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.Automation in Construction 9 2000 369377rlocaterautconParametric design: a review and some experiencesJavier Monedero)Departamento de Expresion Grafica Arquitectonica, Uniersitat Politecnica de Catalunya, Diagonal 649, 08028 Barcelona, SpainAbstractDuring the last few years there has been an extraordinary development of computer-aided tools intended to present orcommunicate the results of architectural projects. But there has not been a comparable progress in the development of toolsintended to assist design to generate architectural forms in an easy and interactive way. Even worse, architects who use thepowerful means provided by computers as a direct tool to create architectural forms are still an exception. Architecturecontinues to be produced by traditional means using the computer as little more than a drafting tool. The main reasons thatmay explain this situation can be identified rather easily, although there will be significant differences of opinion. In myopinion, it is a mistake trying to advance too rapidly and, for instance, proposing integrated design methods using expertsystems and artificial intelligence while no adequate tools to generate and modify simple 3D-models are available. Themodeling tools we have at the present moment are unsatisfactory. Their principal limitation is the lack of appropriateinstruments to modify interactively the model once it has been created. This is a fundamental aspect in any design activity,where the designer is constantly going forward and backwards, re-elaborating once and again some particular aspect of themodel, or its general layout, or even coming back to a previous solution that had been temporarily abandoned. This paperpresents a general summary of the actual situation and recent developments that may be incorporated to architectural designtools in a near future, together with some critical remarks about their relevance to architecture. q2000 Elsevier Science B.V.All rights reserved.Keywords: Geometric modeling; Architectural and building models; Parametric design1. Current 3D-modelsIn architecture, 3D-models are elaborated by somecommercial version of one of the following tech-niques: polygonal meshes, solid models or paramet-ric surfaces such as nurbs. Most architectural modelsare still produced using the first method, togetherwith some appropriate interface that allows the useof commands such as 3dfaces, polylines withwidth and thickness or revsurfs, tabsurfs,rulesurfs, etc. This is due to the characteristics of)Corresponding author. E-mail: javier.monederoegal.upc.esarchitectural models that are mainly composed ofplanar surfaces. Many architects work with what canstill can be called 2.5D-models wide lines or poly-.lines depicting walls extruded to a particular heightthat can be used both as drawing planes and simple3D-models. Solid models are also widely used due tothe fact that they allow boolean operations to createmore complex forms. Nurbs or the like are rarely.used except by Frank Gehry , as common budgetsdo not favor sculptured or free-form surfaces. Thehistory of 3D geometric modeling is studied and canbe found in well-known computer books like Foleysgeneral exposition of computer graphics or Morten-sons more specialised textbook on geometric model-0926-5805r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.PII: S0926-5805 99 00020-5()J. MonederorAutomation in Construction 9 2000 369377370ing. This justifies a very shortened summary. Theintention of this summary is not only to locate thesubject in the adequate context but also to stress thedistance in time that has separated a published paperand a generally used technique. As we will see, thisdistance is approximately the same that separates thefirst published papers on parametric design from ourimmediate future, let us say 2 or 4 years. That is tosay, the situation is mature for a change in thecurrent techniques used in CAAD; it has alreadyhappened in CADrCAM although most of the archi-tects that work with computers are unaware of it.1.1. Eolution and limitations of CAD modeling toolsThe first methods and techniques were put intopractice during the 1960s and included basic 2D-primitives, as well as new entities like splines. Thework of Bezier and De Casteljau goes back to thisperiod. This was extended to 3D wireframes andsurfaces patches. New graphical methods are to beassociated to the name of Sutherland and to the year1963, in which his thesis was published. Polygonalmeshes were used at the end of the 1960s; soon therewere techniques to visualize them by such methodsas what is now currently known as flat-shading.Bouknight, 1970 or, better, Gouraud shading 1971.or, even better, Phong shading 1975 . This is wheremost systems stop nowadaysmore than 22 years.thereafter! . Free-form or sculptured surfaces weredeveloped extensively during the 1970s. The mostadvanced method currently used, nurbs non-uniform.rational b-splines can be traced back to an article byA.R. Forrest in 1980. AutoCad has incorporated it, a.couple of years ago 15 years after it was introduced ,.through an extra moduleAutoSurfthat came to-gether with version 13.Solid modeling using a primitive form of CSGwas also born at the beginning of the 1960s at the.MAGI labs in USA , and evolved rather slowly untilsome complete products appeared in Europe andUSA at the beginning of the 1970s. The first impor-tant commercial packages, like Romulus, commer-cialized by Evans and Sutherland in 1980, appearedat the end of the 1970s. A very much quoted articleby Requicha that summarized the state of the art atthat time, with five principal