Automation in Construction 12 (2003) 365 – 379 www.elsevier.com/locate/autcon
Building assembly detailing using constraint-based modeling K. Nassar a,*, W. Thabet b, Y. Beliveau c a
Department of Civil Engineering and Construction, Bradley University, 126 Jobst Hall, 1501 W. Bradley Avenue, Peoria, IL 61625, USA b 123 D Burruss Hall, Blacksburg, VA 24061-0156 540.818.4604, USA c 122 E Burruss Hall, Virginia Tech., Blacksburg, VA 24061-0156 540.818.4602, USA Accepted 4 September 2002
Abstract Constraint-based geometric modeling entails specifying geometric constraints to control the locations of the components in an assembly. Consequently, any future modifications of the components are governed by these constraints. In this paper, a set of constraint-based assembly operations for generating 3D details of building assemblies are presented. The operations constrain the locations and orientations of the components in a building assembly through a series of constructive steps and therefore allow for easier modification. These operations are used in a modeling system that extends the idea of constraint-based modeling to detailing architectural building assemblies. The system utilizes the constraint-based assembly operations, which employ traditional geometric constraints integrated with a set of constructive assembly operations. The constraint-based assembly operations allow for a more systematic generation of the assembly details, which can save repetitive work and reduce mistakes resulting from copying and pasting old details. Also, the technique allows the assemblies to be studied and analyzed. To illustrate this idea, a prototype 3D constraint-based system for assembling three-dimensional architectural details was developed. With the proposed system, the details of building assemblies do not need to be reinvented for every project. Examples of the proposed approach are provided and its limitations and benefits are discussed. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Constraint-based modeling; Assemblies; Building details
1. Introduction During the early and mid-1980s, CAD was gaining ground and becoming an efficient alternative to the drafting table. With the increased use of CAD, architects were continuously devising ways to automate drafting and design tasks in order to increase their efficiency. Repetitive tasks were automated using * Corresponding author. E-mail addresses:
[email protected] (K. Nassar),
[email protected] (W. Thabet).
predefined scripts, utilizing the various scripting languages offered in the CAD systems (e.g. AutoCAD’s AutoLISP). Object-oriented data was added to lines, arcs and circles, and systems began recognizing them as doors, windows and doors. Object data was then extended to the third dimension, so architects could work in 2D and 3D. A number of software tools were devised in which architects can define their designs in 3D and the complete object model is maintained by the system. This started with simple ‘‘house modeling’’ software marketed to help non-architects define their ‘‘dream house’’ (e.g. Home Architect, Home
0926-5805/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0926-5805(02)00090-0
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Designer, etc.. . .). The idea was then extended to professional software like Triforma, Architectural Desktop and ArchiCad. Concurrently, in the mechanical design realm, parametric modelers were being introduced. The concept behind these modelers is that a user defines a set of parameters that in turn drives a 3D model. This means that changes in any parameter are propagated to the rest of the model. Additionally, various 2D details can be extracted from the model. In the architecture realm, Revit [14] first introduced this concept commercially. Revit is a parametric modeler that acts on parametric components (e.g. doors, windows and doors), and annotations (e.g. dimensions and grids) and parametric views (e.g. plans and sections) to ensure bidirectional association between the elements of design. When changing the location or size of a window in a floor plan, for example, the change is reflected in all views like elevations and perspectives. If a dimension measuring from the end of a wall to the center of a window is changed, not only will Revit move the window, but also any other windows parametrically related to it. This parametric model of the building, which is driven from a single integrated database, is what makes Revit unique. Simultaneously in the mechanical design realm, constraint-based modelers, like Mechanical Desktop [8], were being introduced and used. Constraint-based geometric modeling entails specifying geometric constraints to control the locations of the components in the assembly. Consequently, any future modifications of the components are governed by these constraints. The constraints are used to relate two components within an assembly to control their positions and orientation relative to one another. Similar concepts in architecture were described in a number of research studies as early as the 1960s [4]. Gross [1] described a system where building components can be assembled using ‘‘Lego-style’’ constraints that guide the placement of the components in the building. The constraints mainly relate to the various grids and modules used for the various systems in the building. Harfmann and Chen [5] and Harfmann et al. [6] also proposed a system where the various components of the building are linked together using constraints. An integrated database that stores all this information is maintained by the system. Frazer [2,3] described how constraints could be used
