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Buildings enclose and partition space and are built from assemblies of connected components. The many different forms of spatial and material partitioning and connectedness found within buildings can be represented by topology. This paper introduces the ‘Topologic’ software library which integrates a number of architecturally relevant topological concepts into a unified application toolkit. The goal of the Topologic toolkit is to support the creation of the lightest, most understandable conceptual models of architectural topology. The formal language of topology is well-matched to the data input requirements for applications such as energy simulation and structural analysis. In addition, the ease with which these lightweight topological models can be modified encourages design exploration and performance simulation at the conceptual design phase. A challenging and equally interesting question is how can the formal language of topology be used to represent architectural concepts of space which have previously been described in rather speculative and subjective terms?
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316 AAG2018 317
Topologic: Tools to
explore architectural
topology
Robert Aish, Wassim Jabi, Simon Lannon, Nicholas
Mario Wardhana, Aikaterini Chatzivasileiadi
Robert Aish
robert.aish@ucl.ac.uk
Bartlett School of Architecture, University College London, United Kingdom
Wassim Jabi
jabiw@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Simon Lannon
lannon@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Nicholas Mario Wardhana
wardhanan@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Aikaterini Chatzivasileiadi
chatzivasileiadia@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Keywords:
Non-manifold topology, idealised model, material model
316 AAG2018
317
Abstract
Buildings enclose and partition space and are built from assemblies
of connected components. The many different forms of spatial and
material partitioning and connectedness found within buildings can
be represented by topology. This paper introduces the ‘‘Topologic’’
software library which integrates a number of architecturally relevant
topological concepts into a unified application toolkit.
The goal of the Topologic toolkit is to support the creation of the
lightest, most understandable conceptual models of architectural
topology. The formal language of topology is well-matched to the data
input requirements for applications such as energy simulation and
structural analysis. In addition, the ease with which these lightweight
topological models can be modified encourages design exploration and
performance simulation at the conceptual design phase.
A challenging and equally interesting question is how can the formal
language of topology be used to represent architectural concepts of
space which have previously been described in rather speculative and
subjective terms?
1. Introduction
This paper focusses on the conceptual issues surrounding the use of
topology in architecture. It builds on previous research and proof of
concept studies (Aish and Pratap 2013; Jabi 2014; Jabi et al. 2017). Other
concurrently published papers describe in greater detail the implemen-
tation of the Topologic toolkit and specific applications of Topologic in
building analysis and simulation (Jabi et al. 2018; Chatzivasileiadi, Lannon,
et al. 2018; Wardhana et al. 2018).
Topology and in particular non-manifold topology are vast subjects that
span algebra, geometry and set theory. It is beyond the scope of this paper
to delve into the mathematical constructs and proofs that precisely define
non-manifold topology. Topology has applications in biology, medicine,
computer science, physics and robotics among others. Since the motiva-
tion for this research is to address the needs of architects and engineers,
this research focusses on a specific application of non-manifold topology
in the representation of significant spatial relationships in the design of
buildings using computer-aided three-dimensional geometric processing.
316 AAG2018
317
Topologic: Tools to
explore architectural
topology
Robert Aish, Wassim Jabi, Simon Lannon, Nicholas
Mario Wardhana, Aikaterini Chatzivasileiadi
Robert Aish
robert.aish@ucl.ac.uk
Bartlett School of Architecture, University College London, United Kingdom
Wassim Jabi
jabiw@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Simon Lannon
lannon@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Nicholas Mario Wardhana
wardhanan@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Aikaterini Chatzivasileiadi
chatzivasileiadia@cardiff.ac.uk
Welsh School of Architecture, Cardiff University, United Kingdom
Keywords:
Non-manifold topology, idealised model, material model
316 AAG2018 317
Abstract
Buildings enclose and partition space and are built from assemblies
of connected components. The many different forms of spatial and
material partitioning and connectedness found within buildings can
be represented by topology. This paper introduces the ‘‘Topologic’’
software library which integrates a number of architecturally relevant
topological concepts into a unified application toolkit.
The goal of the Topologic toolkit is to support the creation of the
lightest, most understandable conceptual models of architectural
topology. The formal language of topology is well-matched to the data
input requirements for applications such as energy simulation and
structural analysis. In addition, the ease with which these lightweight
topological models can be modified encourages design exploration and
performance simulation at the conceptual design phase.
A challenging and equally interesting question is how can the formal
language of topology be used to represent architectural concepts of
space which have previously been described in rather speculative and
subjective terms?
1. Introduction
This paper focusses on the conceptual issues surrounding the use of
topology in architecture. It builds on previous research and proof of
concept studies (Aish and Pratap 2013; Jabi 2014; Jabi et al. 2017). Other
concurrently published papers describe in greater detail the implemen-
tation of the Topologic toolkit and specific applications of Topologic in
building analysis and simulation (Jabi et al. 2018; Chatzivasileiadi, Lannon,
et al. 2018; Wardhana et al. 2018).
Topology and in particular non-manifold topology are vast subjects that
span algebra, geometry and set theory. It is beyond the scope of this paper
to delve into the mathematical constructs and proofs that precisely define
non-manifold topology. Topology has applications in biology, medicine,
computer science, physics and robotics among others. Since the motiva-
tion for this research is to address the needs of architects and engineers,
this research focusses on a specific application of non-manifold topology
in the representation of significant spatial relationships in the design of
buildings using computer-aided three-dimensional geometric processing.
318 AAG2018 319
We can contrast this approach with more conventional representations
of buildings as a collection of physical building components, typically
modelled as manifold solids, as demonstrated by Building Information
Modelling (BIM) applications. While BIM can be used to model the physical
structure of the building, architecture is usually conceived in terms of an
overall form and a series of related spatial enclosures (Curtis 1996). This
spatial conceptualization is a key aspect of architectural design because
it directly anticipates how the resulting building will be experienced.
However, there are no practical design tools which support the creation
of this spatial representation of architecture. Non-manifold topology
is ideally suited to create a lightweight representation of a building as
an external envelope and the subdivision of the enclosed space into
separate spaces such as rooms, building storeys, cores, atria, etc. This
lightweight representation also matches the input data requirements for
important analysis and simulation applications, such as energy analysis,
(Ellis, Torcellini, and Crawley 2008).
Conventional BIM applications, in contrast, do not explicitly model the
enclosure of space. Although it might be possible to indirectly infer the
enclosed spaces from the position of the physical building components,
the fidelity of this representation depends on the precise connectivity of
the bounding physical components, which cannot be relied upon. Even
if this approach was viable, the level of detail of BIM models is often too
complex for this type of analysis (Maile et al. 2013). Detailed BIM models
are also cumbersome to change which may inhibit design exploration at
the conceptual design stage.
One option might be to explore spatial modelling with existing solid
modelling applications. However most of these applications are based
on conventional manifold modelling techniques and do not support
non-manifold topology. Indeed, many regular manifold modelling applica-
tions treat non-manifold topology as an error condition.
The objective of this research is to develop design tools based on
precise topological principles but presented in ways which are under-
standable by architectural users who may have little previous experience
of topology. The intention is that Topologic can be an effective interme-
diary between the abstract world of topology and the practical world of
architecture and building engineering.
318 AAG2018
319
2. Background
2.1 The distinction between manifold and non-manifold
Topology
In a previous paper (Aish and Pratap 2013) the following distinctions
were made between manifold and non-manifold topology:
“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 practical terms, a manifold body without internal voids
can be machined out of a single block of material.
“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.
2.2 The distinction between an idealized and a
material model
One of the key themes which runs through this research is the distinc-
tion between an ‘‘idealised’’ model (of a building) and a ‘‘material’’ model
of the physical building components. An early demonstration of this
principle was made in 1997 (Aish 1997) and further developed (Hensen
and Lamberts 2012).
Typically, idealised models are far less detailed than material models,
therefore lighter and more easily edited. In addition, the different
topological components of the idealised model (faces, edges, vertices)
can be used as the ‘‘supports’’ for related building components in the
material model. The connectivity of the components in the material
model need not be directly modelled. Instead this connectivity can be
represented through the topology of the idealised model.
2.3 Previous research
The case for non-manifold topology as well as its data structures and
operators for geometric modelling were comprehensively set out by
(Weiler 1986). In his introduction, Weiler explains why non-manifold
topology is needed:
318 AAG2018
319
We can contrast this approach with more conventional representations
of buildings as a collection of physical building components, typically
modelled as manifold solids, as demonstrated by Building Information
Modelling (BIM) applications. While BIM can be used to model the physical
structure of the building, architecture is usually conceived in terms of an
overall form and a series of related spatial enclosures (Curtis 1996). This
spatial conceptualization is a key aspect of architectural design because
it directly anticipates how the resulting building will be experienced.