systems quoted wasalso published in 1980. At the present time, mostsystems currently used combine two systems, B-Repsand CSG or use B-Reps as a shell that allowsmultiple representations and favors the transit fromone to the other. This is the case with ACIS Alan,.Charles and Ian Systemused by AutoCad sinceversion 13 after dropping AME, a CSG system thatdid not work as it should.1.2. Editability of current 3D representationsAll these systems suffer from severe limitationsfrom the point-of-view of an interactive approach todesign: Lack of resources to edit surfaces. This is particu-larly clear in the case of sites that must bereworked and adjusted to receive a building. Lack of resources to edit volumes in a reallyinteractive way. Lack of resources to maintain relations betweenparts of a volume during modifications. Lack of integration between surfaces and solids.In the CADrCAM-community, the methods cur-rently used to create 3D architectural models havebeen abandoned a long time ago. Different types ofresearch have been carried out to improve the situa-tion. We offer some hints before getting into para-metric design.1.3. Object-oriented 3D-model: E-RepsWith a solid model such as the kind currentlyused in the architectural community, if one wishes tomodify, for instance, a hole in a wall, one has to editthe csg tree, locate the primitive and then order thesystem to rebuild the tree. With an object-orientedapproach, interaction will be more convenient andeasier to manage. The internal data structure and theimplementation of the algorithms able to modify it,are hidden in the object. In this way, the orders sentto the object do not need to specify how a modifica-tion shall be done but only what is to be done for.instance, change the position of a hole in a wall .The mechanisms of inheritance that relate classes tosuperclasses or subclasses assure that the previouslyspecified relations will be maintained. Unfortunately,this requires an internal representation of data that isstill lacking in current CAD systems. In general, arepresentation that uses a chain of references that()J. MonederorAutomation in Construction 9 2000 369377371links entities in the model is called a model graph.w xHoffman 8 has introduced the term of E-Rep edita-.ble representation to denote this kind of structure.This has implications being of great interest in thefuture. This structure is similar to a CSG graph butwith some important differences. The leaf nodes ofthe graph, in the CSG are usually the lowest primi-tives of the system, i.e., half spaces, whereas in theE-Reps, there usually are B-Reps. Also, in a CSG,the nodes are a few operators, mainly boolean opera-tors, while in an E-Rep, the nodes may represent awide range of types including sketches, sweeps,feature attachments, blends or dimensions. On theother hand, the CSG-graphs have a well-definedsemantics and a guaranteed validity. This is not thecase with E-Reps so it seems that there is still someexperimentation needed.2. Parametric designParametric design is, in a sense, a rather restrictedterm; it implies the use of parameters to define aform when what is actually in play is the use ofrelations. I will use the term in a wide sense thatcovers what can be found in the literature underother headings such as relational modeling or varia-tional design or constraint-based design or othertitles that will be quoted to some extent in thefollowing paragraphs.It should also be noted that, from an elementarypoint-of-view, there is not a clear boundary betweenwhat can be called parametric design and what iscurrently called computer-aided drafting or model-ing. In these cases, forms are created by combiningbasic entities that are inserted in the model after abasic template, which includes their proper param-eters, is filled. A line, for example, is an entity thatbecomes part of a model once two parameters, itslength and its direction, are specified. A polyline is aset of lines joined at their vertices whose positionparameters must also be specified when it is created.A prismatic meshed volume is inserted in a modelthrough four parameters, its location, length, width,and height. Besides this, we can also define blocks.AutoCad , cellsMicrostationsymbols ponentsother systemsthat combine andkeep together these primitive forms with differentoverall values. There are also, in current CAD sys-tems, tools that allow us to make some modificationsa posteriori regarding these primitive entities. How-ever, this does not work for complex elements wherewe want relations to be maintained while modifyingtheir parts independently. We can define a metalwindow as a block but if we change the scale at themoment of insertion, frame sections will change inthe same proportion as the overall magnitude and wewill not be able to keep a standard frame withdifferent opening dimensions. But we can still definea procedure, through some programming languagelike AutoLisp, in such a way that only the relationsare specified and the adequate dimensions are de-fined only at the moment of insertion in the model.This is already parametric design in a literal andfundamental sense. And, it is obviously of interest inthe case of architecture due to the fact that a veryimportant number of building elements can begrouped in families that tend spontaneously to beparameterized. And, if this can be done in a satisfac-tory way, it can save a lot of time and computermemory and will also help the management of theseelements. As the notion of family is important in aparametric design we can define it formally: a set ofelements that only differ in the dimension of theirparts. To describe a family, to