easier to handle.The most recent ontology languages DAML�OIL andOWL are based on description logics (Baader et al., 2003)as a decidable subset of ®rst order predicate logic. Onthe other hand logics for frame-based systems havebeen introduced (Kifer et al., 1995), which resembleobject-orientated programming schemes. We use theFrame-Logic notation in this paper to exemplifyontological descriptions and rules for di�erent kindsof shape reasoning. An example for a reasoning systembased on Frame-Logic (F-Logic) is given in Deckeret al. (1999).

2.3 Shape semantics and shape reasoning

Studying the relevance of approaches to declarative,machine-processable semantics and ontologicalreasoning is motivated by the authors belief that suchapproaches provide a ¯exible platform to improve andextend the applications of reasoning techniques oninformation handled in CAx beyond the possibilitiesof current feature-based approaches.

A research area that today addresses ontologyaspects of shape to a broader extent than featuretechnology is Qualitative Spatial Reasoning (QSR),where qualitative knowledge on topology, distance andorientation, as well as spatial changes of shape, areexplored to study spatial concepts from a cognitivepoint of view. In the work described in Haarslev et al.(1999), for instance, a description logic is applied toQSR over topological relations in 2D space. QSR issuccessfully applied, for instance, to geographic

194 G. BRUNETTI AND S. GRIMM

information systems and robotic navigation. A goodintroduction to QSR and an overview about itstheoretical results and application areas can be foundin Cohn and Hazarika (2001). QSR, however, deals withdiscrete geometric surface and simplicial topologicalmodels of space and shape, which does not cover theapplication areas for reasoning along the product lifecycle addressed in this paper. Nevertheless, QSRdemonstrates the possible application of qualitativeconceptualisation and reasoning techniques to shaperelated problem domains. It therefore contributes to themotivation to enhance computer-aided support for anintegration of the product life cycle processes byontological reasoning methods.

In engineering and CAx several authors alreadydiscussed the close relationship between ontologies andshape semantics, but the exploitation of this relationshipis still mostly limited to the de®nition of taxonomies anddoes not extend to reasoning scenarios. In van der Vegteet al. (2002), for instance, ontologies are used to connectproduct function, user actions and environmentbehaviour in the conceptual design phase. Anotherexample where ontologies are used to formaliseknowledge about the conceptual design phase in thearchitectural domain is given in Emdanat and Vakalo(1998). Ontology-based approaches towards improvedfeature speci®cations can be found in Pulles et al. (1999),Horva th et al. (1998) and Ovtcharova (1997).

3 A LAYER MODEL FOR REASONING ABOUT SHAPE

KNOWLEDGE

CAx systems are typically organised in di�erent layers,each handling a certain type of information andproviding a set of operations mapped on thesubsequent layer in the hierarchy (Brunetti, 2003).Often these layers are realised as separate modules ofCAx systems, with clearly de®ned interfaces betweenthem. Historically, the introduction of di�erent layers toCAx followed the sequence bottom-up, which alsorepresents a shift from a micro-view on the lowestgeometric layer to the macro-views in the di�erentlayers' handling features. Vice versa, the granularity ofthe semantics handled in the di�erent layers changestop-down from abstract and coarse to ®ne, whereconcepts and relationships of the upper layers aremodelled in terms of concepts and relationships of thesubsequent layers. Figure 1 shows the layering, on whichwe will base our examples.

Ontological reasoning can be carried out on any layerand applied in di�erent application tasks, as feature-basedmodelling or shape retrieval. In the case of modelling theconsequences of a high-level operation, as for exampleconnecting two parts by a screw, changes can bepropagated to lower levels by rules and consistencychecks can be performed. In the case of retrieval, thematching of shape models with semantic requirement

speci®cations can be computed, based on cross-layerinferencing.

Every layer will be shortly introduced, indicating itsbasic elements and the ontological concepts andrelationship to describe these elements. To exemplifythe usage of ontologies for handling shape informationin CAx we use the F-Logic formalism (Kifer et al.,1995). An overview of the F-Logic constructs used in theexample scenarios is given in Table 1.