to describe the rules of the physical and spatial structure of architecture designs, which he called plastic modeling. Kilkelly [7] described a comprehensive approach for construction drawings. The approach employs object-oriented entities to specify the composition of construction drawings and details. This paper presents a graphical modeling system that extends the idea of constraint-based modeling to detailing architectural building assemblies. The system utilizes constraint-based assembly operations, which employ traditional geometric constraints integrated with a set of constructive assembly operations. The constraint-based assembly operations allow for a more systematic generation of the assembly details, which can save repetitive work and reduce mistakes resulting from copying and pasting old details. Also, the technique allows the assemblies to be studied and analyzed more rationally than traditional techniques. To illustrate this idea, a prototype 3D constraint-based system for assembling three-dimensional architectural details was developed. In the next section, the concept of constraint-based assembly operations is presented.
2. Constraint-based modeling for architecture details 2.1. Overview One of the current practices for generating the details is to store details of the various assembly types in a detail library (which can be in an electronic format) and retrieve the details for each new design. However, the possible permutations and combinations that can be encountered are too many and oftentimes the current detail can be different from the retrieved library detail, resulting in design errors. The shapes, locations or number of components in the new selected detail can be different. Therefore, the retrieved detail becomes invalid and must be modified or drawn again. This paper introduces the use of constraint-based assembly operations to help the designer in the generation of building assembly details and overcoming the need to recreate the detail for each new design. Constraint-based assembly operations are essentially a set of constructive operations that act on components of the assembly to place them in the correct position within the assembly.
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In architectural practice the details are generally drawn separately from the main plan, elevations, and sections. In constraint-based modeling, on the other hand, the generated detail is based on an abstract 3D representation of the assembly. The designer provides a 3D model of the building in terms of abstract building assemblies (such as that of Fig. 1). This is analogous to many of the commercial CAD tools (e.g. AutoDesk’s Architectural Desktop, Graphisoft’s ArchiCad, and Bentely’s TriForma, and recently Revit). In this abstract representation of the building, each assembly is modeled as a separate 3D entity. Once the building is modeled in 3D, the constraint-based modeling operations can be used to generate the detail for a specific assembly (or a set of assemblies). Of course, it is possible to generate a complete set of details for all the building. However, this is generally not needed in practice and would make the model undecipherable. Architects usually concentrate and generate details of specific assemblies that are critical or need more explanation. Also, once the detail is generated, the
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original abstract 3D representation of the building still exists. This allows for viewing the complete 3D model of the building at different levels of detail. Constraint-based modeling operations can help to cut the time it takes to modify the detail and generate new ones and also to minimize the errors resulting from current cut-and-paste practice of details. In order to illustrate this concept, the properties of the abstract 3D representations of the assemblies and the components used in the proposed building assembly detailing system are first presented. Then, the set of constraintbased modeling operations are described next. This is followed by a discussion of the syntax and use of the system along with an example. Finally, the computer implementation is described and conclusions are drawn. 2.2. Abstract representations and work-features Once the building is modeled as a set of abstract building assemblies in 3D (e.g. Fig. 1), it is possible to
Fig. 1. An example of an abstract 3D model of a house modeled in ArchiCad.