elaborate a primarydesign of a family, we only need two things: atopological description specifying the parts that con-stitute it and the relations they maintain with eachother and a dimensional scheme specifying prioritiesand dimensional constraints. In this way, we candefine an abstract collection of elements and insertthem in our models. This is good for a start, but whathappens if after the element is inserted we want tomodify it? This is where parametric design, in apromising way, properly started out in CADrCAM afew years ago in relation with the fundamental no-tion of constraint.3. ConstraintsA fundamental problem in CAD is how to makeexplicit some intuitive knowledge we have aboutsomething in such a way that a machine can interpretand treat it in an automatic way. This problemreveals its magnitude as soon as we try to formulate()J. MonederorAutomation in Construction 9 2000 369377372what is comfortably referred to as common sense.From an architectural point-of-view, this is likeknowing that floors shall always be horizontal orthat windows belong to a wall and trying toformulate this knowledge in such a way that amachine could not violate such an obvious rule. Thisis dealt with by means of constraints. Constraintsappeared in CAD as early as 1963, in the pioneerwork of Sutherland. As it happens with the verynotion of parametric design, the notion of constraintis present, in a basic way, in any CAD system. Apolyline, for example, can be understood as a collec-tion of curves with vertices constrained to remainattached. But, in general, the notion of constraintimplies a model with an extended database. A con-straint is a relation that limits the behavior of anentity or a group of entities. Examples of constraintsare: a group of lines constrained to be parallel operpendicular or collinear, a line constrained to betangent to an arc, two cylinders constrained to beconcentric, a dimension constrained to be less than aparticular magnitude or equal to a multiple of aparticular magnitude. The notion of constraint im-.plies the notions of degree of freedom DOF , over-constrained, and underconstrained models, as well asthe notion of tolerance. A model can be conceptual-ized as a topological description of a complex formwith n variables or independent dimensions. Eachconstraint diminishes the alternatives by one step. Onthe other hand, the bigger the number of constraints,the more difficult it is to manage in such a way thatit will remain consistent under different values as-signed to the remaining free dimensions. If a modelis underconstrained, it cannot be resolved becausesome additional parameter must still be specified. Ifa model is overconstrained, it cannot be resolvedbecause there is a contradiction somewhere. Con-straint modeling requires that all the defined con-straints shall be fulfilled before the model is evalu-ated or, in other words, that the DOF of the modelhave to be reduced to zero. The power of a system todeal with underconstrained or overconstrained mod-els is a proof of its efficiency. Some programsinform the user that the model cannot be resolvedbut leave the user with the task of locating the fault.A program properly designed should have a con-straint management module able to provide defaultparameters in case of an underconstrained model andto inform the user of this or any other contradictoryparameter that may have been specified. Constraintscan also be of two different types that sometimes arereferred to as geometric constraints and physical orengineering constraints. Parallelism, perpendicular-ity, tangency, dimensionality are geometric con-straints. But a model can also be based on formulalike areasforcerpressure. Constraints can also bespecified as conditional relations such as: If D1qD2)D3 then D1s10 cm else D1s20 cm. Amajor difference between systems is the way inwhich the constraints are input and controlled. Ingeneral, this imposes some extra job on the userwho, besides choosing an entity, marking its positionand assigning some dimensions to it, must specifythe relation that it shall keep with other entities inthe model.4. Evolution of parametric design techniquesBesides the above-mentioned pioneering work ofw xIvan Sutherland, Hillyard and Braid 1 proposed asystem around 1978 that allowed the specification ofgeometric constraints between part co-ordinates insuch a way that possible variations remain restrictedto a range given by some particular tolerances. Thisproposal was not developed in the sense that couldbe expected from our present point-of-view. Gossardw xand Light 2 mention this work as a basis for theirown, which can be quoted as the primary referencefor what can be called parametric design in a moremature sense. The work of Gossard and Light thatwill commented below as a basis for what is calledvariational geometry or variational design, was amajor step as it provided geometrical representationswith new mathematical and geometrical tools thatopened the way to the generalization of a model.Around the end of the 1980s, when the maintechniques of geometrical modeling, free-form sur-faces and solid modeling were already assimilated,there was a growing sense that modeling techniquesshould advance in the direction of an increasinginteractivity and ability to modify a model after ithad been sketched. There were a number of impor-tant articles and books already published and, also, afew articles by researchers directly involved in thedevelopment of this field that attempted to resume()J. MonederorAutomation in Construction 9 2000 369377373the state-of-the-art. It is clear that there are still, atthe present time, two big groups, one