3.1 Geometry layer

Geometric modelling plays a special role in CAx. Todayit is still the lingua franca of engineering and recognisedas a research area of its own. It studies computer-basedrepresentations of geometry and related information neededfor supporting various computer-based applications inengineering design, analysis, manufacturing, and otherareas with similar requirements. According to thede®nition of Shah and MaÈ ntylaÈ (1995) it involves thestudy of data structures, algorithms and ®le formatsfor creating, representing, communicating andmanipulating geometric information of physicalobjects, as well as related numerical and symbolictechnical information. Neutral representations that cansupport a variety of applications are of particularinterest.

Figure 1 The typical layer model of a feature-based parametricCAx system

Table 1 F-Logic constructs (Kifer et al., 1995)

F-Logic Meaning

C1::C2 Class C1 is a subclass of C2

O:C O is an instance of class C

C1[A)C2] For the instances of C1 an attribute A is defined,whose value must be an instance of C2

O[A!V] The instance O has an attribute A, whose valueis V

C1[A )) C2] For the instances of C1 an attribute A is defined,whose value must be a set of instances of C2

O[A !! V] The instance O has an attribute A, whose valueis a set which V belongs to

195FEATURE ONTOLOGIES FOR THE EXPLICIT REPRESENTATION OF SHAPE SEMANTICS

The geometric primitives handled on the geometry layerof a CAx system are points, curves and surfaces, whichhave parameters according to the underlyingmathematical representation form. An ontology aboutgeometry knowledge would have these primitives asconcepts as well as more specialised ones, such as `circleor cylinder', as special kinds of curves and surfaces,respectively.

Reasoning in the geometric layer is concerned withthe geometric characteristics and interrelationships ofgeometric primitives. During the modelling processreasoning maps parameters of geometric concepts toconcrete geometric elements. Figure 2 shows an examplewhere a cylindrical surface is orthogonally intersectedwith a plane creating a circle with radius equal to that ofthe cylinder. Figure 3 illustrates an excerpt of anontology that models shape knowledge on thegeometry layer. The example covers those concepts forprimitives and operations necessary to express thesemantics of the intersection shown in Figure 2 as anentailment rule that derives a consequence (theintersection curve is a circle with radius R) from anappropriate set of premises. It captures the knowledgethat the parameters of a resulting circle in 3D space canbe concluded from the parameters involved in theintersection. The radius and normal can be directlymapped to the intersection of the cylinder and the plane.In this case the premise is that a given cylinder andplane, speci®ed by their respective parameters, intersectorthogonally. The rule only applies, if the direction ofthe cylinder's axis is equal to the plane normal.

3.2 Topology layer

The topology of an object is handled within a boundarymodel, representing the object in terms of its boundaries,i.e. its skin (also called boundary representation ±BRep). The topological primitives of a boundarymodel are vertices, edges and faces that either enclosea volume in the case of a solid model or are open, as in

the case of a surface model (see Figure 4 for anillustration). Sequences of edges building a closed ringare called a loop. Face-sets that are not connected(topological separated skins) are called shells. A detailedreview about the evolution of boundary models is givenby Shah and MaÈ ntylaÈ (1995).

Every topological primitive has a relation to ageometric primitive de®ning its geometric characteristics:a face is related to a surface, an edge is related to acurve, and a vertex corresponds to a point. In theexample of Figure 4 the shape and position of every faceis de®ned by a corresponding plane. Every face isbounded by four edges, which are lines representing theintersection of the planes of two adjacent faces.Accordingly, every edge is bounded by two verticesde®ned by the intersection point of the three lines of theedges meeting in a corner. Accordingly, the concepts ofan ontology representing topological knowledge wouldconsist of vertices, edges, loops, faces and shells.

Operations on boundary models are based on thepoint-set theory. Any point-set can be classi®ed as in,out, or on the boundary. Boolean operations like union,di�erence, or intersection are used to build topologicallyvalid objects. A cylinder, for instance, is de®ned as the

Figure 2 A circle de®ned as the intersection of a plane with a cylindrical surface

Figure 3 Ontological modelling of geometric knowledge

196 G. BRUNETTI AND S. GRIMM

intersecting point-sets of three half-spaces: all pointsinsight the half-space de®ned by the top-plane, all pointsinsight the half-space of the bottom face, and all pointsinside the cylindrical surface (see Figure 2). Note that onthe geometric level planes and cylinders have in®niteextensions dividing the space into two regions: theregion in the direction of the surface normal de®ningoutsight and all points belonging to insight on the otherside of the surface. All points of the boundary are alsoconsidered as being in. It follows the importance oforientation to boundary models.

