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Spatial Information Modeling of Buildings Using Non-Manifold Topology with ASM and DesignScript

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Much of the discourse in architectural geometry has focused on the geometric design and physical optimisation of the material ‘Building Model’, specifically the building structure and envelope, and the digital fabrication of facades. In this paper we want to “go behind the façade’ and consider architecture not so much as a physical building model, but at a more abstract level, as the ‘enclosure of space’. The intent is to explore related geometric and topological concepts which can be the foundation of appropriate computational design tools. The objective of these tools is to support the design of a ‘spatial’ architecture and the use of the spatial analysis of building models in related engineering design processes. To achieve this we are using the concept of nonmanifold topology implemented in ASM (the Autodesk Shape Manager), but in a novel way. In this approach the interior of what would normally be referred to as a ‘solid body’ is not thought of as being composed of solid material, but rather as an enclosed void that can be used in an architectural sense to represent the ‘enclosure of space’.
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Spatial Information Modeling of Buildings using
Non-Manifold Topology with ASM and DesignScript
Robert Aish, Aparajit Pratap
Autodesk
Abstract. Much of the discourse in architectural geometry has focused on the
geometric design and physical optimisation of the material ‘Building Model’,
specifically the building structure and envelope, and the digital fabrication of
facades. In this paper we want to “go behind the façade” and consider
architecture not so much as a physical building model, but at a more abstract
level, as the ‘enclosure of space’. The intent is to explore related geometric and
topological concepts which can be the foundation of appropriate computational
design tools. The objective of these tools is to support the design of a ‘spatial’
architecture and the use of the spatial analysis of building models in related
engineering design processes. To achieve this we are using the concept of non-
manifold topology implemented in ASM (the Autodesk Shape Manager), but in a
novel way. In this approach the interior of what would normally be referred to as
a ‘solid body’ is not thought of as being composed of solid material, but rather as
an enclosed void that can be used in an architectural sense to represent the
‘enclosure of space’.
1 Introduction
Architecture has been described as the ‘enclosure of space’. Indeed most buildings
are conceived in two ways:
- as a 3D geometric envelope (that separates the outside from the inside)
- and the partitioning of the enclosed space into constituent spaces (or rooms)
We might call this a ‘spatial’ or idealized model of the building. Most
conventional ‘Building Information Modeling’ applications adopt a different
approach, by providing design tools which support the placement and editing of
components (such as walls, floors, columns and beams, etc.) that represent the
material aspects of the building. We might call this a material or physical model of
the building.
It is of course recognized that at the end of an architectural design process the
design, engineering and construction teams should have produced a complete
unambiguous ‘building information model’.
R. Aish and A. Pratap
However during an exploratory design process it is important that the
architects and engineers can build the lightest possible model using the least effort
that gives the most accurate feedback about their design and engineering concepts.
Our contention is that a modeling process that combines spatial modeling (via
non-manifold topology) and associative parametric modeling (via scripting) can
facilitate this light weight least effort maximum feedback” design
methodology.
It is envisage that the resulting spatial information model (and associated
topological queries) can be used for:
- early structural analysis, using such tools as Robot Structural Analysis
- early design energy analysis using tools such as Green Building Studio
- fire analysis (using CFD)
- egress analysis
as well as the topological and geometric support model for the material model of
the building (see Fig. 1 (left)).
Figure 1(left): A single non-manifold solid, consisting of three cells constructed by the
non-regular union of two (blue) cubes. One of the faces of the inner (red) cell has been used
as the supporting geometry for a wall component (yellow).
Figure 1(right): A spatial information model built with ASM. This is a cut-away model and
illustrates a number of non-regular modeling operations that are unique to non-manifold
topology. The initial solid was ‘sliced’ horizontally with floor planes and then vertically
(with wall planes in X and Y). Finally a conical solid representing the atrium was
‘imposed’. The resulting cellular topology structure can be interrogated with topological
query functions.
Spatial Information Modeling of Buildings using Non-Manifold Topology
To realise this concept, we have implemented a set of special non-regular Boolean
operations to create non-manifold bodies and a series of topological classes to
allow the designer to access the topology of the resulting spatial models.
Topological query functions are provided to allow the designer to make a traversal
of the spatial model of the building.
For a given building we can distinguish between the spatial model, different
analytical models and the material model of the building:
- The spatial model of the building is the partitioning of the building envelope
into discrete cells representing the interior spaces or rooms.