that is becom-ing obsolete and the other that attracts a growingnumber of researchers:w x1. What we can call, as Roller 7does, variantsprogramming or static generation of alternativemodels by means of a programming procedure.These systems can rely on current internal repre-sentations of models.2. Graphic generation or interactive methods bymeans of more elaborated systems that allow themodification of dimension and constraints afterthe model has been created. These systems implya modification or an extension of the internalrepresentation of the model.The main disadvantage of the first group is that itcannot do what the second group does, that is, tochange some of the characteristics of a model in aninteractive way. On the other hand, it is a mode ofwork that can adapt to current CAD programs if theuser has some knowledge of simple programmingtechniques. The main disadvantage of the secondgroup is that we will have to wait a few years until aconsistent parametric modeler, based on some of thedifferent alternatives still under research enumeratedbelow, is integrated in some of the programs cur-rently used by architects.4.1. Variants programming by macros or proceduralmodelingOne of the simplest ways of using a very rudi-mentary form of parametric design is to record ascript of the commands and data values used tocreate an element. If this script is edited and the datavalues are changed, we will get a family of variantsof the same type with different dimensions. We canrefine this method by using a programming lan-guage, like AutoLisp, to write a macro, a routine or alittle program that performs the suitable actions tomodel the elementthe difference between thesethree terms can be assimilated to a difference inquantity, i.e., a few lines for a macro or a few pages.for what might be called a simple program . In thisway, the model can incorporate some kind of interac-tion with the user, that is, it can record the mainparameters of the element as variables and requesttheir values from the user once the program isactivated. It can also incorporate conditional expres-sions or simple equations that may extend the inter-est of the method.Variants programming is equivalent to one of theprimitive forms of geometric modeling: primitiveinstancing. This consists also in the generation ofmodels or elements by means of a procedure that callin sequence the commands needed to build the model.To prevent errors and secure the validity of therepresentation, values used for input have to be partof a pre-defined range. The main difference betweenthis method and the ones that we will see below isthat the commands used are already part of a CAD-modeler. The program reads the values as input fromthe user and executes the sequence of commands thatcreate the model, which are provided by the modeler.The main limitations of this method are: the numberand the range of variables is limited as there is, ingeneral, no proper way for controlling variants thatmight produce not valid results. Moreover, the re-sults cannot be edited; the only way to change themodel is to repeat the process. However, it is amethod of modeling widely used in industry and thatcan be very effective if one needs to incorporate to amodel simple elements that are not supposed to bemodified. It has been used extensively in architec-ture.4.2. History-based constraint modelersA graphically interactive parametric modeler al-lows the user to create a master model that can beused as a base to input parameters to the system andto request from the user the specification of con-straints that will fix the model through a closeddescription of its components. This ensures that noerrors should appear whenever any new variant isspecified. As we have said before, this means that anextended or alternative internal representation mustbe used. There are different methods used to gener-ate a new model after parameters are changed. Themost widely used presently is perhaps what is some-timescalledhistory-baseddesignorproperparametric design as opposed to variational de-.sign or constructive parametric design.Many commercial parametric modelers availableat the present time use a data structure keeping trackof the sequence followed to create a model. Any()J. MonederorAutomation in Construction 9 2000 369377374operation, together with the data used to complete it,is recorded in the order that it occupied during theprocess of building a particular model. The opera-tional parameters can be geometric entities as well asexpressions. The model can be modified by substitut-ing the data used in a particular operation. Recom-puting the model will have the effect of changingsome of its geometric characteristics while maintain-ing the connections, that is, the intended relationsbetween the different entities. This method is alsocalled constructive parametric design, as the se-quence incorporates and requests directly from theuser, the specification of secondary entities such asline or plane axes or a circle used to define an arc,etc. These constructive elements are also constrainedin a similar way to the rest of the entities thatconstitute the model. One drawback of some com-mercial systems is that they try to present the con-structive planes or axes as something offered to theuser when it is rather something required by thesystem. Once the model is completed and DOF arefix to zero, and the model is neither underconstrainednor overconstrained, a construction plan is produced.The history is recorded by means of a directed graphwhere nodes represent entities and arcs operations.The direction of the graph follows the sense ofconstraint propagation. The result