However, there are no practical design tools which support the creation
of this spatial representation of architecture. Non-manifold topology
is ideally suited to create a lightweight representation of a building as
an external envelope and the subdivision of the enclosed space into
separate spaces such as rooms, building storeys, cores, atria, etc. This
lightweight representation also matches the input data requirements for
important analysis and simulation applications, such as energy analysis,
(Ellis, Torcellini, and Crawley 2008).
Conventional BIM applications, in contrast, do not explicitly model the
enclosure of space. Although it might be possible to indirectly infer the
enclosed spaces from the position of the physical building components,
the fidelity of this representation depends on the precise connectivity of
the bounding physical components, which cannot be relied upon. Even
if this approach was viable, the level of detail of BIM models is often too
complex for this type of analysis (Maile et al. 2013). Detailed BIM models
are also cumbersome to change which may inhibit design exploration at
the conceptual design stage.
One option might be to explore spatial modelling with existing solid
modelling applications. However most of these applications are based
on conventional manifold modelling techniques and do not support
non-manifold topology. Indeed, many regular manifold modelling applica-
tions treat non-manifold topology as an error condition.
The objective of this research is to develop design tools based on
precise topological principles but presented in ways which are under-
standable by architectural users who may have little previous experience
of topology. The intention is that Topologic can be an effective interme-
diary between the abstract world of topology and the practical world of
architecture and building engineering.
318 AAG2018 319
2. Background
2.1 The distinction between manifold and non-manifold
Topology
In a previous paper (Aish and Pratap 2013) the following distinctions
were made between manifold and non-manifold topology:
“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 practical terms, a manifold body without internal voids
can be machined out of a single block of material.
“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.
2.2 The distinction between an idealized and a
material model
One of the key themes which runs through this research is the distinc-
tion between an ‘‘idealised’’ model (of a building) and a ‘‘material’’ model
of the physical building components. An early demonstration of this
principle was made in 1997 (Aish 1997) and further developed (Hensen
and Lamberts 2012).
Typically, idealised models are far less detailed than material models,
therefore lighter and more easily edited. In addition, the different
topological components of the idealised model (faces, edges, vertices)
can be used as the ‘‘supports’’ for related building components in the
material model. The connectivity of the components in the material
model need not be directly modelled. Instead this connectivity can be
represented through the topology of the idealised model.
2.3 Previous research
The case for non-manifold topology as well as its data structures and
operators for geometric modelling were comprehensively set out by
(Weiler 1986). In his introduction, Weiler explains why non-manifold
topology is needed:
320 AAG2018 321
‘‘A unified representation for combined wireframe, surface, and solid
modelling by necessity requires a non-manifold representation, and is
desirable since it makes it easy to use the most appropriate modelling
form (or combination of forms) in a given application without requiring
representation conversion as more information is added to the model.’’
Non-manifold topology allows an expansion of the regular Boolean
operations of union, difference, and intersection. This expanded set
includes operators such as merge, impose, and imprint. For a full
description of non-manifold operators, please consult (Masuda 1993).
Representing space and its boundary was the focus of early research
into BIM (Björk 1992; Chang and Woodbury 1997) and into ‘‘product
modelling’’ (PDES/STEP) (Eastman and Siabiris 1995) and was proposed
as an approach to the representation of geometry definition for input to
Building Performance Simulation in the early design stages (Hui and
Floriani 2007; Jabi 2016). However, this is not emphasised in modern
BIM software where the building fabric is represented through manifold
geometry and energy models from are derived from the fabric models.
Separately, non-manifold topology has been successfully used in the
medical field to model complex organic structures with multiple internal
zones (Nguyen 2011; Bronson, Levine, and Whitaker 2014).
Our focus is to create a schema which separates abstract topological
concepts from domain specific and pragmatic concerns of architecture,
engineering and construction. We maintain this separation, but also explore
important connections: how buildings can be represented by topology and
how a topological representation can potentially assist architectural users
in the conceptualisation and analysis of new buildings. Therefore, our
focus is not to create new non-manifold data structures, but rather to har-
ness existing geometry and topology kernels in an innovative way; indeed,
it is completely feasible that the Topologic schema could be implemented
with different data structures or with different kernels.
A comprehensive and systematic survey of topological modelling
kernels, which support non-manifold topology, was carried out by the
authors and published elsewhere (Chatzivasileiadi, Wardhana, et al.
2018). Features and capabilities of kernels were compared in order to
make an informed decision regarding what underlying kernel to use.
Popular geometric kernels, such as CGAL, were discounted due to their
inability to represent higher dimensional entities such as CellComplexes
and for their more limited set of irregular Boolean operations.
320 AAG2018
321
3. The Topologic toolkit
The core Topologic software is developed in C++ using Open Cascade
(https://www.opencascade.com/) with specifi c C++/CLI variants deve-
loped for different visual data fl ow programming environments (Wardhana
et al. 2018). Topologic integrates a number of architecturally relevant
topological concepts into a unifi ed application toolkit. The features and
applications of Topologic are summarised in Figure 1 and Figure 2.
Figure 1: The Topologic application toolkit summarised in eight key
points.
320 AAG2018
321
‘‘A unified representation for combined wireframe, surface, and solid
modelling by necessity requires a non-manifold representation, and is
desirable since it makes it easy to use the most appropriate modelling
form (or combination of forms) in a given application without requiring
representation conversion as more information is added to the model.’’
Non-manifold topology allows an expansion of the regular Boolean
operations of union, difference, and intersection. This expanded set
includes operators such as merge, impose, and imprint. For a full
description of non-manifold operators, please consult (Masuda 1993).
Representing space and its boundary was the focus of early research
into BIM (Björk 1992; Chang and Woodbury 1997) and into ‘‘product
modelling’’ (PDES/STEP) (Eastman and Siabiris 1995) and was proposed
as an approach to the representation of geometry definition for input to
Building Performance Simulation in the early design stages (Hui and
Floriani 2007; Jabi 2016). However, this is not emphasised in modern
BIM software where the building fabric is represented through manifold
geometry and energy models from are derived from the fabric models.
Separately, non-manifold topology has been successfully used in the
medical field to model complex organic structures with multiple internal
zones (Nguyen 2011; Bronson, Levine, and Whitaker 2014).
Our focus is to create a schema which separates abstract topological
concepts from domain specific and pragmatic concerns of architecture,
engineering and construction. We maintain this separation, but also explore
important connections: how buildings can be represented by topology and
how a topological representation can potentially assist architectural users
in the conceptualisation and analysis of new buildings. Therefore, our
focus is not to create new non-manifold data structures, but rather to har-
ness existing geometry and topology kernels in an innovative way; indeed,
it is completely feasible that the Topologic schema could be implemented
with different data structures or with different kernels.
A comprehensive and systematic survey of topological modelling
kernels, which support non-manifold topology, was carried out by the
authors and published elsewhere (Chatzivasileiadi, Wardhana, et al.
2018). Features and capabilities of kernels were compared in order to
make an informed decision regarding what underlying kernel to use.
Popular geometric kernels, such as CGAL, were discounted due to their
inability to represent higher dimensional entities such as CellComplexes
and for their more limited set of irregular Boolean operations.
320 AAG2018 321
3. The Topologic toolkit
The core Topologic software is developed in C++ using Open Cascade
(https://www.opencascade.com/) with specifi c C++/CLI variants deve-
loped for different visual data fl ow programming environments (Wardhana
et al. 2018). Topologic integrates a number of architecturally relevant
topological concepts into a unifi ed application toolkit. The features and
applications of Topologic are summarised in Figure 1 and Figure 2.
Figure 1: The Topologic application toolkit summarised in eight key
points.
322 AAG2018 323
Figure 2: Boolean Operations implemented in Topologic.
322 AAG2018
323
3.1 Class hierarchy
The Topologic class hierarchy is designed to provide the architectural
end-user with a conceptual understanding of topology. It also functions
as an ‘‘end-user programmers’ interface” (EDPI). This user-oriented
class hierarchy is distinct to the implementation-oriented class hierarchy
within the Topologic core.
The Topologic superclass (Fig. 1, section 1) is abstract and imple-
ments constructors, properties and methods including a set of Boolean
operators. These operators can be used with both manifold and non-
manifold topology (Fig. 2). Topologic implements the expected concepts
such as: Vertex, Edge, Wire, Face, Shell, and Cell. The interesting addi-
tional topological concepts are:
CellComplex which is a contiguous collection of Cells and is
non-manifold.
Cluster which is a universal construct and allows any combination
of topologies, including other ‘‘nested” Clusters, to be represented. A
Cluster may represent non-contiguous, unrelated topologies of different
dimensionalities.