- The material model of the building is the collection of physical components
that will make up the constructed, tangible building. The material model
might use the topology of the spatial model (for example, the cells, faces,
edges and vertices) as supporting geometry for the individual solid models
presenting these typical physical building components.
- There can be a mumber of different analytical models of the building
(for example, for structure or for building performance).
Our proposal is that the different analytical models can be derived by attributing
the spatial model and without the need to build a material building model. Indeed
the material model should only be built after the analytical models have served
their purpose in the design process.
In this process the topological and geometric modelling functionality is
combined with the DesignScript associative modelling language. Spatial
Information Modeling and parametric/associative modeling work well together
and allow the designer to experiment with ‘what-if’ scenarios. Changes to the
spatial model can automatically update any downstream engineering analysis (such
as Green Building Studio) and the dependent material model.
2 Manifold and Non-manifold solids
A 3D manifold body has a boundary that separates the enclosed solid from the
external void. The boundary is composed of faces, which have (interior) solid
material on one side and the (exterior) void on the other. In a 3D manifold body
each edge represents the meeting of exactly two faces, so that everywhere where
faces join there is always solid material on one side of the boundary and a void on
the other side.
The boundary of a body does not have to be connected - a body can have
several disjoint pieces of boundary, as long as each connected piece of the
boundary is closed. This means a single body can contain disjoint volumes of
material, and a single volume can have one or more interior voids, where each is
defined by a closed boundary with material on one side and an interior void on the
other.
In practical terms, a manifold body without internal voids can be machined out
of a single block of material.
R. Aish and A. Pratap
A non-manifold body also has a boundary [composed of faces] that separates the
enclosed solid from the external void. Faces are either external [separating the
interior (enclosed space) from the exterior (void)] or internal [separating one
enclosed space (or cell) from another].
Furthermore a non-manifold solid can have edges where more than two faces
meet.
3 Regular and Non-regular Boolean Operations
One way to construct non-manifold bodies is by using non-regular Boolean
operations. When Boolean operations are used to create a new body from a
number of input bodies, these inputs are often configured so that all or part of one
input body intersects with the other input body, see Figure 1(a).
Generally with regular boolean operations, external faces of the input bodies
that are within the resulting body are removed.
Generally with non-regular boolean operations, external faces of the input
bodies that are within the resulting body are retained
Figure 2: The result of different regular or non-regular operations with manifold inputs.
Note: some operations (union and intersection) are symmetric, while other operations
(difference, impose) are asymmetric. With asymmetric operation there is the convention
that one input is referred to as the ‘part’ (A), the other input is referred to as the ‘tool’ (B).
A
B
A
B
A
B
union intersection difference impose imprint slice
A
B
A
B
A
B
A
non-regular operations regular operations regular inputs
2
1
3
1 body multiple bodies
1 body with
multiple cells
[plane]
N/A N/A
N/A N/A
only imprint edges
on external faces,
no cells created
imprint external
faces of B within
A, creating cells
Spatial Information Modeling of Buildings using Non-Manifold Topology
We can compare:
- Regular union operation (where all external faces of the input bodies within
the output body are removed)
- Non-regular union operation (where all external faces of the input bodies
within the output body are retained [for example, in Figure 1 (left), generating
three cells])
- Non-regular impose operation (literally ‘impose the tool on the part’), so that
the internal faces within the output body that are derived from the ‘tool’ input
remain, but the internal faces within the output body that are derived from the
‘part’ are removed [in this example, generating two cells])
Note:
- There is no regular impose operation, because all regular operations remove
the external faces of the tool from the interior of the resulting body.
- There are no non-regular intersection or difference operations, because with
these operations there are no external faces of the input (tool) body within the
interior of the resulting body.
Figure 1(right) showed a practical example of applying multiple non-regular
Boolean operations. In this example there were multiple ‘slice’ operations using
planes in different X, Y and Z directions, followed by an ‘impose’ operation. This
illustrates that even if the modeling process starts with manifold bodies, the results
(after the first non-regular operation) will be a non-manifold body.