A classical approach to reasoning about the validity ofoperations on the boundary models is the Euler-PoincareÂformula: a (manifold) boundary model is valid, if thenumber of vertices v, the number of edges e, the numberof faces f, the number of shells s, the number of interiorloops in faces (rings, representing holes in faces) r, andnumber of through holes h hold the equation:vÿ e� f � 2�sÿ h� � r.

Another area is the reasoning about topologicalequivalence. For instance, a block is topologicallyequivalent to a sphere; a block with a hole istopologically equivalent to a torus.

The example in Figure 5 demonstrates an entailmentrule modelling a basic topological knowledge. The ruleconcludes that a sequence of edges is a loop if the startand end vertex are identical.

It should be noted that most feature recognitionapproaches operate on topological concepts, which arelinked by composition to geometrical concepts. Forinstance, refer to Cicirello and Regli (2001) for a shapereasoning approach based on topological machiningfeatures to compare mechanical parts.

3.3 Parametrics layer

Parametric modelling supports the generation of modelvariations through the modi®cation of dimensional andtopological parameters. In dimensional parametrics, thegeometry, position or values of geometric parameters(distance, radius, etc.), of an object can be constrainedor varied, but not the topological structure. Topologicalparametrics, in turn, allow us to constrain or modify thetopological structure. Today, most engineers considerthe parametrics of a model as the most relevant layerwhere engineering knowledge about an object iscaptured and maintained.

The basic primitives of the parametric layers aregeometric and topological constraints (Brunetti, 2003;Shah and MaÈ ntylaÈ , 1995). Geometric constraints arethose de®ning geometric relationships between vertices,edges and faces, or their related points, curves andsurfaces, respectively. Examples are parallelism,coaxiality, orthogonality, etc. Another type of geometricconstraints are functions specifying relationships betweengeometric parameters associated with geometric primitives(e.g. radius) or geometric constraints (e.g. the distancebetween two parallel linear edges or planar faces) andinequations to specify the range of parameter values(e.g. radius > 0). Topological constraints can be used,for instance, to make sure that a through hole maintainsits topological nature throughout the dimensionalchanges of the model or to declare that it is notpermitted to cover a hole by subsequent operations.

Again, ontological concepts at the parametrics layercoincide with the basic primitives of this layer, which arethe di�erent types of constraints and parameters.Reasoning on this layer is mainly concerned withavoiding over-constraint situations that have nosolution or with completing under-constraint models.Another relevant aspect is to verify whethermodi®cations in the parametric layer lead to validmodels in the underlying topological layer.

Figure 6 illustrates an example of an object that hasbeen modelled by a Boolean union operation, where theplanar faces f1 and f2, and f2 and f3, respectively, havebeen de®ned to be orthogonal. As orthogonalitybetween f1|f2, and f2|f3 implies that f1 and f3 have to

Figure 4 Boundary model of a block: the volume is bounded by six planar faces, each bounded by four linear edges building a loop.Each edge, in turn, is bounded by two vertices

Figure 5 Ontological modelling of topological knowledge

197FEATURE ONTOLOGIES FOR THE EXPLICIT REPRESENTATION OF SHAPE SEMANTICS

be parallel, this relationship can be added to theparametric model also creating the correspondingdistance parameter between these two planar faces.

As with the previous paragraphs, we show anexample of a part of an ontology that modelsparametric knowledge (see Figure 7). It covers thedeclaration of the facts, that orthogonal and parallelrelationships can be applied to planar faces. Here theparametric concept PLANARFACE is linked to thetopological concept FACE by subsumption. The ®rsttwo entailment rules ensure the symmetry of theserelations. The third rule infers that two planar faces areparallel if they are orthogonally linked via a third.