3.2 Topological relationships
Topologic supports the building and querying of three different types of
topological relationships (Fig. 1, section 2)
Hierarchical relationships: between topological entities of different
dimensionality. These relationships are created when a higher dimensional
topology construct is composed from a collection of lower dimensional
topologies. Subsequently the compositional relationships may be queried:
cellComplexes =
vertex.Edges.Wires.Faces.Shells.Cells.
CellComplexes;
Conversely, the decompositional relationships may also be queried, for
example from higher dimensional topologies down to the constituent
collections of lower dimensional topologies:
vertices = cellComplex.Vertices;
322 AAG2018
323
Figure 2: Boolean Operations implemented in Topologic.
322 AAG2018 323
3.1 Class hierarchy
The Topologic class hierarchy is designed to provide the architectural
end-user with a conceptual understanding of topology. It also functions
as an ‘‘end-user programmers’ interface” (EDPI). This user-oriented
class hierarchy is distinct to the implementation-oriented class hierarchy
within the Topologic core.
The Topologic superclass (Fig. 1, section 1) is abstract and imple-
ments constructors, properties and methods including a set of Boolean
operators. These operators can be used with both manifold and non-
manifold topology (Fig. 2). Topologic implements the expected concepts
such as: Vertex, Edge, Wire, Face, Shell, and Cell. The interesting addi-
tional topological concepts are:
CellComplex which is a contiguous collection of Cells and is
non-manifold.
Cluster which is a universal construct and allows any combination
of topologies, including other ‘‘nested” Clusters, to be represented. A
Cluster may represent non-contiguous, unrelated topologies of different
dimensionalities.
3.2 Topological relationships
Topologic supports the building and querying of three different types of
topological relationships (Fig. 1, section 2)
Hierarchical relationships: between topological entities of different
dimensionality. These relationships are created when a higher dimensional
topology construct is composed from a collection of lower dimensional
topologies. Subsequently the compositional relationships may be queried:
cellComplexes =
vertex.Edges.Wires.Faces.Shells.Cells.
CellComplexes;
Conversely, the decompositional relationships may also be queried, for
example from higher dimensional topologies down to the constituent
collections of lower dimensional topologies:
vertices = cellComplex.Vertices;
324 AAG2018 325
or
vertices =
cellComplex.Cells[n].Shells[n].Faces[n].Wires[n].
Edges[n].Vertices;
Lateral relationships: these occur within a topological construct when
the constituents share common topologies of a lower dimensionality.
adjacentCells = cellComplex.Cells[n].AdjacentCells;
adjacentFaces = shell.Faces[n].AdjacentFaces;
Connectivity: The path between two topologies can be queried.
path = topology.PathTo(otherTopology);
3.3 Idealised representations
Three different idealized models are considered (Fig. 1, section 4)
Energy Analysis: a CellComplex can represent the partitioning and
adjacency of spaces and thermal zones.
Structural Analysis: a Cluster can be used to represent a mixed-dimen-
sional model, with Faces representing structural slabs, blade columns
and shear walls, Edges representing structural columns and Cells
representing building cores.
Digital Fabrication Analysis: a CellComplex can represent the design
envelope where topology can inform the shape and interface between
deposited material (Jabi et al. 2017).
Circulation Analysis: a dual graph of a CellComplex can represent the
connectedness of spaces.
324 AAG2018
325
3.4 Cell as a space or as a solid
A Cell is defined as a closed collection of faces, bounding a 3D region.
However, this same topology can represent two distinctly different
application concepts: a Solid and a Space (Fig. 1, section 5). A Solid is
interpreted as a single homogeneous region of material and its boundary
defines where the material ends and the void begins. This is the inter-
pretation of the Cell as used in ‘‘Solid Modelling’’ and BIM applications.
A Space is a more abstract concept and may include an implied
conceptual distinction between the material which is ‘‘contained’’
(represented by the enclosed 3D region of the Cell) and the ‘‘container’’
(represented by the Faces of the Cell). A Face may represent a
boundary which is intended to be materialized with a defined thickness
or may represent a ‘‘virtual’’ (e.g. adiabatic) barrier which is not intended
to be materialized.
Solids and Spaces have exactly the same Cell topology, but the
domain specific semantics and expected behaviour of this topology may
be different. Consider a boolean ‘‘difference’’ operation representing
a hole drilled into a Cell (as a solid). A new part of the Cell boundary
would be created, but the result would still be a Cell.
What result would the user expect if the same Cell represented a
Space? Would the boolean ‘‘difference’’ only apply to a specific Face
(as part of the Space’s boundary)? Would the user expect the boolean
operation to create an internal boundary within the selected Face?
Would the user expect this operation to destroy the integrity of the
enclosure, changing the Cell into an open Shell?
This example helps to explain the difference between a material
model (the Cell as a Solid) and an idealised model (the Cell as a
Space). More generally this example demonstrates the need for the
architectural users to customise the application of abstract topological
concepts with the domain semantics which suits their purpose.
This relationship between application semantics and abstract con-
cepts works both ways. Sometimes more generally applicable concepts
emerge by abstracting ideas from other specialist domains. For example,
the concept of a topological Cell may have originated as an abstracted
analogy of a biological cell, with similarities in terms of the homogeneity
and continuity of the contained 3D region and the role of the cell wall as
a closed container with selective permeability (Fig. 3).
324 AAG2018
325
or
vertices =
cellComplex.Cells[n].Shells[n].Faces[n].Wires[n].
Edges[n].Vertices;
Lateral relationships: these occur within a topological construct when
the constituents share common topologies of a lower dimensionality.
adjacentCells = cellComplex.Cells[n].AdjacentCells;
adjacentFaces = shell.Faces[n].AdjacentFaces;
Connectivity: The path between two topologies can be queried.
path = topology.PathTo(otherTopology);
3.3 Idealised representations
Three different idealized models are considered (Fig. 1, section 4)
Energy Analysis: a CellComplex can represent the partitioning and
adjacency of spaces and thermal zones.
Structural Analysis: a Cluster can be used to represent a mixed-dimen-
sional model, with Faces representing structural slabs, blade columns
and shear walls, Edges representing structural columns and Cells
representing building cores.
Digital Fabrication Analysis: a CellComplex can represent the design
envelope where topology can inform the shape and interface between
deposited material (Jabi et al. 2017).
Circulation Analysis: a dual graph of a CellComplex can represent the
connectedness of spaces.
324 AAG2018 325
3.4 Cell as a space or as a solid
A Cell is defined as a closed collection of faces, bounding a 3D region.
However, this same topology can represent two distinctly different
application concepts: a Solid and a Space (Fig. 1, section 5). A Solid is
interpreted as a single homogeneous region of material and its boundary
defines where the material ends and the void begins. This is the inter-
pretation of the Cell as used in ‘‘Solid Modelling’’ and BIM applications.
A Space is a more abstract concept and may include an implied
conceptual distinction between the material which is ‘‘contained’’
(represented by the enclosed 3D region of the Cell) and the ‘‘container’’
(represented by the Faces of the Cell). A Face may represent a
boundary which is intended to be materialized with a defined thickness
or may represent a ‘‘virtual’’ (e.g. adiabatic) barrier which is not intended
to be materialized.
Solids and Spaces have exactly the same Cell topology, but the
domain specific semantics and expected behaviour of this topology may
be different. Consider a boolean ‘‘difference’’ operation representing
a hole drilled into a Cell (as a solid). A new part of the Cell boundary
would be created, but the result would still be a Cell.
What result would the user expect if the same Cell represented a
Space? Would the boolean ‘‘difference’’ only apply to a specific Face
(as part of the Space’s boundary)? Would the user expect the boolean
operation to create an internal boundary within the selected Face?
Would the user expect this operation to destroy the integrity of the
enclosure, changing the Cell into an open Shell?
This example helps to explain the difference between a material
model (the Cell as a Solid) and an idealised model (the Cell as a
Space). More generally this example demonstrates the need for the
architectural users to customise the application of abstract topological
concepts with the domain semantics which suits their purpose.
This relationship between application semantics and abstract con-
cepts works both ways. Sometimes more generally applicable concepts
emerge by abstracting ideas from other specialist domains. For example,
the concept of a topological Cell may have originated as an abstracted
analogy of a biological cell, with similarities in terms of the homogeneity
and continuity of the contained 3D region and the role of the cell wall as
a closed container with selective permeability (Fig. 3).
326 AAG2018 327
Figure 3: The cell wall as a separator and as a connector, in biology and
in architecture (with acknowledgement to Wix, 1994).
3.5 Apertures and Contexts
A Face may have internal boundaries which may represent an aperture.
The location of an aperture within the host Face is defined by a Context.
