Left: An early digital model of the Bird’s Nest Beijing National Stadium as modeled inside Digital Project. Right: the final model. Image courtesy of: Gehry Technologies LLP (www.gehrytechnologies.com). 

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... Secondly, coupled with the visualization, it must also be an analysis tool that is able to perform all the computations required for the design process. This includes structural analyses, mechanical services, electrical analyses, and other analytical processes that are required to validate and optimize the design [1]. Thirdly, it should be a platform that promotes ease of collaboration by enabling the same model to be accessed and modified by multiple designers in different locations simultaneously (Coons, 1963). The notion of the internet and online collaboration was not even close to reality in 1963. ARPANET (Advanced Research Projects Agency Network), the forerunner of the Internet, was only introduced in 1968 [5]. The idea described in the paper [1] depicts a situation that was only realizable in the early 90s when the Internet had reached one-million users worldwide [5]. Finally, a CAD system must be highly generic to accommodate the creative activities that reside in a trans-disciplinary design domain. The general problems of architects and engineers need a system that is flexible and adaptable to multiple specific domains [1]. Apart from Steve Coon’s manifesto, Kasik et al. has reviewed the progress of CAD departing from Ivan Sutherland’s Sketchpad application and presented ten challenges of CAD and classified them into three different categories: “ computational geometry, interactive techniques, and scale” [6]. A number of those challenges have been answered in recent developments of parametric modeling tools. There are profusion of CAD software that perform solid modeling but are not parametric. The scope of this review only covers CAD packages that perform flexible 3D parametric modeling and are referred as parametric modeling tools from this point forward. Parametric modeling was first introduced as a means for design reuse [7]. Parametric modeling uses parameterized relationships between components in the design to define forms [8]. A parametric model comprises variable attributes, which are called parameters and fixed attributes, which are called constraints [4]. A parametric model responds to changes of parameter value or definition without erasure of parts of the model or starting the design model from scratch. Designers alter the value of the parameters to explore design variations that can be generated from the same model [4]. Parametric design tools, such as GenerativeComponents by Bentley Systems, Digital Project by Gehry Technologies (an adaptation from the powerful and expensive CATIA software used by the aerospace industry for the AEC industry), ArchiCAD by Graphisoft, and the Revit family of products by Autodesk, have been taken up more widely by the AEC design and design education communities worldwide only during this decade. In the previous decade, its use was known but through more isolated and research-led projects in practice and academia. AutoCAD was the main software utilized in industry but it was not parametric. The rise of the usage of parametric modeling tools is due to its power to manipulate geometry and generate variations by simply changing its parameters. Geometry manipulation is not limited to simple ex- trusion or Boolean operations. Parametric modeling tools .support the construction of a single model that has many varying geometrical instances. Initially, parameterized mathematical associations between objects in the model need to be defined. For some parameters, it may be possible to determine a range, or the maximum and minimum values based on design criteria. Then by iterative refinement of both the mathematical associations and the values of the parameters in the model, various design options are explored. These design options can be compared and analyzed further and criteria determined for selection of the better and best solutions. The Sagrada Família church in Barcelona (Fig. 1 – Left), which was started in 1883 and left unfinished by the architect Antoni Gaudí who died in 1926, is an example of a building and a design system in which there is a clearly defined parametric geometry that provides the key to the design process. With the help of parametric ‘recipe’ left by Gaudi in his plaster models and drawings, the ongoing design and construction of the Sagrada Família relies on Gaudí’s technique of prescribing variations of complex geometries based on simple forms exploiting the variation of geometric parameters of those forms. One example of the subsequent influential work to interpret and model Gaudí’s intentions digitally and parametrically is the columnets model, in which variation of the surface parameters, rotation and Boolean operations are applied on trimmed hyperbolic paraboloids to generate the forms [9]. Two examples of the more recent projects using parametric design tools for design exploration are the Dubai Towers (Fig. 1 – Right), designed by TVS using Generative Components by Bentley Systems, and the “Bird’s Nest” Beijing National Stadium (Fig. 2), designed by Herzon and de Meuron using Digital Project by Gehry Technologies. We perceive two different groupings of parametric design tools given the varying approach to parametric design. The first group of parametric design tools is based on associative-geometry , where parameterized mathematical descriptions and associations between points, curves, surfaces, and solids are possible. The tools belonging to this group include Bentley GenerativeComponents and Rhino Grasshopper. The second group of parametric design tools are focused on BIM , where parametric relationships encapsulate parametric descriptions of components of a building design across multiple disciplines [10]. BIM stands for Building Information Modeling, which is regarded as “a data-rich, object-oriented, intelligent and parametric digital representation of the facility” by the American General Contractors (as quoted in [11]). The Autodesk Revit 2010 package (Revit Architecture 2010, Revit MEP 2010, Revit Structure 2010) belongs to this group as well as Gehry Technologies’ Digital Project. Revit 2010, however, is unable to handle NURBS geometry modeling [12] and therefore Revit is not generally used for modeling complex curved geometries. Digital Project is known to be a very powerful parametric CAD package that handles both complex parametric geometric associations as well as parametric design representations referring to diverse libraries across multiple disciplines. Nevertheless, it is also known to be the most expensive CAD package that is currently around and customiz- ing model via the script interface is not trivial. The first group of tools can also be used for parametric representations that link different disciplines, however, BIM high- level object definitions are not included in the tools by default. In a reflective mode, we review the existing parametric modeling tools and revisit the CAD requirements by the CAD visionary and retrospectively raise the question – are we there yet? The following evaluation is raised in the light of the use of the current parametric modeling tools and processes. This section evaluates the existing parametric modeling tools’ capabilities to process and manage the geometries in the design using graphical and symbolical means. The abstractions of the design in parametric modeling tools are often represented in a symbolic diagram. These features are now intrinsic to all the existing parametric design tools. GenerativeComponents (GC) encompasses a 3D interactive view, a symbolic view, and an object view [13]. One distinguishing feature of GC is the way it displays both the textual and symbolic representation of the parametric associations between components in the model. This feature is also available in Grasshopper, the new extension of Rhino. The symbolical representation of a parametric model is analogous to an object diagram of a software application. In fact, the notion of components, parameters, constraints, and associations in a parametric model resemble those of the object-oriented programming paradigm. The graphical and symbolical representations undoubtedly assist designers to rethink their design in the light of the components and their associations in the model as well as the parametric variations they would like to generate from the model. Both the graphical and symbolical representations visualize design intent that is captured within the tool, particularly during the early design stage when design options need to be generated rapidly. Revit 2010 uses the more rigid tree structure to represent the higher level of abstraction of the model. Geometrical associations between components in the model are not visualized in the tree structure. Since each component in a Revit model is an instance of a Revit family type (e.g. an instance of a 36’ flush panel type of the door family), the tree structure provides the abstraction and the detailed view of the instances of each type and family that are created in the model. Symbolic representations are used to view the 3D model as engineering plans. However, there is no existing symbolical abstraction to represent the parametric associations of all the parts in a Revit model. Considering that Revit is aimed to be a BIM software, the tree structure is useful for viewing abstract representations of parts of the model to give a non discipline specific overview. CATIA/Digital Project (DP) primarily uses a hierarchy of linked files. No single file need be very large. It also uses simple graphical files that just show the geometry for representing large extents of the model where it might otherwise take hours or days to open the Part and Product files. There is a tree structure in CATIA/DP that is an organizational and navigational tool and another that directly maps the model’s parametric relationships. To date, CAD tools (i.e. parametric design tools) and analysis tools have been distinct and autonomous. Cross-disciplinary analysis is a ...