is a cyclic graph.To change a dimension is equivalent to substitute thevalues of the related geometric constraint. Adding ageometric relation is more complicated and requireschecking possible overconstraints, finding the appro-priate dimensional value and rebuilding the graph.The entities and operations involved, in general,must be such that can be constructed by rule andcompass. Also, a single change in the procedure canforce the system to recalculate, as average, a 50% ofthe geometry. In any case, once the graph is automat-ically reconstructed, the parameters are re-evaluatedand the model is recomputed.4.3. Variational geometry and ariational designContrary to the previous method, parametric de-sign based on variational geometry can recompute adesign taking into account the actual situation, inde-pendently of the sequence that has been followed toreach this situation. The method relies on the de-scription of parameters by means of equations andthe availability of a system able to solve them. Themain foundational reference is given by the articleswxpublished by Gossard and Light 2,3 . The methodrequires, as before, that the system is neither under-constrained nor overconstrained. The system has theadvantage, contrary to the previous one, that it isindependent of the way the model has been createdand can accept any situation or any model as input.Dimensions are considered as constraints that affecta particular set of points in the model. An object in aspace, defined by the three co-ordinates of theirN-vertices will have 3N DOF. To compute the newgeometry, after any of these vertices has changed,.3N equations with 3N variables will have to besolved. Many of these equations can be derivedeasily, such as the equation of a plane given by threevertices or any equation that forces four points to becoplanar. Similarly, simple quadrics like cones orspheres can be represented in this way. As distancesare also implied, the constraint equations will bequadratic and are, for this reason, in general, non-lin-ear. Numerical methods are used to solve them andthe method proposed by Gossard and Light reducesthe number of necessary equations to solve the modelusing a Jacobian matrix to find the parameters and apropagation systems that runs in both directions.Still, the method is computational expensive. It isdoubtful, for the time being, that it could be appliedto architectural models.4.4. Rule-based ariants: geometric reasoning byexpert systemsThe previous method has a number of importantdifficulties, such as the need to specify an exactnumber of constraints or to solve a large number ofequations by numerical methods. To avoid these andother problems, a few alternatives have been pro-posed. Among them, some derived from ArtificialIntelligence and Expert Systems can be quoted.w xw xw xBruderlin 4 , Sunde and Kallevik 5 , Aldefeld 6 orw xVeroust et al.9are among the first and mainresearchers in this field.These alternative techniques consider the modelas something that can be described by a series offacts relating to geometric entities and constraintsbetween them. A form is described by a series oflogical predicates using languages like Prolog or()J. MonederorAutomation in Construction 9 2000 369377375Lisp. A set of rules is specified to relate theseconstraints. These rules are applied through an infer-ence engine that gives as output a particular modelthat satisfies the initial constraints and the productionrules. The predicates can specify dimensions such asthe distance between two lines i.e., distance l1, l2,.dor geometrical relations i.e., parallel l1, l2 or.on-line p,l1 . The inference rules may look like thisexpression:on_line p,l1 ,on_line p,l2 ,not_equal l1,l2.pis intersect_lines l1,l2.deducing that point p is on the intersection of linesl1, l2, from the three predicates on the left of theexpression.The method is still under research. Direct specifi-cation of predicates is tedious, non-intuitive anderror prone. It is also difficult to determine thenumber of constraints a particular form needs to plete uniqueness problem . There are somesystems that help to solve these difficulties by meansof additional predicates and geometric master modelsproposed by the user from which the set of initialimplicit logical predicates can be automatically gen-erated. Still the method is very expensive computa-tionally and has to be refined.4.5. Parametric feature-based designWhat is a feature in CADrCAM? A direct an-swer could be that a feature is something that can beextracted from a prismatic piece of material througha particular sequence of machine operations. Fea-tures areslots,holes,blind holes orpockets, chamfers, fillets, protrusionsand the like. But this is a CAM point-of-view thatdoes not necessarily coincide with a CAD point-of-view, mainly during the first steps in the designprocess. From a more general standpoint, we can saythat a feature is an entity that belongs to a semanticorder higher than the geometric one. In literature,also the definition of feature as a form with adefined function in a specific context is found.The first work in this field is probably a PhD byA.R. Grayer from Cambridge University, in 1976A Computer Link between Design and Manufac-.tureattempting to automate the relationship be-tween a CAD- and a NC-system. This work comesfrom a group of researchers that had already workedin well-known modeling systems such as BUILD,ROMULUS or ACIS. By the middle of the 1980s,this topic had evolved until it became one of themost active fields of research in CADrCAM. At theend of the 1980s, the first commercial prototypessupporting features and parametric design