Apertures can represent windows or doors. (Fig. 1, section 6) (The
representation of Apertures is discussed in more detail in section 4.4
‘‘Regional Topology’’)
3.6 Material representations
While all Cells have a common topology (a closed 3D region bounded
by Faces) different configurations of Cells may be generated from
different types of foundational topologies using different geometric
operations (Fig. 1, section 7), for example:
Point location connector components: may be based on Vertices.
Linear components such as columns or beams: may be based on Edges
(or Wires) using operations where a cross section Wire is extruded
along a path.
Area based components such as slabs, floors, walls may be based on
Faces: using offset operations with a specified thickness and direction.
326 AAG2018
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Volume based components such as a containment vessel may be based
on Cells using thin-shell operations and a specified wall thickness.
Conformal cellular structures, used in 3D printing, may be based on
CellComplexes.
Complex sub-assemblies of material components can be modelled as
Clusters.
3.7 Integration of idealized and material models
The integrated BIM model uses the idealized non-manifold spatial model
to define the location and connectivity of the material model. (Fig.1,
section 8). The defining centre lines or centre faces of walls and floors
of the material model may be offset from the edges and faces of the
idealized model. We can now appreciate the difficulty of attempting to
reverse the direction of the arrow to recover an idealized spatial model
from a material model.
In traditional BIM, the 3D material representation is the defining
model while the drawings are the derived models. With architectural
topology the idealized non-manifold topological representation becomes
the defining model and the 3D material representation is now a derived
model.
The idealised non-manifold spatial model acts as a useful conceptual
and practical intermediary between the user and the material model (Fig 4).
In this workflow the user is not manually placing specific material com-
ponents on specific Faces or Edges of the idealised model. If such a
workflow had been adopted, then any change in the idealised topology
might have removed these specific Face and Edge and orphaned (or
potentially deleted) the material components. Also such a change to the
idealised topology might have created new Faces and Edges which the
user would be required to populate with material components.
Instead, the populating of the idealised topology is rule-based using
the Visual Data Flow programming tools available in the host applica-
tion. The rule-based generation of the material model allows alternative
building configurations to be easily explored via the manipulation of the
idealised spatial model as previously suggested (Aish and Pratap 2013).
326 AAG2018
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Figure 3: The cell wall as a separator and as a connector, in biology and
in architecture (with acknowledgement to Wix, 1994).
3.5 Apertures and Contexts
A Face may have internal boundaries which may represent an aperture.
The location of an aperture within the host Face is defined by a Context.
Apertures can represent windows or doors. (Fig. 1, section 6) (The
representation of Apertures is discussed in more detail in section 4.4
‘‘Regional Topology’’)
3.6 Material representations
While all Cells have a common topology (a closed 3D region bounded
by Faces) different configurations of Cells may be generated from
different types of foundational topologies using different geometric
operations (Fig. 1, section 7), for example:
Point location connector components: may be based on Vertices.
Linear components such as columns or beams: may be based on Edges
(or Wires) using operations where a cross section Wire is extruded
along a path.
Area based components such as slabs, floors, walls may be based on
Faces: using offset operations with a specified thickness and direction.
326 AAG2018 327
Volume based components such as a containment vessel may be based
on Cells using thin-shell operations and a specified wall thickness.
Conformal cellular structures, used in 3D printing, may be based on
CellComplexes.
Complex sub-assemblies of material components can be modelled as
Clusters.
3.7 Integration of idealized and material models
The integrated BIM model uses the idealized non-manifold spatial model
to define the location and connectivity of the material model. (Fig.1,
section 8). The defining centre lines or centre faces of walls and floors
of the material model may be offset from the edges and faces of the
idealized model. We can now appreciate the difficulty of attempting to
reverse the direction of the arrow to recover an idealized spatial model
from a material model.
In traditional BIM, the 3D material representation is the defining
model while the drawings are the derived models. With architectural
topology the idealized non-manifold topological representation becomes
the defining model and the 3D material representation is now a derived
model.
The idealised non-manifold spatial model acts as a useful conceptual
and practical intermediary between the user and the material model (Fig 4).
In this workflow the user is not manually placing specific material com-
ponents on specific Faces or Edges of the idealised model. If such a
workflow had been adopted, then any change in the idealised topology
might have removed these specific Face and Edge and orphaned (or
potentially deleted) the material components. Also such a change to the
idealised topology might have created new Faces and Edges which the
user would be required to populate with material components.
Instead, the populating of the idealised topology is rule-based using
the Visual Data Flow programming tools available in the host applica-
tion. The rule-based generation of the material model allows alternative
building configurations to be easily explored via the manipulation of the
idealised spatial model as previously suggested (Aish and Pratap 2013).
328 AAG2018 329
Figure 4: An idealised spatial model built with non-manifold topology
can be used as a convenient intermediate representation to manipulate
a material model, involving:
a. creating a cell from a lofted solid.
b. dividing the cell using several faces, resulting is a
CellComplex.
c. the individual cells can be derived from the CellComplex.
d. introduce a cylinder outside the CellComplex.
e. move the cylinder into and imposed on the CellComplex:
new cells are created.
f. move the cylinder further into the centre: the cells update
accordingly.
g. h. i. corresponding material models are derived from the
NMT models in d, e, f.
The workflow includes detecting vertical and non-vertical edges,
sweeping a circle along vertical edges to create cylindrical columns
328 AAG2018
329
and a rectangle along non-vertical edges to create rectangular beams.
The depth of the beams are parametrically computed according to their
length. For visualisation purposes, the surfaces are thickened slightly
into solids and made translucent.
4. Using non-manifold topology to
represent relevant architectural concepts
Non-manifold topology embraces fi ve concepts with architectural
relevance:
4.1 Non-manifold Cell
A non-manifold Cell may contain internal Faces which are not part of
the external Cell boundary. Both sides of such internal Faces point to
the same enclosed region. The concept of a non-manifold Cell is
required to model internal ‘‘semi-partitions’’ of architectural spaces which
do not fully divide the cell. (Fig. 5)
Figure 5: Different confi gurations of non-manifold Cells.
4.2 Cellular Topology
Cellular Topology is implemented as a CellComplex, where some Faces
of the Cell are also the external boundary, while other Faces form the
boundary between adjacent Cells. Cellular Topology can be used to
model a building which is partitioned into different architectural spaces
(Fig. 6).
328 AAG2018
329
Figure 4: An idealised spatial model built with non-manifold topology
can be used as a convenient intermediate representation to manipulate
a material model, involving:
a. creating a cell from a lofted solid.
b. dividing the cell using several faces, resulting is a
CellComplex.
c. the individual cells can be derived from the CellComplex.
d. introduce a cylinder outside the CellComplex.
e. move the cylinder into and imposed on the CellComplex:
new cells are created.
f. move the cylinder further into the centre: the cells update
accordingly.
g. h. i. corresponding material models are derived from the
NMT models in d, e, f.
The workflow includes detecting vertical and non-vertical edges,
sweeping a circle along vertical edges to create cylindrical columns
328 AAG2018 329
and a rectangle along non-vertical edges to create rectangular beams.
The depth of the beams are parametrically computed according to their
length. For visualisation purposes, the surfaces are thickened slightly
into solids and made translucent.
4. Using non-manifold topology to
represent relevant architectural concepts
Non-manifold topology embraces fi ve concepts with architectural
relevance:
4.1 Non-manifold Cell
A non-manifold Cell may contain internal Faces which are not part of
the external Cell boundary. Both sides of such internal Faces point to
the same enclosed region. The concept of a non-manifold Cell is
required to model internal ‘‘semi-partitions’’ of architectural spaces which
do not fully divide the cell. (Fig. 5)
Figure 5: Different confi gurations of non-manifold Cells.
4.2 Cellular Topology
Cellular Topology is implemented as a CellComplex, where some Faces
of the Cell are also the external boundary, while other Faces form the
boundary between adjacent Cells. Cellular Topology can be used to
model a building which is partitioned into different architectural spaces
(Fig. 6).
330 AAG2018 331
Figure 6: Cellular Topology modelled as a CellComplex.
4.3 Mixed dimensionality Topological models
In non-manifold topology it is possible to construct a single topological
model composed of entities of different types and dimensionality. The
concept of a mixed dimensionality topology is implemented as a Cluster
and can be used to create an idealized model of the structure of a
building (Fig. 7).
Figure 7: A mixed dimensional model with Edges representing the
column centre lines and Faces representing floor slabs, blade columns
and shear walls. Cells are used to represent the building cores.
330 AAG2018
331
4.4 Regional Topology
In conventional topological modelling, higher dimensional topological
entities are constructed from lower dimensional ones. Higher
dimensional topological entities are connected because they share
common lower dimensional entities. For example, adjacent Cells within a
CellComplex may share a common Face.