3.4 Form feature layer

Form feature models are built by application independentform features and generic feature relationships. Formfeatures are de®ned in terms of parametric, topologicaland geometric characteristics and represent commonlyused generic shapes (Brunetti, 2003). Examples of formfeatures are cylindrical or rectangular through holes,pockets, ribs, slots, steps, blendings, etc. Today, mostCAD systems allow the de®nition of arbitrary pro®leson a face of a boundary model, which are then extrudedalong a curve (e.g. extrusion of a circle along a linegenerates a cylinder). Depending on the direction of theextrusion curve, into or out of the object, this operation

generates either a depression (concavity) or protrusion(convexity). In the case of a depression the user maycontrol, if the depression should be a through hole or ablind hole, i.e. a pocket. This interference between theform features of a model (the main body of an object isalso considered to be a form feature) is modelled byfeature relationships. In the example above, suchrelationships may control the relative position of thepro®le within the face it was de®ned. The di�erencebetween a blind and a through hole is established bydi�erent sets of geometric and topological constraints,making sure that the design intention is maintainedwhen instantiating the feature or when varying modelparameters.

Di�erent form feature taxonomies have been proposed(Ovtcharova, 1997; Shah and MaÈ ntylaÈ , 1995), which tosome extent are equivalent, although they depend on thespeci®c functionality of the underlying layers. In anycase, the features of such a taxonomy can be used tode®ne a hierarchy of form feature concepts for acorresponding form feature ontology modelling genericshape knowledge.

Reasoning about these generic shapes, i.e. formfeatures and their characteristics, takes place atdi�erent stages of the object life cycle. The ®rst is thereasoning about how to specify a form feature in termsof underlying parametric, topologic and geometricconcepts. The second is reasoning about the validity ofform features after model modi®cations. Furtherreasoning is that of feature recognition. Figure 6(a),for instance, shows an object that has been modelled astwo rectangular ribs on a basic block. The same modelcould be recognised as consisting of a block with thedimensions of the bounding box of the model having arectangular slot. The parameters of the slot would be thewidth, which is the distance between the parallel innerfaces of the slot as discussed above, and the depth,which would coincide with the height of the ribs.

The example illustrated in Figure 8 de®nes the conceptof a rectangular hole and a possible entailment rule thatdescribes it in terms of four faces that build a sequenceof orthogonal relationships on the parametric layer. Ahole is determined as being of type RECTANGULARHOLE,

Figure 6 Constraint reasoning

Figure 7 Ontological modelling of parametric knowledge Figure 8 Ontological modelling of form feature knowledge

198 G. BRUNETTI AND S. GRIMM

if any sequence of three neighbouring planar faces hassequential orthogonality constraints and its overallnumber of faces is four.

The form feature layer is suitable for anchoring modelretrieval. It is closely related to feature recognition. Anexample could be to retrieve all models that have acircular through hole with a speci®c radius ®tting with apart that has a corresponding cylindrical protrusion.One goal could be to ®nd all possible pairs of parts thatcan be assembled to a revolute joint. In this case theretrieval would make use of ontological knowledge asshown in Figure 8 in order to map form feature leveldescriptions to lower-level constraints and parametervalues. A block having a rectangular hole could beretrieved without being semantically tagged as such.

3.5 Application feature layer

Concepts in the application feature layer are allmeaningful elements within an application domain.Application domains can be understood in two ways.One is the application domain de®ned by the phase ofthe product life cycle, where design, planning,manufacturing, maintenance and recycling might bedistinguished. Another is the application area, like, forinstance, mechanical engineering, plant design, orarchitecture. In either case, application features arelinked to underlying form features by subsumption orcomposition on the ontological level.

Application features typically de®ne additional, notnecessarily shape related, parameters relevant to theapplication domain. Examples could be material andmaterial properties, costs, or durability (Borg andGiannini, 2003; Staub-French et al., 2002). Due to thedegree of abstraction from model details, the applicationfeature layer is also the predestinated layer forcommunication between interdisciplinary engineeringteams or between engineers and customers. Typicalapplication features that can be found in current CAxsystems are, for instance, screw holes matching with acatalogue of available screws (form: cylindrical orsinkhole, through hole or blind hole, type of screwthread, depth, etc.), or a catalogue of pipe elements forplant and ship design.

