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Topologic - A toolkit for spatial and topological modelling

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This paper describes non-manifold topology (NMT) as it relates to the field of architecture and presents Topologic, an open-source software modelling library enabling hierarchical and topological representations of architectural spaces, buildings and artefacts through NMT. Topologic is designed as a core library and additional plugins to visual data flow programming (VDFP) software. The software architecture and class hierarchy are explained and two domain-specific demonstrative tools (TopologicEnergy and TopologicStructure) are presented to illustrate how third-party software developers could use Topologic to build their own solutions. The paper concludes with a reflection on the benefits and limitations of NMT in the design and simulation workflows and outlines future work.
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Topologic
A toolkit for spatial and topological modelling
Wassim Jabi1, Robert Aish2, Simon Lannon3,
Aikaterini Chatzivasileiadi4, Nicholas Mario Wardhana5
1,3,4,5Cardiff University 2University College London
1,3,4,5{jabiw|lannon|chatzivasileiadia|wardhanan}@cardiff.ac.uk 2robert.
aish@ucl.ac.uk
This paper describes non-manifold topology (NMT) as it relates to the field of
architecture and presents Topologic, an open-source software modelling library
enabling hierarchical and topological representations of architectural spaces,
buildings and artefacts through NMT. Topologic is designed as a core library and
additional plugins to visual data flow programming (VDFP) software. The
software architecture and class hierarchy are explained and two domain-specific
demonstrative tools (TopologicEnergy and TopologicStructure) are presented to
illustrate how third-party software developers could use Topologic to build their
own solutions. The paper concludes with a reflection on the benefits and
limitations of NMT in the design and simulation workflows and outlines future
work.
Keywords: Non-manifold topology, Visual data flow programming, Building
performance simulation, Structural analysis, Computational design, Building
information modelling
WHY NON-MANIFOLD TOPOLOGY
While the field of topology is a vast and fascinating
area of study in mathematics with precise concepts
and terminology, in this paper we define terms and
consider issues of topology and geometry narrowly
and more simply as they apply to the field of architec-
ture and computational design. Thus, our definitions
of topological concepts will necessarily be less pre-
cise than those used by mathematicians, but more di-
rectly applicable to the field of architecture. The term
‘topology’ is derived directly from the Greek τόπος
(place), and λόγος (study), and therefore can be de-
fined as the study of place - or the study of space
[1]. This is precisely our aim - mainly to enhance the
representation of space in computational design sys-
tems through the use of topological concepts. Topol-
ogy defines the relationships between entities. For
example, two spaces can be thought as topologically
adjacent, if they share a common face. In contrast
to geometry, topology is concerned with the prop-
erties of space that remain constant when it is sub-
jected to deformations. Yet, geometry and topology
are fundamentally inter-linked. A geometric opera-
tion on an object fundamentally changes its topol-
Draft - eCAADe 36 |1
ogy. For example, removing one outer face of a pris-
matic closed cell transforms it into an open shell and
thus alters its topology.
The difference between manifold and non-
manifold geometry
Computer-aided design (CAD), building information
modelling (BIM), and parametric visual data flow pro-
gramming (VDFP) software usually rely on low-level
geometric engines (kernels) and software develop-
ment kits (SDK). These geometric kernels are usu-
ally classified as manifold or non-manifold (Chatzi-
vasileiadi, Wardhana, et al. 2018). Simply put,
manifold kernels represent three-dimensional enti-
ties with a series of connected boundary elements
that separate the outside world from its solid inte-
rior. Manifold entities (also called 2-mainfold) with
a boundary, such as a circle or a torus, can be un-
folded into a continuous flat plane. In contrast, non-
manifold Topology (NMT) entities (also called 3 or
more manifold) such as a T-junction cannot be un-
folded into a continuous flat wire or surface (see fig-
ure 1).
NMT can represent the space inside an object
and allows subdivision of an outer boundary with in-
ner zero-thickness boundaries. In addition, NMT al-
lows entities with mixed dimensionalities to co-exist
in the same entity. Manifold geometry kernels usu-
ally struggle to model and represent non-manifold
entities and instead consider them modelling errors:
“Some tools and actions in Maya cannot work prop-
erly with non-manifold geometry. For example, the
legacy Boolean algorithm and the Reduce feature do
not work with non-manifold polygon topology [...]