However, in the domain of architecture there are other forms of con-
nectedness which cannot be directly expressed in this way. For example,
a column can be idealised as an Edge. A fl oor or ceiling can be idealised
as a Face. We intuitively understand that a column (Edge) may connect
a fl oor (Face) to a ceiling (Face), but how can this be described if the
column is in the middle of the fl oor and when there is no topology within
the defi nition of the fl oor and ceiling Faces which is shared with the
Vertices defi ning the column’s Edge? (Fig. 8).
Figure 8: Defi ning the ‘‘Context’’ to describe the connectedness of two
topologies where one entity exists within the region of the other entity and
when the two entities do not share any common constituent topology.
Similar issues arise when we consider an internal boundary within a Face.
For example the Face may represent a wall and the internal boundary may
defi ne an Aperture such as a window or a door. We intuitively under-
stand that the Aperture (as a single 2D region) is contained within the
2D region of the Face, with no shared topology.
To address these issues, Topologic introduces the concept of a
context to represent the connectivity between two topological entities
which do not otherwise share common topology. In this example, the
Aperture is the subject (representing a window) and is defi ned within
the region (or context) of the host Face (representing the wall). The
330 AAG2018
331
Figure 6: Cellular Topology modelled as a CellComplex.
4.3 Mixed dimensionality Topological models
In non-manifold topology it is possible to construct a single topological
model composed of entities of different types and dimensionality. The
concept of a mixed dimensionality topology is implemented as a Cluster
and can be used to create an idealized model of the structure of a
building (Fig. 7).
Figure 7: A mixed dimensional model with Edges representing the
column centre lines and Faces representing floor slabs, blade columns
and shear walls. Cells are used to represent the building cores.
330 AAG2018 331
4.4 Regional Topology
In conventional topological modelling, higher dimensional topological
entities are constructed from lower dimensional ones. Higher
dimensional topological entities are connected because they share
common lower dimensional entities. For example, adjacent Cells within a
CellComplex may share a common Face.
However, in the domain of architecture there are other forms of con-
nectedness which cannot be directly expressed in this way. For example,
a column can be idealised as an Edge. A fl oor or ceiling can be idealised
as a Face. We intuitively understand that a column (Edge) may connect
a fl oor (Face) to a ceiling (Face), but how can this be described if the
column is in the middle of the fl oor and when there is no topology within
the defi nition of the fl oor and ceiling Faces which is shared with the
Vertices defi ning the column’s Edge? (Fig. 8).
Figure 8: Defi ning the ‘‘Context’’ to describe the connectedness of two
topologies where one entity exists within the region of the other entity and
when the two entities do not share any common constituent topology.
Similar issues arise when we consider an internal boundary within a Face.
For example the Face may represent a wall and the internal boundary may
defi ne an Aperture such as a window or a door. We intuitively under-
stand that the Aperture (as a single 2D region) is contained within the
2D region of the Face, with no shared topology.
To address these issues, Topologic introduces the concept of a
context to represent the connectivity between two topological entities
which do not otherwise share common topology. In this example, the
Aperture is the subject (representing a window) and is defi ned within
the region (or context) of the host Face (representing the wall). The
332 AAG2018 333
user may optionally specify that the context defines a locational ‘‘link’’
between the subject and the host. Here the vertices of the subject are
defined in the parameter space of the host and are now dependent on
any changes which are applied to the host. (Fig. 9).
The context with parametric coordinates is only used when there is
no shared topology connecting the two entities (Fig. 10).
4.5 Variable topology
In architecture, spatial divisions may be ‘‘hardcoded’’ as distinct rooms
separated by physical walls. While buildings appear to be solid, one of the
central tenets of architecture is that the use of space within a building is
or should be flexible. We think of multi-use or reconfigurable spaces.
There appears to be no established architectural methodology which
prescribes how the topology of a building emerges. In fact, the archi-
tectural design process is quite imprecise. It may start with an occupancy
model and a description of the anticipated activities of the occupants.
Activities may vary in time and space. Activities may overlap. Alexander
(1965) noted that neither activities nor space could be adequately
described by a simple hierarchical decomposition. The process by which
activities get translated into specific spatial enclosures and the choice
as to which boundaries of these enclosures are actually materialised as
walls or are left as purely virtual, is often a matter of contention (Fig. 11).
Virtual partitions may also be used in the topological representation of
Figure 9: The option to ‘‘link’’ the subject topology to the host topology.
332 AAG2018
333
Figure 10: Given the intersection of an Edge (red) and a Face (grey) in
different configurations, then the concept of the context (with parametric
coordinates) is used when the resulting Vertex occurs within a region of
the intersecting topologies.
other building sub-systems. For example, an atrium may be considered
as a single continuous space, or it may be considered to be subdivided
into different air conditioning zones without physical partitions. Depending
on the simulation parameters, virtual Faces could be inserted and can be
represented in the analytical model either as adiabatic or diathermic.
More generally, architecture is often characterized by degrees of
spatial partitioning and connectedness. How can these different and
sometimes ambiguous architectural concepts of space be represented with
topology? Topology provides a formal way to represent connectedness, but
332 AAG2018
333
user may optionally specify that the context defines a locational ‘‘link’’
between the subject and the host. Here the vertices of the subject are
defined in the parameter space of the host and are now dependent on
any changes which are applied to the host. (Fig. 9).
The context with parametric coordinates is only used when there is
no shared topology connecting the two entities (Fig. 10).
4.5 Variable topology
In architecture, spatial divisions may be ‘‘hardcoded’’ as distinct rooms
separated by physical walls. While buildings appear to be solid, one of the
central tenets of architecture is that the use of space within a building is
or should be flexible. We think of multi-use or reconfigurable spaces.
There appears to be no established architectural methodology which
prescribes how the topology of a building emerges. In fact, the archi-
tectural design process is quite imprecise. It may start with an occupancy
model and a description of the anticipated activities of the occupants.
Activities may vary in time and space. Activities may overlap. Alexander
(1965) noted that neither activities nor space could be adequately
described by a simple hierarchical decomposition. The process by which
activities get translated into specific spatial enclosures and the choice
as to which boundaries of these enclosures are actually materialised as
walls or are left as purely virtual, is often a matter of contention (Fig. 11).
Virtual partitions may also be used in the topological representation of
Figure 9: The option to ‘‘link’’ the subject topology to the host topology.
332 AAG2018 333
Figure 10: Given the intersection of an Edge (red) and a Face (grey) in
different configurations, then the concept of the context (with parametric
coordinates) is used when the resulting Vertex occurs within a region of
the intersecting topologies.
other building sub-systems. For example, an atrium may be considered
as a single continuous space, or it may be considered to be subdivided
into different air conditioning zones without physical partitions. Depending
on the simulation parameters, virtual Faces could be inserted and can be
represented in the analytical model either as adiabatic or diathermic.
More generally, architecture is often characterized by degrees of
spatial partitioning and connectedness. How can these different and
sometimes ambiguous architectural concepts of space be represented with
topology? Topology provides a formal way to represent connectedness, but
334 AAG2018 335
Figure 11: The choice of spatial confi guration often starts with identi-
fying underlying activities of the occupants (1). These activities and their
spatial requirements may overlap. It may be inappropriate to describe
these as a simple hierarchical decomposition (with acknowledgement
to Alexander, 1965). The process by which activities are translated into
defi ned conceptual spaces (2) and are further translated into recognisable
enclosures (3) or into specifi c rooms (4) often refl ects architectural
intuition rather than a defi ned methodology.
334 AAG2018
335
when applied to architecture, it requires the user to choose what is being
connected.
If two adjacent regions have exactly the same contents with the
same behaviour and are so intimately connected that there is no effec-
tive barrier between them, then perhaps they should be considered as a
single region. So, the ultimate form of connectedness is the unification
of two adjacent regions into a single region or Cell. Therefore, a Cell
is more than just a continuous 3D region. It also implies that what is
contained represents a level of homogeneity, which has appropriate
meaning within the application domain.
If Cells represent spaces and Faces represent walls (or partitions)
then operations which add or remove the Faces of Cells within a Cell-
Complex can radically change the topology. The result of a modelling
operation to an existing topological construct may change the ‘‘type’’ of
that construct. The advantage of Topology is that it tells the architectural
users exactly what has been modelled in terms of partitioning and
connectedness and the type of the result (Fig. 12).
The general conclusion is that, where possible, the user should
define a single canonical non-manifold topology model describing the
maximal partitioning of space. Different subdivisions may be combined
to represent the spaces required for different activities. Different dual
graphs can be constructed as required by different analysis and simula-
tion applications (Fig. 13).
Figure 12: Editing operations to add or remove topological components
can have a radical affect, including changing the type of topological
construct.