One kind of reasoning at the application layer mapsapplication concepts to lower-level entities. Anotherkind of reasoning is concerned with the validity ofmodels. The example in Figure 9 shows how theaccessibility of a building (Figure 10) can be deducedby an entailment rule. The rules of the example implythat a building has a door, if some wall has a slot. Herethe combination of two rules map the lower-levelproperty HASSLOT of the form feature concept BLOCK

to the higher-level property HAS DOOR of the applicationfeature concept BUILDING via appropriate variablebindings.

A retrieval example in the shoe-manufacturingdomain could be to ®nd female shoe models with a

heel higher than 5 cm.

3.6 Assembly layer

Finally there is the assembly layer where parts areassembled to products. Consequently the concepts ofthis layer are parts, which subsume application featuresand connectors. Connectors are either joints withremaining degrees of freedom to build mechanisms orthey are mating relationship to ®x parts together.Reasoning in this layer is concerned with thesemantics of the functionality of complex assemblies.Assembly structures are already de®ned in the earlyconceptual and embodiment design phase, where thefunction of a product and its layout composed by partsand their interrelationships are de®ned, and thendetailed further in lower layers.

Some authors treat the assembly feature layer as justa special domain for application features. Here,however, we prefer to see the assembly layer asseparate and the top-most layer, because it representsan interface to product data and product life cyclemanagement systems (PDM and PLM). Today, CAxmodels for PDM/PLM are typically black boxes, wherethe interpretation of the content of CAx models isderived from a previously de®ned product structure andnot formalised meta-information, which is associated

Figure 9 Knowledge on the application level

Figure 10 Front wall of a building

199FEATURE ONTOLOGIES FOR THE EXPLICIT REPRESENTATION OF SHAPE SEMANTICS

with the CAx models by their designers. Approaches tolook inside these black boxes are currently limited tocomputational expensive geometric and topologicalreasoning methods as presented in Bespalov et al. (2003).To enrich management systems by ontology-basedreasoning methods allowing access to formalisedsemantics kept in the CAx models, as introduced inthe following section, would add signi®cant knowledgeto engineering systems and provide for improvedinterfaces to knowledge management systems and tosemantic web technology applied to engineering. Anexample for applying ontologies to PDM-speci®cconcepts and relationships is given in BuÈ chner et al.(1999).

4 REALISATION ISSUES

In the previous section we have shown what ontologicalreasoning about shapes might look like on di�erentlayers of abstraction in CAx applications by providingexemplary scenarios. For a concrete CAx application ithas to be decided individually on which layers theontological approach should be applied in order for theapplication to ful®l its tasks. For the example of 3Dmodelling the lower layers like geometry and topologyare already well covered by algorithmic implementationsperforming e�cient operations. The parametrics andform feature layer, are in turn, seen as semanticnetworks and hierarchical constraint satisfactionproblems, which already o�er a system structuresuitable for applying ontological reasoning techniques.It would therefore, be worthwhile to exploit the synergybetween ontological reasoning approaches and theseCAx model layers further in order to improve thesemantics' capabilities of such systems.

Today, engineering environments can be divided intotwo families of systems. The ®rst family is that of theCAx systems. The second is product data management(PDM) systems, which engineers use to organise the

logical structure of designs, for instance, assemblystructures. Furthermore, PDM systems are used forrevision management. The latest developments headtowards the management of product con®gurations andthe management of the total product life cycle (PLM).PDM/PLM systems refer to CAx models as documentsfor which they maintain relevant meta data. It istherefore, feasible to integrate ontological reasoningtechniques into PDM/PLM, which would be anapproach harmonising with that of Semantic Webapplications. Kopena and Regli (2003), for instance,discuss in the application of Semantic Web to designrepositories and PDM, presenting an ontology forelectromechanical devices together with thecorresponding reasoning services. However, thereasoning is performed on meta data, which have tobe explicitly provided by the designers. The designmodels remain black boxes. In order to allowapplications to bene®t from knowledge modelled onany of the layers for cross-level inferencing on a broadrange, it is necessary to realise e�cient interfacesbetween CAx and PDM/PLM systems. The authorsbelieve that the previously discussed feature layers(form, application and assembly feature layers) are theright entry points for realising these interfaces and forapplying a broad range of ontological reasoning servicesfor domain-speci®c semantics.