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concentrate on a specific assembly (or set of assemblies) and generate the details accordingly. In the 3D building model, a solid model or CADREP (short for CAD representations) represents each of the assemblies in the building and components in the detail. Hence, two types of CADREPs are identified here: assembly CADREPs and component CADREPs. Various component CADREPs are shown in Fig. 2. In order to generate the 3D solid model of a complete assembly detail, some constraints that describe how these component CADREPs fit together within the context of the whole assembly have to be added. When two parts are constrained (which can be either two component CADREPs, or one component CADREP and one assembly CADREP), generally one geometric feature of one part is related to another geometric feature of the second part. Geometric features that can be used to create constraints are faces (both planar and curved), axes, points (end, mid, center, and others), and edges. A cube, for example, has 12 edges, 6 faces, and 16 standardized points. In this paper, these geometric features are called work-features. Therefore, work-features can either be work-points, work-axes
or work-planes (as shown on the upper right component CADREP in Fig. 2). These work-features are referenced in the constraint-based operation (discussed next) to place the components in their correct positions. Each workfeature can be either relative or absolute. A relative work-feature relates to the main 3D assembly in relative proportions only. For example, one can define a work-axis to be in the center of the assembly CADREP, or a work-point to mark the upper left corner of an assembly, or a work-plane relates to the upper surface of the assembly CADREP. These relative work-features allow the CADREP to be scaled, rotated or transformed, and still retain these workfeatures in their corresponding relative positions. The absolute work-features on the other hand, relate to discrete locations on the assembly of the CADREP of the component. For example, a work-axis can be defined so that it is 1 in. from the left edge of the assembly. Given the assembly and the component CADREPs and their respective work-features, the next step then is to place the components in their correct position
Fig. 2. Examples of component CADREPs.
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within the assembly using the work-features and the constraint-based operations. 2.3. Constraint-based assembly operations The constraint-based operations used here are essentially declarative constraints packaged within a set of assembly operations. First, the declarative constraints are discussed and then the suggested assembly operations are presented. 2.3.1. Declarative constraints Declarative constraints relate the location of two objects together. Declarative constraints can be used to restrict the locations or orientations of certain objects in the model. For example a mate constraint can be used to insure that the beam object is geometrically located flush with a column as seen in Fig. 3. In this case, the mate constraint takes four parameters: the two objects to be constrained and two vectors on the objects to describe how to mate them. Once the constraint is specified, any modifications to the assembly have to comply with the set constraints, and a new assembly detail can be generated. The new details reflect the correct location of the components. So if the size of the beam in Fig. 3 changes for example (or the column is moved or resized), the model will be updated to reflect the new size marinating the flush constraint. The mate constraint in Fig. 3 is only one type of constraint. Various generic constraint sets have been
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proposed in the literature. However, there are, as yet, no standards for specifying or representing constraints [13]. Fig. 4 shows an example of generic classification of declarative constraints [12]. The constraints are divided into two main groups: orientation and position. The position constraints are used to define distances between two points as constraints. They specify the distance measure from a reference entity to a target entity. The orientation constraints are divided into five types: parallel, perpendicular, angle, coplanar and coaxial. Another set of declarative constraints is offered in a commercial constraint-based modeler, AutoCad Mechanical Desktop. This program allows users to specify four kinds of constraints: AMINSERT (insert), AMANGLE (angle constraint), AMFLUSH (flush constraint), and AMMATE (mate constraint) as shown in Table 1. Mechanical Desktop was used as the constraint-based engine for the prototype system developed in this research, and hence these constraints are used here. Next, a description of how these declarative constraints are integrated within the constraint-based assembly operations is presented. 2.3.2. Assembly operations Although the discrete parameters in traditional constraint-based modelers like Mechanical Desktop can be changed (e.g. the length or width of an element, a radius of cam, etc.. . .), the parameters of the declarative constraints (the CADREPs themselves) have to be changed manually. For example, in order to
Fig. 3. Examples of constraints.