334 AAG2018
335
Figure 11: The choice of spatial confi guration often starts with identi-
fying underlying activities of the occupants (1). These activities and their
spatial requirements may overlap. It may be inappropriate to describe
these as a simple hierarchical decomposition (with acknowledgement
to Alexander, 1965). The process by which activities are translated into
defi ned conceptual spaces (2) and are further translated into recognisable
enclosures (3) or into specifi c rooms (4) often refl ects architectural
intuition rather than a defi ned methodology.
334 AAG2018 335
when applied to architecture, it requires the user to choose what is being
connected.
If two adjacent regions have exactly the same contents with the
same behaviour and are so intimately connected that there is no effec-
tive barrier between them, then perhaps they should be considered as a
single region. So, the ultimate form of connectedness is the unification
of two adjacent regions into a single region or Cell. Therefore, a Cell
is more than just a continuous 3D region. It also implies that what is
contained represents a level of homogeneity, which has appropriate
meaning within the application domain.
If Cells represent spaces and Faces represent walls (or partitions)
then operations which add or remove the Faces of Cells within a Cell-
Complex can radically change the topology. The result of a modelling
operation to an existing topological construct may change the ‘‘type’’ of
that construct. The advantage of Topology is that it tells the architectural
users exactly what has been modelled in terms of partitioning and
connectedness and the type of the result (Fig. 12).
The general conclusion is that, where possible, the user should
define a single canonical non-manifold topology model describing the
maximal partitioning of space. Different subdivisions may be combined
to represent the spaces required for different activities. Different dual
graphs can be constructed as required by different analysis and simula-
tion applications (Fig. 13).
Figure 12: Editing operations to add or remove topological components
can have a radical affect, including changing the type of topological
construct.
336 AAG2018 337
5. Applying topology in analysis,
simulation and fabrication
Vitruvius distinguished between the practical aspects of the architecture
(fabrica) and its rational and theoretical foundation (ratiocination) (Pont
2005). Establishing topological relationships was found to be an essential
component of the setting out of the conceptual principles of a design
project (Jabi et al. 2017). Non-manifold topology was also found to be a
consistent representation of entities that can be thought of as loci, axes,
spaces, voids, or containers of other material.
This concept was previously explored by the authors in the context of
energy analysis, façade design, and additive manufacturing of conformal
cellular structures (Jabi 2016; Fagerström, Verboon, and Aish 2014; Jabi
et al. 2017).
5.1 Energy analysis
A proof of concept implementation of non-manifold topology for energy
analysis allowed the user to create simple regular manifold polyhedral
geometries and then segment them with planes and other geometries
to create a non-manifold CellComplex (Chatzivasileiadi, Lannon, et al.
2018; Wardhana et al. 2018). The tool can create complex geometry that
produces outputs that are highly compatible with the input requirements
for energy analysis software. Cells within the CellComplex are conver-
ted to spaces with surfaces, and bespoke glazing sub-surfaces, and set
to their own thermal zones.
5.2 Digital fabrication
A proof of concept implementation of non-manifold topology for digital
fabrication allowed a CellComplex to be conformed to a NURBS-based
design envelope (Jabi et al. 2017).The resulting model used topological and
geometric queries amongst adjacent Cells to create rules for depositing
material. These query results were used to identify boundary conditions
and to deposit material only where needed. This improved the material
efficiency and resulted in a higher mechanical and structural profile for
the 3D printed model.
336 AAG2018
337
Figure 13: Dual graphs can be constructed which describe alternative
connectivity of the Cells representing architectural spaces and used as
different analytical models.
336 AAG2018
337
5. Applying topology in analysis,
simulation and fabrication
Vitruvius distinguished between the practical aspects of the architecture
(fabrica) and its rational and theoretical foundation (ratiocination) (Pont
2005). Establishing topological relationships was found to be an essential
component of the setting out of the conceptual principles of a design
project (Jabi et al. 2017). Non-manifold topology was also found to be a
consistent representation of entities that can be thought of as loci, axes,
spaces, voids, or containers of other material.
This concept was previously explored by the authors in the context of
energy analysis, façade design, and additive manufacturing of conformal
cellular structures (Jabi 2016; Fagerström, Verboon, and Aish 2014; Jabi
et al. 2017).
5.1 Energy analysis
A proof of concept implementation of non-manifold topology for energy
analysis allowed the user to create simple regular manifold polyhedral
geometries and then segment them with planes and other geometries
to create a non-manifold CellComplex (Chatzivasileiadi, Lannon, et al.
2018; Wardhana et al. 2018). The tool can create complex geometry that
produces outputs that are highly compatible with the input requirements
for energy analysis software. Cells within the CellComplex are conver-
ted to spaces with surfaces, and bespoke glazing sub-surfaces, and set
to their own thermal zones.
5.2 Digital fabrication
A proof of concept implementation of non-manifold topology for digital
fabrication allowed a CellComplex to be conformed to a NURBS-based
design envelope (Jabi et al. 2017).The resulting model used topological and
geometric queries amongst adjacent Cells to create rules for depositing
material. These query results were used to identify boundary conditions
and to deposit material only where needed. This improved the material
efficiency and resulted in a higher mechanical and structural profile for
the 3D printed model.
336 AAG2018 337
Figure 13: Dual graphs can be constructed which describe alternative
connectivity of the Cells representing architectural spaces and used as
different analytical models.
338 AAG2018 339
6. Conclusions
New design technologies often emerge in response to the limitations of
existing technologies and have the potential to benefit the architectural
design process. Understandably, the founding concepts and terminology
may be unfamiliar to architectural practitioners which may inhibit
adoption of these technologies.
The challenge in developing Topologic has been to maintain the
theoretically consistent use of topological concepts and terminology,
yet relate these to the more ambiguous concepts of space and
‘‘connectedness’’ found in architecture. The application of topology as
a direct link between architectural conceptual modelling and relevant
analysis applications is becoming established. A more challenging
task is to explore how topology can contribute to the way in which
architecture as the ‘‘enclosure of space’’ can be conceptualised.
Acknowledgments
The Topologic project is funded by a Leverhulme Trust Research Project
Grant (Grant No. RPG-2016-016).
338 AAG2018
339
References
Ale xA nde r, ch r is To ph e r. 1965.
“A City is Not a Tree.” Architectural Forum, 122 (1): 58–62.
Aish, rob erT. 1 997.
“MicroStation/J.” In Next Generation CAD/ CAM/CAE Systems, NASA Con-
ference Publication 3357, edited by Ahmed K. Noor and John B. Malone, 167–80. Hampton, Virginia:
National Aeronautics and Space Administration. Accessed June 25 2018 https://www.researchgate.
net/publication/320507941_MicroStationJ
Aish, rob erT, An d ApA rA Ji T pr ATAp. 2013.
“Spatial Information Modeling of Buildings Using
Non-Manifold Topology with ASM and DesignScript.” In Advances in Architectural Geometry 2012,
edited by Lars Hesselgren, Shrikant Sharma, Johannes Wallner, Niccolo Baldassini, Philippe Bompas,
and Jacques Raynaud, 25–36. Vienna: Springer Vienna. doi:10.1007/978-3-7091-1251-9.
b r K, bo- ch r isTe r . 1992.
“A Conceptual Model of Spaces, Space Boundaries and Enclosing
Structures.” Automation in Construction 1 (3): 193-214. doi:10.1016/0926-5805(92)90013-A.
bronson, Jon AThA n, Jo sh uA A. levi ne , An d ros s Wh iTAKe r. 2014.
“Lattice Cleaving: A
Multimaterial Tetrahedral Meshing Algorithm with Guarantees.” IEEE Transactions on Visualization and
Computer Graphics 20 (2): 223–37. doi:10.1109/TVCG.2013.115.
chA nG , T.W., An d ro be r T Wo od b ur y. 1997.
“Efficient Design Spaces of Non-Manifold Solids.” In
Second Conference on Computer-Aided Architectural Design Research in Asia, 335–44. Taiwan:
CAADRIA.
chATz i vAs il e iA di , AiK ATe r in i, sim on lAn n on , WAs si m JAb i, nicholAs mAr io WArd hA nA , An d
rob e rT Aish. 2018.
“Addressing Pathways to Energy Modelling through Non- Manifold Topology.
In SIMAUD 2018: Symposium for Architecture and Urban Design, edited by Daniel Macumber,
Forrest Meggers, and Siobhan Rockcastle. Delft, the Netherlands: Society for Modeling & Simulation
International (SCS).
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lAn no n . 2018.
“A Review of 3D Solid Modeling Software Libraries for Non-Manifold Modeling.” In
CAD’18 - the 15th Annual International CAD Conference. Paris, France: CAD Solutions, LLC.
cur Ti s, Wi l li Am J. r. 1996.
Modern Architecture Since 1900. London: Phaidon Press.