As a more concrete sketch of how shape-relatedontologies and modelling applications work together wepresent an overall scenario combining the levels ofapplication, data and ontological knowledge inFigure 11. For the application part consider, forexample, a semantically enabled retrieval componentthat has the capability to make use of ontologies for®nding relevant documents with respect to a userrequest. The application component can exploit thestructure on di�erent layers as deeply as it has access toknowledge about the elements residing in a certain layer.In the most simple case this would amount to havingaccess to a domain ontology on the application layer

Figure 11 Synergy between a semantic retrieval system and a 3D modelling system

200 G. BRUNETTI AND S. GRIMM

that models knowledge about elements occurring in 3DCAx models. In this case, the retrieval system cannotexploit the structure that exposes further details aboutthe objects described in a CAx ®le, to which its level ofgranularity in access is restricted. However, if theretrieval component also includes a domain-speci®cshape ontology or feature ontology, the semantics ofelements of a feature library could also be taken intoaccount. The excerpts in Figures 8 and 9 could be takenas examples of parts of such ontologies that semanticallymap form features to application objects or capturefeature knowledge, respectively. To provide the retrievalcomponent with an even deeper insight into the shapedata, it could involve domain independent top-levelontologies covering the layers of geometry, topologyand parametrics. In this case reasoning algorithms couldoperate on the ®nest level of access granularity in across-layer manner. An example here could be themodelling of knowledge as shown in Figures 5 and 7.

This is the level at which we are currently focusingour work on. Exploiting ontological knowledge aboutfeatures, our aim is to combine the functionality of asemantically rich document retrieval system forengineering and an intuitive virtual 3D modellingenvironment, both being subject to ongoing projects atthe Fraunhofer-IGD. Data on the lower three layers willbe enriched by semantic meta data according to shapeand feature ontologies such that the retrieval system caninterpret the meta data structures later on in anintelligent way. At the same time, such an integrationwould allow users of the virtual modelling system to geta semantics-based, hence more intuitive, access to designrepositories during their modelling sessions.

5 CONCLUSIONS AND FUTURE WORK

This paper discusses the bene®cial integration of featuretechnology as a means of representing design andengineering semantics in current CAx systems andontological semantics as it is used to explicitlyrepresent semantics, for instance, for Semantic Webapplications. It exempli®es how the synergy of theseapproaches can be achieved by feature or shapeontologies and corresponding ontological reasoningmechanisms applied to the respective abstraction andinformation layers of design models that can be found intoday's CAx systems. Finally, the paper also describeshow engineering tasks can utilise feature ontologies as abasis for the application of speci®c shape reasoningacross several modelling layers. The authors believe thatthe presented roadmap represents a sophisticated meansto realise the integration of engineering knowledge andintelligence into product development and relatedprocesses as demanded by industry (respectiverequirements are presented, for instance, in Mbangand Haasis (2003).

In the short term the authors will further elaborate,test and revise the current ideas in the context of theEuropean Network of Excellence [email protected] of AIM@SHAPE is to advance research inthe direction of semantic-based shape representationsand semantic-orientated tools to acquire, build, transmitand process shapes with their associated knowledge. Theauthors' work in this project is concerned with theformalisation of shape knowledge and shape ontologies,interoperability between shapes and knowledge-baseddesign of shapes.

The ideas presented in this paper will be veri®ed andvalidated in a prototype realisation, which integratestwo developments of Fraunhofer-IGD. One is thevirtual 3D modelling system `SmartSketches', wherewe currently integrate previous developments from thearea of feature-based parametric modelling. The other is`WIDE', which targets semantically rich documentretrieval for engineering applications.