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Fig. 4. Different kinds of constraints, adapted from Ref. [12].
change parameters like the shape of an element (e.g. new brick shape), one has to manually do so and then refine the model again. Furthermore, when modeling building assemblies using constraint-based modeling, one often needs to resort to a number of steps in order to achieve the final effect [11]. In building assemblies, for example, there are usually repetitive objects. For example, the CMU units or the metal ties are repetitive objects with the
same solid model. If we were to specify these units separately, the modeling time would increase significantly. A solution might be to define a 3D ARRAY operation that can used to create objects and then constrain the final set of objects as a whole using the traditional geometric constraints. In addition, the sequence of the assembly process itself could be important for further analysis of the properties of the objects.
K. Nassar et al. / Automation in Construction 12 (2003) 365–379 Table 1 Constraints in mechanical desktop Constraint
Description
Mate Insert
To join points, axes, planes, or non-planar faces. To align two circles, including their center axes and planes, use the Insert constraint. To make two planes coplanar with their faces aligned in the same direction, use the Flush constraint. To control an angle between two planes or two vectors, use the Angle constraint.
Flush
Angle
Therefore, a set of constraint-based assembly operations is proposed. These operations can be used to specify the sequence of operations to constrain the locations and orientations of certain objects in relation to others. The set of constraining operations are constructive steps that place geometric elements relative to each other. This approach is often called constructive specification [10,11]. The operations and the constraints associated with them are shown in Table 2. They are a combination of constraints and standard solid modeling operations. Each operation takes component CADREPs of a particular type as its parameters. For example, the ‘‘LAYOUT’’ operation in Fig. 5 operates on CADREPs that are to be placed at certain intervals and can take, for example, the metal ties CADREPs. Each operation also has a set of parameters associated with it. The ‘‘LAYOUT’’ operation, for example, has the spacing parameter ‘s’ to determine the spacing between the elements. Note that in the LAYOUT constraint, all the work-features are on the same plane. The ‘‘ASSEMBLE’’ operation is the operation used to connect components together. It can also be
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used to place a component or assembled components in relation to an assembly. The ‘‘STACK’’ operation is used for masonry type CADREPs and can take a brick or a CMU CADREP as an input. This is a combination of a 3D ARRAY command and both an ANGLE and FLUSH constraints. ‘‘COVER’’ is the operation for overlaying material over a surface like tiles, plyroofing, etc.. . . ‘‘CUT’’ operation is used to penetrate or trim components, e.g. wood. This is a standard 3D SUBTRACT command followed by an ASSEMBLE constraint. 2.4. Operations syntax Constraints usually have a target and a reference entity. The target entity is the entity that is to be constrained, while the reference entity is the entity the target is constrained to. The target and reference entities can be component CADREPs within an assembly or they can be assembly CADREPs themselves. In order to specify the constraints in each operation, the target and reference entities are actually the workfeatures on the assembly and component CADREPs. For example, the ‘‘ASSEMBLE’’ operation will take two points, e.g. one on the component CADREP and the other on the assembly CADREP (these have to satisfy a coincide constraint along with two directions that have to satisfy a coaxial constraint). In effect, this constraining operation is equivalent to combining more than one of the Mechanical Desktop constraints in relation to building elements. For example, the LAYOUT ðObject A; P1; D1; Object B; P2; D2; sÞ This is equivalent to a standard 3D ARRAY operation followed by a MATE constraint and a FLUSH
Table 2 The defined constraining operations Operation
Geometric work-feature parameters on reference
Geometric work-feature parameters on target
Building parameters
Example
Layout Assemble Cover
one point, one line one point, one line one point, one line
spacing – angle, spacing, overlap
metal ties, fixtures bolts, screws tiles, sheet rock
Cut Stack
one point one point, one line
one point, one line one point, one line one point, one line, start point, end point one point, one line one point, one line, start point, end point
angle vertical joint spacing, horizontal joint spacing
sawing wood masonry
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Fig. 5. The LAYOUT and ASSEMBLE operations.