338 AAG2018
339
6. Conclusions
New design technologies often emerge in response to the limitations of
existing technologies and have the potential to benefit the architectural
design process. Understandably, the founding concepts and terminology
may be unfamiliar to architectural practitioners which may inhibit
adoption of these technologies.
The challenge in developing Topologic has been to maintain the
theoretically consistent use of topological concepts and terminology,
yet relate these to the more ambiguous concepts of space and
‘‘connectedness’’ found in architecture. The application of topology as
a direct link between architectural conceptual modelling and relevant
analysis applications is becoming established. A more challenging
task is to explore how topology can contribute to the way in which
architecture as the ‘‘enclosure of space’’ can be conceptualised.
Acknowledgments
The Topologic project is funded by a Leverhulme Trust Research Project
Grant (Grant No. RPG-2016-016).
338 AAG2018 339
References
Ale xA nde r, ch r is To ph e r. 1965. “A City is Not a Tree.” Architectural Forum, 122 (1): 58–62.
Aish, rob erT. 1 997. “MicroStation/J.” In Next Generation CAD/ CAM/CAE Systems, NASA Con-
ference Publication 3357, edited by Ahmed K. Noor and John B. Malone, 167–80. Hampton, Virginia:
National Aeronautics and Space Administration. Accessed June 25 2018 https://www.researchgate.
net/publication/320507941_MicroStationJ
Aish, rob erT, An d ApA rA Ji T pr ATAp. 2013. “Spatial Information Modeling of Buildings Using
Non-Manifold Topology with ASM and DesignScript.” In Advances in Architectural Geometry 2012,
edited by Lars Hesselgren, Shrikant Sharma, Johannes Wallner, Niccolo Baldassini, Philippe Bompas,
and Jacques Raynaud, 25–36. Vienna: Springer Vienna. doi:10.1007/978-3-7091-1251-9.
b r K, bo- ch r isTe r . 1992. “A Conceptual Model of Spaces, Space Boundaries and Enclosing
Structures.” Automation in Construction 1 (3): 193-214. doi:10.1016/0926-5805(92)90013-A.
bronson, Jon AThA n, Jo sh uA A. levi ne , An d ros s Wh iTAKe r. 2014. “Lattice Cleaving: A
Multimaterial Tetrahedral Meshing Algorithm with Guarantees.” IEEE Transactions on Visualization and
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“A Two-Level Topological Decomposition for Non-Manifold
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“Linking Design and Simulation Using Non-Manifold Topology.” Architectural
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“Topologic: A Toolkit for Spatial and Topological Modelling.” In Computing for a
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“Enhancing
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destud.2017.04.003.
340 AAG2018 341
mAi le , Tob i As, JA m es T. o’do nn e ll , vlA di m ir bAzJA nA c, A nd cod y ro se . 2013. “BIM - Geometry
Modelling Guidelines for Building Energy Performance Simulation.” In BS2013: 13th Conference of
International Building Performance Simulation Association, Chambéry, France, 3242–49. Interna-
tional Building Performance Simulation Association.
mAs ud A, h. 1993. “Topological Operators and Boolean Operations for Complex-Based Nonmanifold
Geometric Models.” Computer-Aided Design 25 (2): 119–29. doi:10.1016/0010-4485(93)90097-8.
nGu ye n, Tru nc du c. 2011. “Simplifying The Non-Manifold Topology Of Multi-Partitioning Surface
Networks.” MA Thesis, Washington University. http://openscholarship.wustl.edu/etd/510/.
pon T, GrAhAm. 2005. “The Education of the Classical Architect from Plato to Vitruvius.” Nexus
Network Journal 7 (1): 76–85. doi:10.1007/s00004-005-0008-0.
WAr dh An A, nicholAs mAr i o, Ai KAT er i ni chAT zi vAs i le iA di , WAs sim JAb i, ro b er T Aish, A nd simo n
lAn no n . 2018. “Bespoke Geometric Glazing Design for Building Energy Performance Analysis.” In
MonGeometrija 2018, edited by Vesna Stojakovi . Novi Sad, Serbia.
Wei ler , Kev in J. 1986. “Topological Structures for Geometric Modeling.” PhD Thesis, Rensselaer
Polytechnic Institute.
Wix , Jef f re y. 1994 “Interoperability: a future context”. Paper presented at the CAMP Autodesk
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... 11,12 Similarly, but more universal, Wassim Jabi and Robert Aish are developing Topologic, which is a kit for non-manifold topologies (NTMs). 13 This toolkit is open-source and allows the user to build topologic relations that combines vertices, lines, wires, faces, shells and cells. ...
... This methodology is likely to be applicable for NTMs 13 and can be used to filter any kind of joint. A joint can be point based, edge based or even face based. ...
Article
Detailing joints are important when designing structures. In this design process, a structure is divided into different joint types. Digital fabrication and algorithmic aided design have changed the conceptions and requirements of joint detailing. However, parametric tools that can efficiently identify joint types based on the solution space are not available. This article presents a methodology that efficiently generates topological relations and enables the user to assign joint instances to joint types. A series of property-based search criteria components is applied to define the solution space of a joint type. Valid joints are coherently filtered, deconstructed and outputted for detailing. The article explains both the methodology and programming-related aspects of the joint type filtering. The article concludes that the developed methodology offers the desired flexibility and may be suitable for other materials and applications.
... Topologic® is a software modelling library enabling hierarchical and topological spatial representations through non-manifold topology [18]. Existing geometry is modelled as Breps (directly modelled or extruded from existing drawings) and then fed as input to the module translating Rhino® 3D Brep object to topologic cells, organizing them and forming topologic complexes. ...
... and Equation 2.4 for non-orientable shapes as: slabs, walls, beams and columns necessitates topological modelling tools that handle non-manifold shapes [Aish et al., 2018]. Nevertheless, manifolds can represent most shell-like structures. ...
Thesis
Full-text available
Shell-like structures allow to elegantly and efficiently span large areas. Quad meshes are natural patterns to represent these surface objects, which can also serve for mapping other patterns. Patterns for these shells, vaults, grid- shells or nets can represent the materialised structure, the force equilibrium or the surface map. The topology of these patterns constrains their qualitative and quantitative modelling freedom for geometrical exploration. Unless topological exploration is enabled. Parametric design supporting exploration and optimisation of the geometry of structures is spreading across the community of designers and builders. Unfortunately, topological design is lagging, despite some optimisation-oriented strategies for specific design objectives. Strategies, algorithms and tools for topological exploration are necessary to tackle the multiple objectives in architecture, engineering and construction for the design of structures at the architectural scale. The task of structural design is rich and complex, calling for interactive algorithms oriented towards co-design between the human and the machine. Such an approach is complementary and empowered with existing methods for geometrical exploration and topology optimisation. The present work introduces topology finding for efficient search across the topological design space. This thesis builds on three strategies for topology finding of singularities in quad-mesh patterns, presented from the most high-level to the most low-level approach. Geometry-coded exploration relies on a skeleton-based quad decomposition of a surface including point and curve features. These geometrical parameters can stem from design heuristics to integrate into the design, related to the statics system or the curvature of the shell, for instance. Graph-coded exploration relies on the topological strips in quad meshes. A grammar of rules allows exploration of this strip structure to search the design space. A similarity-informed search algorithm finds design with different degrees of topological similarity. Designs optimised for single objectives can inform this generation process to obtain designs offering different trade-offs between multiple objectives. A two-colour search algorithm finds designs that fulfil a two-colouring requirement of two-colouring. This topological property allows a partition of the pattern elements that many structural systems necessitate. String-coded exploration relies on the translation of the grammar rules into alphabetical operations, shifting encoding from a phenotype mesh to a genotype string. Modifications, or mutations, of the string transform the genotype and change the phenotype of the design. String or vector encoding opens for the use of search and optimisation algorithms, like linear programming, genetic algorithms or machine learning. Keywords: structural design, topological exploration, patterns, quad meshes, singularities, topology finding, shells, gridshells.
... 11,12 Similarly, but more universal, Wassim Jabi and Robert Aish are developing Topologic, which is a kit for non-manifold topologies (NTM). 13 If a structure is logically clear, a small sorting algorithm may be used to filter the joint types. However, the algorithm is likely to be dependent on a fixed topology. ...
Preprint
Detailing joints are important when designing structures. In this process, a structure is divided into different joint types. Digital fabrication and algorithmic aided design (AAD) have changed the conceptions and requirements of joint detailing. However, parametric tools that can efficiently identify joint types based on the solution space are not available. This paper presents a methodology that efficiently generates topological relations and enables the user to assign joint instances to joint types. A series of property-based search criteria components is applied to define the solution space of a joint type. Valid joints are coherently filtered, deconstructed and outputted for detailing. The paper explains both the methodology and programming-related aspects of the joint type filtering. The article concludes that the developed methodology is satisfactory, offers the desired flexibility and may be suitable for other materials and applications.