ACKNOWLEDGEMENTS

This work was partially supported by the Network ofExcellence AIM@SHAPE (Advanced and Innovative ModelsAnd Tools for the development of Semantic-basedsystems for Handling, Acquiring, and ProcessingKnowledge Embedded in multidimensional digitalobjects), which is funded by the sixth ResearchFramework Programme of the European Community.

REFERENCES

Baader, F., Calvanese, D., McGuinnes, D., Nardi, D. andPatel-Schneider, P. (2003) The Description Logic Handbook,Cambridge University Press.

Bespalov, D., Regli, W.C. and Shokoufandeh, A. (2003)`REEB graph based shape retrieval for CAD', Proceedingsof 2003 ASME Design Engineering Technical Conference(DETC 2003), September 2±6, Chicago, IL, USA,CD-ROM: DETC2003/CIE-48194.

Bidarra, R. (1999) `Validity maintenance in semantic featuremodelling', PhD Thesis, Technische Universiteit Delft,Netherlands.

Borg, J.C. and Giannini, F. (2003) `Exploiting integrated`product' & `life-phase' features', in R. Soennen and G.J.Olling (Eds) Feature Based Product Life-Cycle Modelling,Kluwer, pp.1±18.

Bronsvoort, W.F., Noort, A., van den Berg, J. and Hoek,G.F.M. (2003) `Product development with multiple-viewfeature modelling', in R. Soennen and G.J. Olling (Eds)Feature Based Product Life-Cycle Modelling, Kluwer,pp.57±76.

Brunetti, G. (2003) `Feature-based virtual engineering', inR. Soennen and G.J. Olling (Eds) Feature Based ProductLife-Cycle Modelling, Kluwer, pp.19±40.

BuÈ chner, A.G., Ranta, M., Hughes, J.G. and MaÈ ntylaÈ , M.(1999) `Semantic information mediation among multipleproduct ontologies', Proceedings of the 4th InternationalConference on Integrated Design & Process Technology(IDPT '99), July, Kusadasi, Turkey.

201FEATURE ONTOLOGIES FOR THE EXPLICIT REPRESENTATION OF SHAPE SEMANTICS

Cicirello, V. and Regli, W.C. (2001) `Machining feature-basedcomparisons of mechanical parts', Proceedings of theInternational Conference on Shape Modelling andApplications, sponsored by ACM SIGGRAPH, theComputer Graphics Society and EUROGRAPHICS, IEEEComputer Society Press, May 7, Genoa, Italy, pp.176±185.

Cohn, A.G. and Hazarika, S.M. (2001) `Qualitative spatialrepresentation and reasoning: an overview', FundamentaInformaticae, Vol. 43, pp.2±32.

DAML�OIL (2001) Reference description of the DAML�OIL ontology markup language, http://www.daml.org/2001/03/reference.html.

De Martino, T., Falcidieno, B. and Haûinger, S. (1998) `Designand engineering process integration through a multipleview intermediate modeller in a distributed object-orientedsystem environment', Computer-Aided Design, Vol. 30,No. 6, pp.437±452.

Dean, M., Connolly, D., van Harmelen, F., Hendler, J.,Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F. andStein, L.A. (2002) `Owl web ontology language 1.0reference', http://www.w3.org/TR/owl-ref/.

Decker, S., Erdmann, M., Fensel, D. and Studer, R. (1999)`Ontobroker: ontology based access to distributed andsemi-structured information', Semantic Issues in MultimediaSystems, Kluwer.

Emdanat, S.S. and Vakalo, E-G. (1998) `An ontology forconceptual design in architecture', Proceedings of the ThirdConference on Computer Aided Architectural DesignResearch in Asia (CAADRIA '98), April 22±24, Osaka,Japan, pp.425±434.

Grayer, A.R. (1976) `A computer link between design andmanufacturing', PhD Thesis, University of Cambridge.

Haarslev, V., Lutz, C. and MoÈ ller, R. (1999) `A descriptionlogic with concrete domains and a role-forming predicateoperator', Journal of Logic and Computation, Vol. 9, No. 3,pp.351±384.

Horva th, I., Pulles, J., Bremer, A.P. and Vergeest, J.S.M.(1998) `Towards an ontology-based de®nition of designfeatures', Proceedings of the SIAM Workshop onMathematical Foundations for Features in ComputerAided Design, Engineering and Manufacturing, October22±23, Troy, MI, USA.