Some types of polygon geometry will not work in
Maya. Invalid geometry includes vertices that are not
associated with a polygon edge and polygon edges
that are not part of a face (dangling edges)” [2]. 3D
manufacturing also struggles with non-manifold ob-
jects: “[...] Shapeways requires all objects to be 2-
manifold. This means that each edge should be con-
nected to exactly two faces. ‘Open’ objects are typi-
cally 1-manifold (or even 0-manifold for stray edges),
models containing unwanted faces are 3- or more
manifold” [3]. In addition, manifold kernels have tra-
ditionally focused on geometry far more than topol-
ogy. These systems can rarely recognise, query and
report on topological relationships and if they do, the
processes and representations are particular rather
than universal and ad hoc rather than formal.
Figure 1
Examples of
non-manifold
entities.
At this point the reader may be wondering why any-
one would use NMT if it causes such problems. The
reason is that NMT provides many advantages over
regular manifold modelling (Lee et al. 2009; Chang &
Woodbury 1997; Nguyen 2011; Aish & Pratap 2013).
As described earlier, NMT is well-suited to create a
lightweight representation of a building as an ex-
ternal envelope and the subdivision of the enclosed
space into separate spaces and zones using zero-
thickness internal surfaces. Because NMT maintains
topological consistency, a user can query these cel-
lular spaces and surfaces regarding their topological
data and thus conduct various analyses. For exam-
ple, this lightweight and consistent representation
was found to be well-matched with the input data
requirements for energy analysis simulation software
(Ellis et al. 2008; Jabi 2015).
As we will see later in the paper, because NMT al-
lows entities with mixed dimensionalities and those
that are optionally independent (e.g. a line, a surface,
a volume) to co-exist, structural models can be rep-
resented in a coherent manner where lines can rep-
resent columns and beams, surfaces can represent
walls and slabs, and volumes can represent solids.
In addition, non-building entities, such as structural
loads can be efficiently attached to the structure.
This creates a lightweight model that is well-matched
with the input data requirements for structural anal-
ysis simulation software.
In another paper by the authors we illustrated
how NMT can represent a design envelopeand popu-
2|eCAADe 36 - Draft
late it with bespoke conformal cellular units in prepa-
ration for digital fabrication. Access to topology in-
formation allowed us to create and follow rules about
the shape of and connection between deposited cel-
lular unit to create a more efficient and better con-
nected conformal cellular structure (Jabi et al. 2017).
Finally, we successfully used NMT to spatially
reason about and evaluate the social sustainability
of vernacular courtyard houses. In that research
project, topology information allowed us to build
dual graphs and conduct space syntax analysis effi-
ciently using lightweight models. The software rep-
resented rooms as spaces with zero-thickness divid-
ing surfaces and with embedded apertures such as
door. We then used that information to create a
shape grammar and a computational tool to design
socially sustainable tall buildings (Al-Jokhadar & Jabi
2017).
RATIOCINATION VS. FABRICA
Designing, representing and reasoning about archi-
tectural space is one of the unique and defining prop-
erties of architecture (Ching 2014). Accounts from
the literature indicate that buildings are often first
conceptualised as a hierarchical sequence of related
spaces (Curtis 1996). Only once this spatial arrange-
ment has been defined does the focus shift to how
these spaces will be realised by the use of physical
building components. However, in BIM systems, the
most prevalent approach is to represent a building as
a collection of 3D solid models with each solid rep-
resenting an individual physical building component
(Attia et al. 2011). Each of these solid models uses
manifold topology to define the boundaries that sep-
arate the external void from the internal enclosed vol-
ume representing the material content of the compo-
nent. Modern BIM systems do not require nor advo-
cate the creation of a conceptual spatial model as the
basis of the building fabric model. Consider, for ex-
ample, this first sentence of the Autodesk Revit tuto-
rial on how to get started with building a BIM model:
“Start with the general building components (walls,
floors, roofs). Then slowly refine the design, adding
more detailed components (stairs, rooms, furniture)
as you proceed. [4]. Architects are thus often asked
to postpone the derivation of the conceptual spa-
tial model and other representations to a later stage
and from an overly complex fabric model to conduct
tasks such as energy analysis, structural analysis, spa-
tial reasoning, and fabrication planning. This process
leads to difficulties, errors and an increase in time and
effort.