constraint. The points P1 and D1 are work-features defined on the CADREP of Object A, i.e. a work-point and a work-axis. Similarly P2 and D2 are workfeatures defined on the CADREP of object B. The constraining operations required for the detail shown in Fig. 6 are shown. The user of the system would define the 3D model of the building, similar to the simple block building shown in upper left corner of Fig. 6. The 3D model of the building is defined using
assembly CADREPs (i.e. columns, walls, roofs, etc.. . .), which are instanced from base CADREPs. This is similar to defining 3D blocks in AutoCAD that resemble the different assembly CADREPs and then inserting (rotating, scaling, and moving around) instances of these blocks to define 3D model of the building. The operations required to generate different details would then be defined, such as those required to generate the simple Column – Metal ties – CMU
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Fig. 6. The operations for a simple example.
assembly in Fig. 6. Alternatively, assembly operations can be restored from a library of saved operation sets. These saved sets would specify the operations required to generate different details. Once the operations have been specified for an assembly detail, a user would then select a particular abstract assembly CADREP in the model and apply the defined operations to generate the detail. Furthermore, the same operation set can be used to generate other details with different CMU shapes, spacing, or metal-tie shapes or spacing by changing the parameters of the operations and without the need to draw a new model again. Notice that in this simple example an assembly
Fig. 7. The sectioned 2D details.
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Fig. 8. The example stair assembly.
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CADREP itself (the column CADREP) is used as part of the complete detail. The hidden lines can be removed and the detail can be rendered with texture if required. Once these operations are defined, the same set of operations can be applied to different column CADREPS in the 3D model that are instances of the column CADREP used in the original definition of the assembly (for example, the same detail can be generated by selecting any of the columns in simple block building shown in Fig. 6). The operations relate to actual construction operations. This has the benefit of simplifying constraint definition, since a designer can relate more easily to these operations than abstract geometric operations and constraints. More importantly, since the described operations relate to building components, each component will be associated with the same operation regardless of the CADREP used. For example, a ‘‘Vinyl Tile’’ component will always be associated with the ‘‘COVER’’ operation. This allows us to draw a multitude of building assembly details in 3D with this concise set of operations. The created assembly detail is a solid model. This means that the assembly can actually be sectioned in many ways to produce different 2D details if desired. Examples of 2D details generated from the solid model of the detail of the developed example above are shown in Fig. 7. To increase the robustness of the assembly operations, the resulting ‘‘subassembly’’ of one operation can be used as an input in the following operation. This is demonstrated using the following stair example. 2.5. A stair example Consider the stair example in Fig. 8. Originally, the stair assembly was modeled as an abstract 3D assembly as shown. A set of operations is required so that they can then be applied to the selected abstract assembly CADREP and generate a detailed assembly such as that shown. There are four components represented by CADREPs (T, C, H, L). Given these four components, the sequence of the constraining operations is defined as shown. First, a CUT operation is used on C to cut out the place of T and similarly for the place of H. Then a LAYOUT operation is used to layout C along T. Next, two ASSEMBLE operations are used to assemble the rest of the stair assembly.
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Fig. 9. The modified details of the stair assembly with two carriages.
Notice that the results from one operation can be used as input in the next. There are several benefits from this approach. By representing assemblies in that way, one can easily change the size, shape or number of components or subassemblies in an assembly and the changes can be propagated accordingly. For example, in the previous stair assembly, if the user decides to use two carriages instead of three, then he or she would have to modify the parameters of the LAYOUT operation in step 4 and a modified detail would be generated (Fig. 9). A prototype system that incorporates most of functionalities of constraint-based assembly operations was developed and is described next.