Therefore, subsequent non-regular operations will use non-manifold bodies as
input, as follows:
Figure 3: The result of regular or non-regular Boolean operations with non-manifold inputs
A
B
A
B
A
B
union intersection difference impose imprint slice
A
B
A
B
A
B
non-regular operations regularoperations non-regular inputs
Some laminar
faces created
multiple bodies
each with cells
1 body with
multiple cells
[plane]
N/A N/A
only imprint
edges on external
faces, no new
cells created
imprint external
faces of B within
A, creating cells
faces of the blank
(A) in the tool (B)
are removed
N/A N/A
R. Aish and A. Pratap
4 Topology Classes Implemented
The following classes have been implemented:
Shell: A connected set of Faces in a manifold solid. A solid with a hollow void
inside it has two Shells, one external Shell and another internal Shell.
Cell: A closed, continuous volume enclosing a spatial partition in a
non-manifold solid.
Face: A face can be an interior-exterior face with material on one side and a
void on the other, or it can be a double-sided interior face or a
double-sided exterior face.
Edge: There can be internal edges in a non-manifold model.
Vertex: There can be internal vertices in a non-manifold model.
With the range of manifold and non-manifold classes and the range of regular and
non-regular Boolean operations, the designer is able to create manifold and non-
manifold solid models. By exposing the properties of geometry and topology
classes to the designer, he is able to make his own topological queries. These
queries can be used to build a number of different spatial information models.
Figure 4: The DesignScript geometry and topology classes, with their properties
Spatial Information Modeling of Buildings using Non-Manifold Topology
5 Using a non-manifold spatial model to create alternative
. analytical and material building models
The spatial model of a building and the analytical or material models of the
building are interrelated. The spatial model consists of cells, faces and edges:
- Cells can represent the the enclosed spaces or rooms of the building
- Faces can be used as the supporting geometry for “area” based material
components (walls, floors, roofs, etc.)
- Edges can be used as the supporting geometry for “curvilinear” based material
components, for example structural members (columns, beams)
- Vertices can be used as the location of “point” based connectors
Figure 5: The modelling sequence to construct a non-manifold spatial model of a building
and the use of the edges of this model to construct a structural model.
R. Aish and A. Pratap
5.1 Building a structural model from a non-manifold spatial model
A spatial non-manifold model of the building can be used to:
- extract horizontal edges to define beams
- extract vertical edges to define columns
- extract exterior faces to define roof elements
- extract interior horizontal faces to define floors (slabs)
- extract exterior vertical faces to define exterior walls and facades
- extract interior vertical faces to define interior walls and partitions
Figure 6: Class hierarchy showing the use of topological super classes (face, edge and
vertex) in relation to the sub classes (Plate, Bar and Node) within the Robot namespace.
By using the number and type of faces associated with each edge it is possible to
determine the position of each edge within the spatial model and to populate
different types of edges with an appropriate type of structural component.
Topology
Edge : Topology
+AdjacentFaces: Face[]
+CurveGeometry: Curve
+EndVertex: Vertex
+StartVertex: Vertex
Vertex : Topology
+AdjacentEdges: Edge[]
+AdjacentFaces: Face[]
+PointGeometry: Point
Plate : Face
+Section: Section
+LocalCS: CoordinateSystem
+AreaLoad: Load
Bar : Edge
+Releases: Release[]
+Section: Section
+GammaAngle: double
+LocalCS: CoordinateSystem
+LinearLoad: Load
Node : Vertex
+Fixity: Fixity
+PointLoad: Load
Fixity
+Type: FixityTypeEnum
+UX: bool
+RX: bool
+UY: bool
+...
FixityTypeEnum
+Pinned
+Fixed
+...
MaterialEnum
+Steel
+Wood
+Concrete
+Aluminium
+...
Section
+Type: SectionTypeEnum
+Material: MaterialEnum
+CrossSection: StandardSection
+Width: double
+Height: double
+Thickness: double
+Depth: double
Load
+Type: LoadTypeEnum
+Direction: Vector
+Magnitude: Double
Release
+Type: ReleaseTypeEnum
Structure
+Nodes: Node[]
+Bars: Bar[]
+Plates: Plate[]
+Results: Results
Results
+BarResults: AnalysedBar[]
+NodeResults: AnalysedNode[]
Robot Namespace
Face : Topology
+Area: double
+CellFaces: CellFace[]
+Centroid: Point
+Edges: Edge[]
+Shell: Shell
+SurfaceGeometry: Surface
+Vertices: Vertex[]
Shell CellFaceCell
<<From International Section Library>>
StandardSection
LoadTypeEnum
+PointLoad
+LinearLoad
+AreaLoad
+...