Alternatively, one can follow a Vitruvian ap-
proach by starting with a topological model as a con-
ceptual regulating skeleton that sets out the ratio-
cination - the rational and theoretical setting out of
principles that can then support the creation of fab-
rica - the physicality of fabricating architecture (Pont
2005). Similarly, other researchers have emphasised
the importance of thinking abstractly and strategi-
cally by using a controller (something that controls
something else) and a proxy (something that stands
in for something else) in parametric design software
(Woodbury et al. 2010). These strategies ensure re-
silience within the system in the face of change; thus
a design system that forgoes this strategic definition
of topological relationships risks brittleness and fail-
ure in later design stages (Jabi et al. 2017).
Therefore, one of the primary motivations for this
research is to rethink the BIM design process to focus
first on building a conceptual model that can act as
an ordering framework and support for further de-
sign development. In this process, an NMT concep-
tual model would serve as a defining model for a
derived building fabric model. The NMT conceptual
model would define both the spatial configuration
and topology as well as provide a skeletal framework
that can be ‘thickened’, either manually or using com-
putational algorithms and rules, into actual building
fabric components (Aish & Pratap 2013).
This is, obviously, not a new concept for design-
ers many of whom implement this methodology ef-
fectively, but in a bespoke and ad hoc manner due
to the lack of formal support in BIM systems. A
case in point is the Aviva Stadium in Dublin, Ireland
design by Populous (formerly HOK Sports Architec-
Draft - eCAADe 36 |3
ture) from 2005 to 2007. This project exemplified a
transitional period that saw a shift from computer-
aided solids modelling to fully parametric design pro-
cesses. Initially, the design was first studied through
static 3D models using McNeel’s Rhinoceros platform
[5]. However, the designers quickly realised that this
is an unsustainable approach due to the time and
effort needed to implement changes. The stadium
design was re-considered as a simplified, conceptual
and parametric system, using Bentley’s Generative
Components software [6] (see figure 2).
Figure 2
Parametric
development of the
Aviva Stadium
geometry (Image
courtesy of
Populous).
The parametric model was made of three elements:
“the footprint of the stadium, composed of eight tan-
gential arcs; the plan of the inner roof or drip line,
also composed of eight tangential arcs; and a radial
structural grid that eventually became the support-
ing system of the stadium’s outer surface or skin.”
(Jabi 2013). This controlling lightweight conceptual
model, which could’ve been formalised as an NMT
Cluster of vertices, edges, wires, and faces, was then
shared by the architects and the structural consul-
tants, through nothing more than a Microsoft Excel
spreadsheet with an agreed format. The spreadsheet
was then used as the basis to drive the solution of the
structural model and the cladding system. In this ex-
ample, the thickened fabric of the project was con-
sidered a derived model from the conceptual defin-
ing model of curve centrelines. The Aviva Stadium
case study illustrates the need to formalise this in-
verted design process and enable designers to spec-
ify defining and derived models, and the relation-
ships amongst them, more precisely and formally.
NON-MANIFOLD TOPOLOGY
Because NMT formalises the spatial relationships be-
tween the various entities in a model and describes
how geometric entities are connected, this research
hypothesises that NMT has potential to serve as the
formal mechanism with which to build defining mod-
els and precisely translate them into derived building
fabric models. This approach can serve a wide range
of representations of architectural space with bene-
fits for various design, analysis, and production tasks.
Based on a previous review published by the au-
thors, a topological framework with the following
eight entities, arranged from the highest level of di-
mensionality to the lowest, is proposed: Cluster, Cell-
Complex, Cell, Shell, Face, Wire, Edge, and Vertex.
Each entity may contain other lower-level entities -
with the exception of a Cluster in which another Clus-
ter can be contained (Chatzivasileiadi, Wardhana, et
al. 2018).