wereavailable.Features, in a parametric modeler, belong to fami-lies and are inserted in the model as instances of amaster feature that is included in a features library.These features can be type-oriented or object-ori-ented. In the first case, the representation is given byattributes such as the geometric properties of the.master featurelength, width, radius , tolerances,relations with other characteristics, etc. In the secondcase, the representation is based on procedures thatprocess the main properties of the features. As thefeature is defined externally and is inserted in themodel during the process of design, the position ofthe feature must also be captured by parameters.Also, some features have natural counterfeatures, aswhat happens in CAD with, e.g., a gear rim thatmust fit into an inner gearing or as it could happen inarchitecture with a metal window that must fit into ahole in the wall. This means that the system must beable to support and manage the complex combina-tion of relations of the model.5. Architectural design and building modelsThe previous review was based on the availableliterature on Parametric Design and CAD. The kindof application that this literature is addressing hasmore to do with Mechanical Engineering and Com-puter-Aided Production, although there are a fewpapers related directly with the construction industry.But we are interested in architectural education andarchitectural practice and there are strong differencesbetween these fields. The main one is that CAD, asused by engineers, applies mainly to objects that willbe repeated many times and that are not rooted toany particular site. This is exactly the opposite ofwhat happens in architecture. Keeping these differ-ences in mind, let us now see how the previousreview can relate to our field of interest.()J. MonederorAutomation in Construction 9 2000 369377376 .aVariants programming is a well-establishedtopic among the architects who use CAD and havesome programming knowledge. Small elements, in2D and 3D, can be created by means of somerecorded procedure that requests the value of a fewparameters when it is called by the user, activates theadequate commands from the modeler and producesand inserts a variant of a generic element on themaster model. During the last few years, we haveproduced a wide collection of elements of this kindusing AutoLisp. From such utilities as routines thatopen a hole in a wall, in 2D or 3D, and insert apre-defined door or window, or routines that com-pute the dimensions and create a stair that runs froma given position on a floor to another position on thenext floor, or routines that generate automaticallyother common building elements, etc., to other morespeculative types that can, e.g., create geometricalcompositions in a fixed or random way. We take itfor granted that this kind of work is well-known, sowe will not show any results of this kind in thispaper. Some of these results will be published at ouruniversity and can be acquired by those interested.There is also a book by William Mitchell The Art ofComputer Graphics Programming. A structured in-.troduction for Architects and Designers, 1987 , thatcan still provide a fine introduction to this subjectwith routines written in Pascal but easily translatedto other programming languages. .b Interactive parametric design of 3D elementscan be achieved by means of a dialogue box withedit boxes that will allow the user to modify thevalues of the current parameters and include a graph-ical window pre-visualizing the results. Some com-mercial programs like ArchiCad or 3dStudio Maxprovide something similar to this but we are trying toimplement it in a more general way through VisualCqq and programming tools like Arx. Anyoneworking in this field is invited to share experiences.In any case, we think that the kind of results is easilyanticipated and we can accept that either by meansof personal programs or by commercial facilities,there will soon be tools that will allow us to designsmall elements by means of parameters in an interac-tive way and insert them in an architectural model. .c The big challenge is the architectural model asa whole. There are two current positions concerningthis topic. Some people think that it is not worth thetrouble. Others think that any building can be param-eterized as an assembly in a similar way as anindustrial piece or a car or an aircraft. We are in anintermediate postion. It is doubtful that a buildingcan be treated as an aircraft as this goes against thevery nature of architecture that is rooted to a particu-lar site and, besides, cannot repeat itself in order tojustify fees and make our environment a little moreinteresting. Although it must be said that we have alot to learn from the way these industries managefeatures and databases and parametric models. Thereis some research on specific methods to parameterizea whole building. A recent article by K. Martinipresents an interesting program, still under develop-ment, based on an object-oriented class hierarchy,that can model a building through special primitivesand positioners, using what is called intrinsic vs.contextual geometry in such a way that modifica-tions of the model can be propagated to any part of itafter it has been created.It is clear, however, that any development of thiskind will take a long time before architects can useit. Meanwhile, we are working on the following linesthat we would like to present for discussion toanyone interested in the subject. An architecturalmodel includes many different elements. We canstart by considering only two main groups: .a Floors
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