Spatial Information Modeling of Buildings using Non-Manifold Topology
The following rules may be applied [and have been encoded in DesignScript]:
- an edge defined only by external faces implies that the edge is at an external
position, typically at a corner of the building
-
an edge defined by a combination of external and internal faces, typically
implies an edge at an external mid-facade position
- edges defined by internal faces implies an edge within an internal region
5.2 The use of the spatial information model for energy analysis
Here the key topological elements are the cell and the faces that bound each cell.
In this application each topological element is given additional attributes to
provide a complete data model for an energy analysis (see the Green Building
Studio namespace, Figure 7). Here the space class can be derived from the
topological cell class and a surface class can be derived from a toplogical face
class.
The topological analysis defines which faces are external or are internal and
between cells, and therefore which cells are adjacent. In terms of energy modelling
this enables the different conditions in adjacent spaces and the resultant energy
flows through common surfaces to be directly modelled.
Figure 7: The modelling sequence to construct a non-manifold spatial model of a building.
The cells within this model can be used to construct volumetric and spatial adjacency data
suitable for input into energy analysis applications.
R. Aish and A. Pratap
Figure 8: Class hierarchy showing the use of topological super classes (cell and face) in
relation to the sub classes (space and surface) within the Green Bulding studio namespace.
Additionally it is possible to use the topological relations to traverse the spatial
building model. Starting in one space, it is possible to inspect the constituent
surfaces property, and for each surface inspect its adjacent spaces property. Such a
traversal would ignore spaces and faces previously visited.
The notional thickness of the faces multiplied by the face area can be used to
factor the cell volume, to arrive at a reasonably accurate volumetric data without
the need for a precise building model. Certainly this volumetric data will be within
an acceptable tolerance when compared with the accuracy of the other data
involved.
Figure 9: Using the AIM (analytical information modeling) toolkit, this cellular and face
data can be exported as GBXML to Green Building Studio, with the resulting energy
analysis either returned for display within DesignScript or via other energy analysis
dashboards
.
Building : NonManifold Solid
+Spaces: Space[]
+ContainingCampus: Campus
+BySolid(campus:Campus,solid:Solid)
Space : Cell
+SpaceType: SpaceTypeEnum
+AdjacentSpaces: Space[]
+GBSSurfaces: GBSSurfaces[]
+ContainingBuilding: Building
+InfiltrationFlow: double
+AirChangesPerHour: double
+PeopleNumber: int
+LightPowerPerArea: double
+EquipmentPowerPerArea: double
+Temperature: double
Surface : Face
+SurfaceType: SurfaceTypeEnum
+Material: Material
+Openings: Opening[]
+AdjacentSpaces: Space[]
Solid
+Edges: Edge[]
+Faces: Face[]
+Shells: Shell[]
+Vertices: Vertex[]
NonManifoldSolid : Solid
+Cells: Cell[]
Opening
+Type: OpeneningTypeEnum
+Width: double
+Length: double
+ContainingSurface: GBSSurface
Cell : Topology
+AdjacentCells: Cell[]
+Area: double
+CellFaces: CellFace[]
+Centroid: Point
+SolidGeometry: Solid
+Volume: double
Topology
Campus
+Location: Location
+Buildings: Building[]
+GenerateAnalysis()
MaterialEnum
+Wood
+CMU
+Concrete
+Carbon Steel
+Stainless Steel
+Brick
+Gypsum
+Plywood
+Tile
+...
Face : Topology
+Area: double
+CellFaces: CellFace[]
+Centroid: Point
+Edges: Edge[]
+Shell: Shell
+SurfaceGeometry: Surface
+Vertices: Vertex[]
SurfaceTypeEnum
+InteriorWall
+ExteriorWall
+Roof
+InteriorFloorAndCeiling
+Shade
+SlabOnGrade
Location
+Latitude: double
+Longitude: double
+City: string
SpaceTypeEnum
+ActiveStorage
+ActiveStorageHospitalOrHealthcare
+AirOrTrainOrBusBaggageArea
+AirportConcourse
+AtriumEachAdditionalFloor
+AtriumFirstThreeFloors
+...
GreenBuildingStudio Namespace
Vertex EdgeCell CellFace
Spatial Information Modeling of Buildings using Non-Manifold Topology
6 Integration with DesignScript:
In this research, we are exploring the combination of non-manifold topology and
scripted parametric design tools and related work flows.