... Alternatively, environmental plugins through visual programming language (VPL); Grasshopper (' Grasshopper3d' n.d.) and dynamo ( 'Dynamo BIM' n.d.), are rising due to the reported technical deficiency in the standard schema that caused problems in integration of simulation from early design stage, provoked by the limitations of the bidirectional modelling and simulation (Negendahl 2015). Other plugins, such as ladybug tools (Sadeghipour Roudsari and Mackey n.d.) and topologic are in continuous development to support architects need for fast, iterative and interactive feedback (Aish et al. 2018;Mostapha Sadeghipour Roudsari, Pak, and Smith 2013). The development in the VPL approach claim to achieve rapid and flexible analysis that is more sufficient for architects' use than the current gbxml and IFC schema packages (Negendahl 2015). ...
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The evolution of Building Information Modelling (BIM) is transforming practice in the Architecture, Engineering and Construction (AEC) industry. BIM provided revolutionary ways of generating, visualizing, exchanging, predicting and monitoring information. Over the last decade, delivering sustainable projects has become a high priority along with the recognition of the role the BIM plays to improve efficiency. However, BIM-enabled sustainability practices are still relatively immature and inconsistent. Previous research has identified challenges in the delivery of green-rated buildings, that include: dealing with documentation, evidencing requirements, monitoring progress, and decision making. Limited studies focused on linking workflow obstacles of green projects to potential improvements using current BIM capabilities. Through interrogating existing research via a systematic literature review, this paper takes the original approach of constructing an ‘analysis map’ to ‘bridge the gap’ and highlight current limitations and successes between BIM and sustainability practices. The findings are formulated through two parallel investigation tracks: the first is design task/BIM capability analysis, and the second is green project delivery problem/BIM enabled sustainability application. This research highlights future potential investigation areas, which are categorized into six clusters: representation; performance simulation; transaction and exchange; documentation; automation and standardization and guidance.
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Adaptation of existing building stock is an urgent issue due to aging infrastructure, growth in urban areas and the importance of demolition mitigation for cost and carbon savings. To accommodate the scale of implementation required, there is a need to increase the efficiency of current design and production processes. Computational methodologies have proven to increase design efficiency by generating and parsing through myriad design options based on multivariate (e.g., spatial, environmental, and economic) factors. Modular Construction (MC) is another approach used to increase efficiency of both design and production. This paper combines these approaches in a novel methodology for generating modular design options for extensions of existing buildings (an efficacious form of building adaptation). The methodology focuses on key architectural design metrics such as energy use, daylighting, life cycle impact, life cycle costing and structural complexity, whereby a set of Pareto-optimal exploratory design options are generated for evaluation and further design development. A functional demonstration is then carried out for the extension of Ken Soble Tower in Hamilton, Ontario. The contribution of this research is the efficient development and evaluation of design options for improving existing residential infrastructure in order to meet required energy improvements using modular extensions.
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.
Thesis
Full-text available
En concevant, l’architecte donne à l’espace non seulement une forme, mais aussi des aspects de topologie, d’accessibilité et de confort. Cette production est basée sur un ensemble d’exigences spatiales qualitatives (ESQL) décrites en phase de programmation architecturale. Les pratiques BIM actuelles reposent sur des formats standards qui transforment toute l’information sur le bâtiment en données essentiellement quantitatives, ne permettant pas de prendre en compte ces exigences. Dans ce travail de recherche, nous proposons une nouvelle approche de conception qui permet d’intégrer les ESQL à l’outil BIM (Revit) et de vérifier la conformité de la conception en fonction. Cette approche repose sur un nouveau modèle d’espace incluant et structurant les ESQL. Ce modèle est spécifié sur la base d’un travail d’identification des ESQL les plus fréquemment utilisées pour qualifier les espaces en phase de programmation architecturale. Notre approche est évaluée à travers une démarche de validation expérimentale.
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Effective building performance simulation can reduce the environmental impact of the built environment, improve indoor quality and productivity, and facilitate future innovation and technological progress in construction. It draws on many disciplines, including physics, mathematics, material science, biophysics, human behavioural, environmental and computational sciences. The discipline itself is continuously evolving and maturing, and improvements in model robustness and fidelity are constantly being made. This has sparked a new agenda focusing on the effectiveness of simulation in building life cycle processes. Building Performance Simulation for Design and Operation begins with an introduction to the concepts of performance indicators and targets, followed by a discussion on the role of building simulation in performance based building design and operation. This sets the ground for in-depth discussion of performance prediction for energy demand, indoor environmental quality (including thermal, visual, indoor air quality and moisture phenomena), HVAC and renewable system performance, urban level modelling, building operational optimization and automation. Produced in cooperation with the International Building Performance Simulation Association (IBPSA), this book provides a unique and comprehensive overview of building performance simulation for the complete building life-cycle from conception to demolition. It is primarily intended for advanced students in building services engineering, and in architectural, environmental or mechanical engineering; and will be useful for building and systems designers and operators.
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Much of the research into integrating performance analysis in the design process has focused on the use of Building Information Modeling (BIM) as input for analysis engines. The main disadvantage of this approach is that BIM models are resource intensive and thus are usually developed in the later stages of design. BIM models are also not necessarily compatible with energy analysis engines and thus a conversion and export process is needed. This can lead to data loss, calculation errors, and failures. Starting with the premise that energy analysis is more compatible with earlier design stages where simpler schematic models are the norm, this paper presents a software system that integrates non-manifold spatial topology, a parametric design environment and an energy analysis engine for a more seamless generate-test cycle in the early design stages. The paper includes a description of the system architecture, initial results, and an outline of future work.
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This paper describes the Energy Design Plugin, a new software plugin that aims to integrate simulation as a tool during the earliest phases of the design process. The plugin couples the EnergyPlus whole-building simulation engine to the Google SketchUp™ drawing program. Leveraging the powerful SketchUp application programming interface, we developed a plugin that extends the capabilities of SketchUp to allow EnergyPlus building models to be developed in 3-D while taking advantage of all of the native SketchUp capabilities, including intuitive tools, different rendering modes, and realistic shading. The model geometry can be saved to create an EnergyPlus input file. Existing input files can be opened, edited in the SketchUp environment, and saved again. Already well-established as a popular tool among architects and designers, SketchUp offers a familiar, easy-to-use interface that, when coupled with the plugin, could make building energy simulation more accessible for architects, designers, and students during the design process.
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This paper aims to build a theoretical foundation for parametric design thinking by exploring its cognitive roots, unfolding its basic tenets, expanding its definition through new concepts, and exemplifying its potential through a use-case scenario. The paper focuses on a specific type of topological parameter, called non-manifold topology as a novel approach to thinking about designing cellular spaces and voids. The approach is illustrated within the context of additive manufacturing of non-conformal cellular structures. The paper concludes that parametric design thinking that omits a definition of topological relationships risks brittleness and failure in later design stages while a consideration of topology can create enhanced and smarter solutions as it can modify parameters based on an accommodation of the design context.
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The aim of this paper is to propose a different method to design buildings by using and enhancing a representational technique called non-manifold topology (NMT). The methodology already exists but is ignored by current building information modelling (BIM) software in favour of a component-based approach. While the topological information embedded within NMT has many uses in the spatial representation of architecture, including building occupancy analysis and structural analysis, the focus in this paper is on the efficacy of NMT in linking design and building performance simulation (BPS). The proposed approach avoids the process of simplifying models produced by BIM software to conduct BPS. In particular, NMT allows for a clear segmentation of a building, unambiguous space boundaries, and perfectly matched surfaces and glazing sub-surfaces. The NMT approach was tested through a software prototype that integrates 3D modelling software and an energy simulation engine.
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We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.
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In bio-medical imaging, multi-partitioning surface networks (MPSNs) are very useful to model complex organs with multiple anatomical regions, such as a mouse brain. However, MPSNs are usually constructed from image data and might contain complex geometric and topological features. There has been much research on reducing the geometric complexity of a general surface (non-manifold or not) and the topological complexity of a closed, manifold surface. But there has been no attempt so far to reduce redundant topological features which are unique to non-manifold surfaces, such as curves and points where multiple sheets of surfaces join. In this thesis, we design interactive and automated means for removing redundant non-manifold topological features in MPSNs, which is a special class of non-manifold surfaces. The core of our approach is a mesh surgery operator that can effectively simplify the non-manifold topology while preserving the validity of the MPSN. The operator is implemented in an interactive user interface, allowing user-guided simplification of the input. We further develop an automatic algorithm that invokes the operator following a greedy heuristic. The algorithm is based on a novel, abstract representation of a non-manifold surface as a graph, which allows efficient discovery and scoring of possible surgery operations without the need for explicitly performing the surgeries on the mesh geometry.