In addition to allowing multiple faces to meet at
an edge or multiple edges to meet at a vertex, co-
incident entities (within a user-specified tolerance)
are merged and are ensured to be unique. Further-
more, imported mesh data, in standard vertex/index
format, can be self-merged not only to remove dupli-
cates, but to build the highest dimensional entities
possible automatically. These entities share lower-
dimensional entities where possible. This leads to ef-
ficient and consistent models that avoid the duplica-
tion problems found in regular manifold and polyhe-
dral modelling that do not enforce such rules. For ex-
ample, a mesh model (see left in figure 3) with 7 faces
is converted into a non-manifold cluster object con-
taining one (1) closed cell, one (1) open shell, nine (9)
faces, nine (9) wires, nineteen (19) edges, and twelve
(12) vertices (see right in figure 3). Any duplicated en-
4|eCAADe 36 - Draft
tities are removed and topologically linked. Finally,
notice that what used to be three (3) single rectangu-
lar faces (top and side faces) in the original mesh data
are automatically segmented into two square faces
each in the resulting self-merged NMT model.
Figure 3
Exploded
axonometric of a
mesh model (left),
and the resulting
self-merged
non-manifold
cluster with one
closed cell, and one
open shell (right).
NMT models can be combined and manipulated
using regular Boolean operations. However, NMT
Boolean operations extend the traditional regular
operations of union, difference and intersection to
include the following irregular Boolean operation:
Merge, XOR, Impose, Imprint, Slice, Trim, and Un-
merge (Aish & Pratap 2013). 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 these
faces. As a result, regular operations lead to a man-
ifold result, while non-regular operations lead to a
non-manifold result.
Prior publications by the authors suggest a
strong potential of using geometrical entities with
NMT as a representation of architectural space that is
also highly compatible with the input requirements
of building performance simulation (BPS) engines,
structural design, fabrication planning, and spatial
reasoning (Jabi 2016; Jabi et al. 2017; Al-Jokhadar &
Jabi 2017). The approach afforded by NMT provides
topological clarity that has the potential to allow ar-
chitects to better design, analyse, reason about, and
produce their buildings.
TOPOLOGIC: A NON-MANIFOLD TOPOL-
OGY MODELLING TOOLKIT
This paper presents Topologic, an open-source soft-
ware modelling library enabling hierarchical and
topological representations of architectural spaces,
buildings and artefacts through NMT. Topologic is
designed as a core library and additional plugins to
visual data flow programming (VDFP) applications
(Hils 1992; Marttila-Kontio et al. 2009) and para-
metric modelling platforms commonly used in ar-
chitectural design practice. These applications pro-
vide workspaces with visual programming nodes and
connections for architects to interact with Topologic
and perform architectural design and analysis tasks.
Software architecture
Topologic is implemented using a multi-layer soft-
ware architecture (see figure 4). At the lowest layer,
we use Open CASCADE, an open-source NMT geom-
etry software development kit (SDK) that provides
data structures and modelling algorithms for 3D
solid structures [7]. We also use ShapeOp, an open-
source SDK for surface planarization [8]. Classes
and methods in these two SDKs are encapsulated
in the second software layer containing the Topo-
logicCore and TopologicSupport libraries, written in
C++. TopologicCore implements the core topologic
classes and methods using an object-oriented pro-
gramming (OOP) approach while TopologicSupport
provides added utilities as needed. Above this layer,
we implemented an interface layer, written in the
.NET C++/CLI language, that connects the core and
support libraries to the host geometric editor or vi-
sual data flow programming application. At present,
this layer (Topologic[VDFP]) has been written for Au-
todesk Dynamo software [9] and is thus named Topo-
logicDynamo.
Figure 4
Topologic
multi-layered
software
architecture.
Work is underway to implement a version for McNeel
Rhino/Grasshopper 3D [10] (TopologicGH) which will
be reported on in future publications. Additionally,
we envisage plug-in developers will use this layer to
Draft - eCAADe 36 |5
develop domain-specific applications. By strongly
separating the code written for different platforms,
this architecture ensures high modularity and code
readability. In addition, the soft ware can be easily ex-
tended to other platforms by writing a small library
using the platform’s conventions in the upper layer
to encapsulate the core library.