We see possibilities for designing that may not have existed before in which a
single spatial and topological model can used to drive multiple analytical models,
and then a unified material model (Figure 10).
Figure 10: The three level modelling approach:
(1) a spatial model using topology
(2) a number of different (discpline specific) analytical models
(3) a unified material model, where some material components (for example, a floor)
are essentially multi-functional and combine information and behaviour for multiple
analytical models. Multi-functional components can be implemented in DesignScript via
multiple inheritance.
One of the characteristics of the modelling process presented here is that a minor
change to the modeling of the initial building volumetric geometry can have a
profound effect on the resulting topological model. Cells (and the cells‘ faces and
edges) can appear, disappear and reappear. Additionally faces and edges may be
split or combined.
It is difficult to see how a modeling tool that relied on the user manually
building an analytical or material model could work. Each time a change is made
to the volumetric model, a new topology would be created and previous analytical
and material models would be completely out of date.
A better way to connect the topology of the spatial model to the analytical and
material models is through a rule based script. This can provide a robust
connection which can appropriately respond to the appearance, disappearance and
reappearance of topology and its related geometry.
Topology
Cell: Topology Face: Topology Edge: Topology Vertex: Topology
Space: Cell Surface : Face Bar: Edge: Node: VertexSlab : Face
Green Building Studio Namespace Robot Structural Analysis Namespace
Spatial ModelAnalytical Model(s)Material Model
Floor : Surface + Slab
Material Model Namespace
Wall,
Roof,
etc.
R. Aish and A. Pratap
Additionally, DesignScript supports the use of multiple inheritance to directly
represent the essential multi-functional behaviour of components in the material
model: in this example, representing both structural and building performance.
Overall, this approach combines and unifies topology and geometry, with
different analysis and simulation tools, and with scripting tools which supports
advanced features such as associative and imperative programming and multiple-
inheritance. It is anticipated that this unified toolset can provide the necessary
infrastructure for multi-criteria design optimisation
2
.
Conclusions
This paper presents a novel application of non-manifold topology together with
parametric and associative scripting to model the spatial organization of a building
and to use this information to create different analytical and material models of a
building.
The core of the DesignScript system is a set of unified geometry and topology
classes that can be driven through a number of different programming paradigms.
Without the ability to manipulate such spatial models parametrically and
programatically it is doubtful whether a user could “handcraft” such complex
geometry using interactive direct manipulation techniques or could systematically
explore alternative configurations and options. This supports our contention that a
modeling process that combines spatial modeling (via non-manifold topology) and
associative parametric modelling (via end-user scripting) can facilitate a “light
weight – least effort – maximum feedback” design methodology.
Acknowledgements
The authors would like to acknowledge the contribution of the Autodesk Shape
Manager development team, based in Cambridge, UK for their guidance in
implementing the non-manifold topology described in this paper.
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DOI: … Non-Manifold Topology: Mathematically, Non-Manifold Topology (NMT) is defined as cell-complexes that are subsets of Euclidean Space [15]. Practically, topology refers to the spatial relationships between the various entities in a model and it describes how geometric entities are connected. 'Non-manifold' is a geometric topology term that means 'to allow any combination of vertices, edges, surfaces and volumes to exist in a single logical body' [7]. Such models allow multiple faces meeting at an edge or multiple edges meeting at a vertex. Coincident edges and vertices are merged. Moreover, non-manifold topology models have a configuration that cannot be unfolded into a continuous flat piece and are thus non-manufacturable and not physically realizable. On the contrary, a manifold body without internal voids can be fabricated out of a single block of material [1]. NMT has been successfully applied in various applications, including in the ship building industry, [13], the medical field [17], Computer Aided Engineering [19], Computer Aided Design for Mechanical Engineering [16], structural analyses [18], and Digital Fabrication [9]. Considering its success in these applications, it would be possible to transfer NMT's success to architecture in order to enhance the representation of architectural space [8]. NMT's topological clarity allows architects to better design, analyze, reason about, and produce their buildings. The potential of NMT in the early design stages is already acknowledged and research has been undertaken with regard to the advantages of NMT's application for energy analysis in the early design stages [7], [8]. NMT has already been applied together with parametric and associative scripting to model the spatial organization of a building [1]. This information was then used to create different analytical and material models of a building. Moreover, non-manifold spatial models are considered suitable for early structural analysis, as horizontal and vertical edges can be used to define beams and columns respectively, while internal or external faces can be used to define floors, roof elements and interior or exterior walls, facades and partitions [1]. Topological Characteristics of Non-Manifold Objects: Topological elements of non-manifold objects are hierarchically interrelated and a lower-dimensional element is used as the boundary of each of several higher dimensional ones [21]. An example is shown in Fig. 1(a). Boolean set operations are common set operations that are used to combine solids in order to create more complex objects. They are usually applied to two bodies at a time [3]. The main Boolean operations are union, intersection and difference, which are regular; merge and impose, which are non-regular; and imprint, which can be regular or non-regular. Generally a regular Boolean operation removes any external faces of the input bodies that are within the resulting body, while a non-regular Boolean operation maintains any external faces of the input bodies that are within the resulting body
... In parallel, nonmanifold topology (NMT) is an innovative computerbased representation of architectural entities and can be useful for spatial design, BIM-based design development and building performance analysis for com-plex geometries. Prior publications by the authors suggest that NMT provides topological clarity that has the potential to allow architects to better design, analyse, reason about, and produce their buildings (Aish and Pratap, 2012;Jabi, 2015;Jabi, 2016, Jabi et al., 2017Jabi et al., 2018;Aish et al., 2018. ...