Horva th, I., Vergeest, J.S.M. and Kuczogi, G. (1998)`Development and application of design conceptontologies for contextual conceptualization', Proceedingsof 1998 ASME Design Engineering Technical Conferences(DEC '98), September 13±16, Atlanta, Georgia USA,CD-ROM: DETC98/CIE-5701.

Kifer, M., Lausen, G. and Wu, J. (1995) `Logical foundationsof object-oriented and frame-based languages', Journal ofthe ACM, Vol. 42, pp.741±843.

Kopena, J.B. and Regli, W.C. (2003) `Functional modelling ofengineering designs for the semantic web', IEEE DataEngineering Bulletin, IEEE Computer Society, December1, Vol. 26, No. 4, pp.55±62.

Kyprianou, L. (1980) `Shape classi®cation in computer aideddesign', PhD Thesis, University of Cambridge.

Lassila, O. and Swick, R.R. (1999) `Resource descriptionframework (RDF) model and syntax speci®cation', World

Wide Web Consortium: Recommendation REC-rdf-syntax-19990222, http://www.w3.org/RDF/.

Mbang, S. and Haasis, S (2003) `Integrating of product,process, and resource in car body engineering', Proceedingsof the 10th International Conference on ConcurrentEngineering: Research and Applications (ISPE '03), July26±30, Madeira, Portugal, pp.55±64.

Ovtcharova, J. (1997) `A framework for feature-based productdesign: fundamental principles, system concepts,applications', PhD Thesis, Technische UniversitaÈ tDarmstadt, Germany.

Pratt, M.J. and Wilson, P.R. (1987) `Conceptual design of afeature-oriented solid modeler', Draft Document 3B,General Electric Corporate R&D.

Pulles, J.P.W., Horva th, I. and van der Vegte, W.F. (1999)`Beyond features: an ontology oriented interpretation',Proceedings of the International Conference on EngineeringDesign (ICED 99), August 24±26, Munich.

Shah, J.J. andMaÈ ntylaÈ , M. (1995) Parametric and Feature-basedCAD/CAM: Concepts, Techniques, Applications, NewYork: John Wiley & Sons.

Staub-French, S., Fischer, M., Kunz, J., Paulson, B. and Ishii,K. (2002) `A feature ontology to support construction costestimating', CIFE (Center for Integrated FacilityEngineering) Working Paper No. 69, Stanford University.

van der Vegte, W.F., Kitamura, Y., Mizoguchi, R. andHorva th, I. (2002) `Ontology-based modelling of productfunctionality and use, part 2: considering use andunintended behaviour', Proceedings of the EngineeringDesign in Integrated Product Development (EDIProD2002), October 10, Zielona Go ra, Poland, pp.115±124.

Biographical notes:Gino Brunetti graduated in computer science at the DarmstadtUniversity of Technology, Germany. Since 1995 he has been aresearcher at the Fraunhofer-Institute for Computer Graphicsin Darmstadt (IGD) and project leader of several appliedresearch and development projects in the area of computeraided design and integration of virtual reality technology intothe product development process. From 2001 to 2003 he wasthe scienti®c-technological coordinator of the Centre ofExcellence for Advanced Technologies (CETA-RS) in PortoAlegre, Brazil. His research interests are focused on feature-based parametric modelling and its applications to virtualengineering.Stephan Grimm received his Diploma in computer science

from FH-Karlsruhe in 2001. He went on to graduate as MSin computer science within a jointed programme betweenFH-Karlsruhe and Eastern Michigan University until 2002.Within this programme his work has been focused onsemantically rich information retrieval. Since 2003 he hasworked as a researcher at the Department for IndustrialApplications at the Fraunhofer-Institute for ComputerGraphics (IGD). His research interests are knowledgerepresentation, automated reasoning and arti®cial intelligencemethods. He is currently involved in the EU project WIDE ±Semantic Web-based Information Management and KnowledgeSharing for Innovative Product Design and Engineering.

202 G. BRUNETTI AND S. GRIMM