Class Hierarchy
TopologicCore contains the following main classes
(see figure 5):
Figure 5
Topologic class
hierarchy.
Topology: A Topology is an abstract super-
class that stores constructors, properties and
methods used by other subclasses that ex-
tend it.
Vertex: A Vertex is a zero-dimensional entity
equivalent to a geometry point.
Edge: An Edge is a one-dimensional entity de -
fined by two vertices. It is important to note
that while a topologic edge is made of two
vertices, its geometry can be a curve with mul-
tiple control vertices.
Wire: A Wire is a contiguous collection of
Edges where adjacent Edges are connected
by shared Vertices. It may be open or closed
and may be manifold or non-manifold.
Face: A Face is a two-dimensional region de-
fined by a collection of closed Wires. The ge-
ometry of a face can be flat or undulating.
Shell: A Shell is a contiguous collection of
Faces, where adjacent Faces are connected by
shared Edges. It may be open or closed and
may be manifold or non-manifold.
Cell: A Cell is a three-dimensional region de-
fined by a collection of closed Shells. It may
be manifold or non-manifold.
CellComplex: A CellComplex is a contigu-
ous collection of Cells where adjacent Cells
are connected by shared Faces. It is non-
manifold.
Cluster: A Cluster is a collection of any topo-
logic entities. I t maybe contiguous or not and
may be manifold or non-manifold. Clusters
can be nested within other Clusters.
Several other classes are being actively developed.
These include, but not limited to:
Context: A Context defines a topological re-
lationship between two otherwise indepen-
dent Topologies.
Graph: A Graph is a Wire that is defined by the
topology of a CellComplex or a Shell. It can be
manifold or non-manifold. A dual graph is a
good example of this class.
Written using the Object-Oriented Programming
(OOP) paradigm, at the top level of Topologic’s class
hierarchy resides the Topology class, which is inher-
ited by other classes representing the topological en-
tities. Methods written in these classes can be gener-
ally classified into four categories, namely construc-
tors, queries, Boolean operations, and other entity-
specific methods. Constructors are used to construct
a topological entity from geometric entities or lower-
level topological entities. Query methods retrieve
one or more entities from another entity. Queries can
be further categorised into three: upward queries,
to retrieve higher-level entities which constitute the
argument entity; downward queries, to retrieve the
constituent lower-level entities of an entity; and side-
ways query, to retrieve adjacent entities on the same
level. Boolean operations combine two entities into
one in various ways and are written inside the par-
6|eCAADe 36 - Draft
ent Topology class. Finally, classes may have meth-
ods specially written for them. For example, the Wire
and Shell classes have methods to test if they are
closed. In addition, the Face class has operations to
attach multiple faces as apertures, which can be used
to model glazing as an example.
It should be noted that, in large part, Topologic
does not introduce its own entities or geometric
computations. Instead, whenever possible, it relies
on those either from the underlying SDKs or from
the host application to ensure compatibility. In addi-
tion, the topological classes can be used to represent
their geometry counterparts. For example, a Topo-
logic face may actually represent a planar or an un-
dulating NURBS surface trimmed by a wire, thus pro-
viding an abstraction for a wide variety of surfaces.
Despite TopologicCore being object-oriented
in its design, Topologic[VDFP] follows the VDFP
methodology to ensure compatibility with its host vi-
sual data flow programming workspace. In VDFP, a
program is represented visually by a directed graph
made of nodes and arcs that connect them. Nodes
represent functions and arcs represent the flow of
data between them (Hils 1992; Marttila-Kontio 2011).
Topologic methods are represented as visual
nodes with input and output ports. Topologic en-
tities are immutable at the host application levels.
Thus, modifying the attributes of an entity after the
fact, as is usually done in an OOP environment, is not
possible. Instead, the user has to trace the construc-
tor of the object and modify its input parameters or
create a brand new deep copy of the entity with dif-
ferent attributes.