3. Computer implementation In this section a brief description of the developed prototype system is presented. The prototype, EASYBUILD, was developed as an extension to a popular commercial CAD package: AUTOCAD. One of the reasons AUTOCAD is a popular package is its ease of customization. AUTOCAD offers a multitude of ways to develop customized applications on top of the regular drafting interface. Different tools exist for developing application extensions in AUTOCAD, including AutoLisp, Visual Lisp, C++ and ADS and Visual Basic For Applications (VBA). In this research, the development tool used for implementing EASYBUILD was VBA. The reason for choosing this development tool is its ease of extension and compatibility with several other software packages like databases and spreadsheets [9]. Visual Basic was first introduced in AutoCad Version 14. The assembly generation module of EASYBUILD consists of three main modules, the Assembly/Component Definition
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Module (ADM), the Constraint Editor (CE), and the Modeling Module (MM). 3.1. The Assembly/Component Definition Module (ADM) The ADM has two main functions. Firstly, the ADM is the module that allows the user to define the CADREPs of the different components and assemblies as solid models. These are stored as blocks in AUTOCAD so that they can be retrieved and instanced when drawing the building in the modeling module. Secondly, the ADM is where the users can model the different components and specify the various workfeatures for component CADREPs and assembly CADREPs to be used in the constraint-based operations. This is accomplished by attaching Xdata to the solid model of the component CADREP. Xdata is a method in AUTOCAD for attaching geometric and textual data to models so that they can be retrieved or altered later. The user can specify various work-fea-
tures, like work-points or work-directions on the model of the component as needed. (Fig. 10) shows the interface of the ADM. The components and their work-features defined in the ADM are stored in a library in order to be retrieved when evaluating the constraint-based operations. EASYBUILD also allows the user to specify dummy geometries to be used in the generation of the assembly detail. 3.2. The Modeling Module (MM) The MM allows a user to model the 3D representation of the building using the various CADREPs of the building assemblies. The building is modeled by instancing the blocks of the assembly CADREPs defined earlier in the ADM. These blocks can then be rotated, transformed or scaled to define the building. The system is currently limited to four assembly CADREP types: walls, flat roofs, columns, and isolated footings. Once the building is modeled, the next step becomes to select one of the assembly CADREPs in the
Fig. 10. Defining work features in the Assembly/Component Definition Module (ADM).
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model and apply the appropriate set of constraint-based operations to generate the 3D detail of that assembly. Currently, the MM cannot import 3D models from other architectural modeling software (i.e. Architectural Desktop or ArchiCad) and therefore, the building currently must be modeled in the ADM. However, the ability to import 3D building models would be a useful addition to increase the versatility of the system, and can be accomplished by using recently developed universal standards such as the Industry Foundation Classes (IFCs). 3.3. The Constraint Editor (CE) This module is where the constraint-based operations are defined. The definition of the operations required to generate the 3D building detail is carried out in a text-editor interface. This interface allows the user to specify the operations needed for a particular assembly detail in the form of a set of sequential commands. These commands are then parsed and evaluated for each new design. Alternatively, the user can retrieve a predefined set of operations saved earlier or save the current set of operations to be used later. The user would then select an assembly
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CADREP and apply the loaded set of operations to the selected assembly CADREP in order to generate the 3D building detail. The system retrieves the components from the predefined library of components (defined in the ADM and applies the set of operations, automatically generating the 3D detail. Fig. 11 shows the interface CE. Currently, only the ASSEMBLE, LAYOUT, and CUT operations are functional. Although the modeling succession can be different from the actual construction operations, the designer can visualize the assembly sequentially, in a systematic way. Assembly composition can be analyzed and examined critically, by changing different component shapes and sizes. This helps in analyzing the aesthetics and functionality of the assembly. More of the benefits and limitations of this approach are discussed below.
4. Benefits and limitations The set of defined operation here is only preliminary. Nevertheless, using the limited defined set, one can model a fair number of assembly details. How-
Fig. 11. The Constraint Editor (CE).