... As a consequence, the adjacency information among the spaces as well as other entities is explicitly stored in the building model and spatial queries can be conveniently performed. While NMT is commonly considered as defects in current practice, it has been shown that it can better represent the concept of interconnected spaces and support spatial as well as topological queries (Aish and Pratap 2013;Jabi et al. 2017). There have been precedents in the use of NMT for spatial reasoning. ...
Chapter
Topologic is a software modelling library that supports a comprehensive conceptual framework for the hierarchical spatial representation of buildings based on the data structures and concepts of non-manifold topology (NMT). Topologic supports conceptual design and spatial reasoning through the integration of geometry, topology, and semantics. This enables architects and designers to reflect on their design decisions before the complexities of building information modelling (BIM) set in. We summarize below related work on NMT starting in the late 1980s, describe Topologic’s software architecture, methods, and classes, and discuss how Topologic’s features support conceptual design and spatial reasoning. We also report on a software usability workshop that was conducted to validate a software evaluation methodology and reports on the collected qualitative data. A reflection on Topologic’s features and software architecture illustrates how it enables a fundamental shift from pursuing fidelity of design form to pursuing fidelity of design intent.
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This paper presents a comparison of different pathways for the energy modelling of complex building geometry. We have identified three key modelling questions: first, how can the spatial organisation of the building be appropriately represented for energy analysis? Second, how can curved building geometry be post-rationalized as planar elements given the planar constraints associated with energy simulation tools? And third, how can an exploratory design process be supported using a 'top-down' rather than a 'bottom-up' modelling approach? Using a standard office building test case and EnergyPlus, the following three pathways were explored: (a) OpenStudio using a non-manifold topology (NMT) system based on an open-source geometry library, (b) OpenStudio using the SketchUp 3D modelling tool and (c) through the DesignBuilder graphical interface. The efficacy of the software used in these pathways in addressing the three modelling questions was evaluated. The comparison of the pathways' capabilities has led to the evaluation of the efficacy of NMT compared to other existing approaches. It is concluded that NMT positively addresses the three key modelling issues.
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We have developed a modular approach to the parametric design of a patterned façade for tropical climates, using a "lighter" data set and model that integrates a number of performance considerations. This modular approach separates the façade's design into form, façade pattern, façade density requirements, and façade components, and reintegrates these aspects via a triangular mesh, represented as a fast and convenient data structure based on half-edges. Through this separation, the design team can simultaneously work on the architectural appearance of the design, its performance, and its fabrication, while retaining holistic control through the constant reintegration of design changes via the half-edge data structure. In this way, we retain the advantages of a parametrically driven design process, such as automatic design generation and the integration of performance aspects, while permitting more flexible and non-sequential design explorations by different members of the design team.
Progress towards Multi Criteria Design Optimisation using DesignScript with SMART Form, Robot Structural analysis and Ecotect building performance analysis
  • R Aish
  • A Fisher
  • S Joyce
  • A March
AISH, R. FISHER, A., JOYCE, S., MARCH, A. 2012. Progress towards Multi Criteria Design Optimisation using DesignScript with SMART Form, Robot Structural analysis and Ecotect building performance analysis. ACADIA 2012