A Topologicnode is designed to accept topologi-
cal instances from the library and the native geomet-
ric counterparts from the host application. In addi-
tion, any node that produces a topological entity also
has an extra output port that outputs the geometric
counterpart to allow display using the native host ap-
plication as well as additional workflows external to
Topologic. These design principles guarantee effort-
less connection from and to indigenous nodes in a
single workflow.
DOMAIN-SPECIFIC APPLICATIONS
As explained above, we envisage that our software
will be used by plug-in developers to create domain-
specific applications. To illustrate this process, we
created two demonstrative applications. The first ap-
plication, TopologicEnergyallows the user to quickly
build models that can be sent to EnergyPlus (Craw-
ley et al. 2000) for energy simulation using the Open-
Studio toolkit (Guglielmetti et al. 2011). The second
application, TopologicStructure demonstrates how a
mixed-dimensional structural model can be created
with structural loads applied to it.
TopologicEnergy
A comparative study with traditional workflows was
conducted and reported in previous publications
(Chatzivasileiadi, Lannon, et al. 2018) and thus will
only be summarised here. The experiment analysed
four pathways to the energy modelling of a building
with relatively complex geometry including curved
surfaces and bespoke glazing. From the four path-
ways explored, the NMT pathway using Topolog-
icEnergy was able to model and handle complex ge-
ometry and produce reliable results, while benefit-
ting from the advantages of NMT. As shown in figure
6, the workflow consisted of (a) modelling the exter-
nal envelope and the glazing design on a flat surface,
(b) mapping the glazing unto the curved wall, (c) sub-
dividing and planarizing the wall and mapped glaz-
ing into a set of wall panels and windows, (d) slicing
the building into multiple stories, and finally (e) send-
ing the model to OpenStudio/EnergyPlus for energy
analysis (Wardhana et al. 2018)
Modelling the external envelope and the glazing
design on a flat surface. We start by creating a series of
circular wires that are then lofted into a surface. This
is converted to a Topologic face (see figure 6-1). The
glazing is created as a rectangular face with internal
wires that represent the glazing apertures (see figure
6-2).
Mapping the glazing onto the curved wall. The
flat glazing design is sampled using a user-specified
number of rows and columns and mapped onto the
Draft - eCAADe 36 |7
Figure 6
TopologicEnergy
example workflow.
UV parametric space of the curved wall (see figure 6-
3).
Subdividing and planarizing the wall and mapped
glazing into a set of wall panels and windows. The
curved wall and glazing are then segmented into
quadrilaterals using a user-specified number of rows
and columns (see figure 6-4). The resulting mesh
is then planarized using the ShapeOp library [8].
The glazing is further triangulated and scaled down
slightly in keeping with the requirements of Open-
Studio and EnergyPlus.
Slicing the building into multiple stories. A series
of planes are created to represent floor slabs and con-
verted into Topologic faces(see figure 6-5). Using the
non-manifold slice boolean operation, the building is
sliced into separate floors and a Topologic CellCom-
plex is created (see figure 6-6).
Sending the model to OpenStudio/EnergyPlus. The
Topologic CellComplex is queried for its constituent
Topologic Cells, faces, and sub-faces and those
are translated into OpenStudio spaces and thermal
zones (see figure 6-7). The TopologicEnergy software
then sends the resulting energy model to EnergyPlus
and automatically triggers an energy simulation.
TopologicStructure
The second demonstrative application, Topologic-
Structure, allows the user to quickly build structural
models and apply structural loads in preparation for
structural analysis. The overall aim is to create a
mixed-dimensional topological shape by a list of ver-
tices and indices and apply structural loads to it. The
overall workflow consisted of: (a) creating the model
using an array of vertices and an array of vertex in-
dices, (b) defining a list of locator points, and use
them to find the closest simplest sub-shape of the
model, (c) Apply various kinds of structural loads to
these sub-shapes (see figure 7).
Creating the model using an array of vertices and
an array of vertex indices. We start by creating a
list of vertices, and a list of vertex indices (see fig-
ure 7-1). This is akin to creating a mesh from the
same set of inputs. However, here we are creat-
ing a cluster of mixed-dimensional topology, con-
sisting of columns, walls, and spaces. We save the
vertices and vertex indices as CSV files and load
them in Dynamo using its built-in CSV file reader.