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ever, one of the limitations of the system as it stands, is the lack of error checks during the assembly operations. For example, in the stair example above, a CUT operation can be defined initially to ensure that the length of the ledger component (L) is similar to the width of the stair. However, if the length of the ledger component CADREP used in the assembly detail is smaller than the width of the stair, a problem will arise. Adding conditional statements in conjunction with the assembly operations can solve this problem. Conditional statement can be used to evaluate the different situations and guarantee a more accurate detail. Conditional statement can also be used for further analysis and decision-making about the detail. Another limitation of the current system relates to the number of subassemblies that the system can handle. The system can currently handle only up to five levels of subassemblies. Although five levels of subassemblies are sufficient for most details, this limitation can be easily extended with appropriate modifications to the system. An important feature of this method is that the designer modeling the assembly is concerned with coordinating at most two components at any one time. This is useful when modeling complex assemblies in 3D. Due to the fact that the designer can reuse the solid models of the components and the subassemblies, shorter initial development modeling time over both the traditional solid modeling approach and the constraint-based approach results after a comprehensive library of components and subassemblies has been developed. Furthermore, this method offers an increased ease of modification especially for complex assemblies. Benefits of the constraint-based approach also include the ability to generate an animated sequence of how assemblies are put together. Although the user of this system is mainly the architect, suppliers, contractors, or the construction manager who want to study how these assemblies will be built can also utilize this system. Architects do not always think in terms of the construction sequence. However, if the sequencing is considered in collaboration with the construction manager, many on-site sequencing problems can be avoided. The system can be used before construction to verify and test any sequencing problems before construction starts.
5. Conclusion and recommendations for future research Constraint-based modeling offers an efficient method for generating building assembly details. A set of constraint-based assembly operations was defined. These operations can be used to specify and constrain the components in an assembly through a series of constructive steps. The constraint-based assembly operations described here offer a systematic method to create building assembly details. The described method allows for more efficient modification of 3D assembly details to fit a specific design. With the proposed detailing system, architects do not need to reinvent the details for every project. Instead, they can concentrate their efforts and budget on the overall design and on gradual refinement of the details. With time, a library of details could be built and details from the library could be modified for each project as well as building new project-specific details. Moreover, the progression of the operations can be a useful tool to consider different composition options with real-time visualization. A prototype system was developed and examples to demonstrate the idea were presented. Future work includes refinement of the selected operations to remove redundancy and arrive at the most efficient set of operations to simplify the process of constraint definition. Also, a closer binding between these operations and actual construction sequence needs to be investigated. An integration of the modeling sequence with the construction sequence results in a kind of a 4D model that adds the time dimension. This provides a visual representation of how to actually build the assembly, which in turn can be used for demonstration or educational purposes also. References [1] M.D. Gross, Why can’t CAD be more like Lego? CKB, a program for building construction kits, Automation in Construction 5 (4) (1996) 285 – 300. [2] J. Frazer, An Evolutionary Architecture, Architecture Association Publications, 1995. ISBN 1-870890-47-7. [3] J. Frazer, Plastic modelling—the flexible modeling of the logic of structure and spaces, CAAD Futures ’87, Proceedings of The Second Conference On Computer Aided Architecture Design Futures, 1987, pp. 199 – 208.
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[10] K. Nassar, A framework for the selection and generation of building assemblies, PhD Thesis, Department of Building Construction, Virginia Tech., Blacksburg, VA (1999). [11] K. Nassar, Y. Beliveau, Integrating Parametric Modeling and Construction Simulation, CIB ’99, Vancouver, Canada, 1999. [12] J. Shah, M. Mantyla, Parametric and Feature Based CAD/ CAM; Concepts Techniques and Applications, Wiley, New York, 1995. [13] W. Hower, H. Graf, A bibliographical survey of constraintbased approaches to CAD, graphics, layout, visualization, and related topics, Knowledge-Based Systems 9 (1996) 449 – 464. [14] Revit Technology Corporation, Revit’s Users Manual (2000).