We then pass the list of vertices and vertex indices
to the Topology.ByVertexIndices() node, which con-
verts each row in the data into an independent Topo-
logic entity. The node returns a list of entities - one for
each row in the CSV file. We then pass this list to Clus-
ter.ByTopology() node to create a Topologic Cluster.
The final step is to self-merge the cluster in order to
remove all duplicates, create higher-dimensional en-
tities where possible and topologically connect enti-
ties where appropriate (see figure 7-2).
Selecting sub-shapes to which the loads will be ap-
plied. To identify sub-shapes to which we would
like to apply structural loads, we use a collection
of point locators that fall on or near the desired
sub-shapes (see figure 7-3). We connect the con-
structed model and the locator points to the Topol-
ogy.ClosestSimplestSubshape() node, to find which
“simplest” sub-shapes are closest to the locator
points (see figure 7-4). A sub-shape A is simpler than
another sub-shape B if it has a lower dimension (e.g.
a vertex is simpler than an edge, and an edge is sim-
pler than a surface etc).
Applying structural loads to the model. In Topo-
8|eCAADe 36 - Draft
Figure 7
TopologicStructure
example workflow.
logicStructure, we implemented a mechanism to ap-
ply loads to a topological shape (see figure 7-5). A
single load is applied to a point location on an entity.
A group of loads is called a LoadCluster, and it can be
applied to an edge (linear loads) or to a face (surface
loads). A LoadCluster is only valid if all of its loads are
within the valid range of the edge/face, otherwise an
error message is generated. Loads can have direction
and magnitude and are applied to a parametric loca-
tion on the target entity. For linear loads we use both
a u translation and a u scale to apply the loadCluster
to a region of the edge. Similarly, surface loads use
a u and v translation, scale, and rotation applied to
the loadCluster to locate it within a specific region of
the target surface. Topologic models without forces
(see figure 7-6) can then be combined with those that
have forces applied to them (see figure 7-7). The re-
sulting topological model is highly compatible with
structural analysis software input requirements (see
figure 7-8). We are currently implementing a link to
such software and will report on our progress in a fu-
ture publication.
Topologic and its associated tools are under ac-
tive development. The core toolkit is designed to
be platform-independent and allow third-party de-
velopers to build domain-specific software. Topo-
logicEnergy and TopologicStructure, as described
above, serve as demonstrative domain-specific ap-
plications for energy analysis and structural analysis
that can act as templates for others to follow. We
are in discussions with our industrial partners to in-
tegrate Topologic with their workflows and tools and
will report on that in future publications.
CONCLUSION
Manifold modelling, while needed in later stages of
design to create the models of the fabric and com-
ponents of buildings, is too complex and cumber-
some in the early stages of design and hinders the
use of building performance simulation. Topologic
aims to address these issues by introducing a rigor-
ous class hierarchy and a set of methods that are able
to manage both manifold and non-manifold topolo-
gies. The combination of non-manifold topology
and a versatile 3D software kernel has the poten-
tial to provide a comprehensive solution for archi-
tects while maintaining design creativity and flexibil-
ity. The development of Topologic has made it clear
that there is a need to further investigate and con-
duct user-testing of innovative methods for creating,
displaying and interacting with geometric, topolog-
ical data using advanced interfaces and information
theory. Ultimately, our aim is to help architects and
engineers to: “[...] build the lightest possible model
using the least effort that gives the most accurate
feedback about their design and engineering con-
cepts” (Aish & Pratap 2013).
ACKNOWLEDGEMENTS
This research project is a collaboration between
Cardiff University and University College, London and
is funded by a Leverhulme Trust Research Project
Grant (Grant No. RPG-2016-016). We would like
to thank the National Renewable Energy Labora-
tory (Daniel Macumber), BuroHappold Engineering
(Al Fisher), and Grimshaw architects (Radu Gidei) for
their help with and contribution to this project.
Draft - eCAADe 36 |9
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[1] http://en.wikipedia.org/wiki/Topology
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[6] http://www.bentley.com/en/products/product-line
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[8] http://www.shapeop.org
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[10] http://grasshopper3d.com
10 |eCAADe 36 - Draft
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