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Automated multi-zone building energy model generation for
schematic design and urban massing studies
Timur Dogan1, Christoph Reinhart1, and Panagiotis Michalatos2
1 Massachusetts Institute of Technology, Cambridge, USA
2 Harvard Graduate School of Design, Cambridge, USA
In this paper we present an algorithm for automated multi-zone build-
ing energy model production for urban and schematic design. By re-
viewing current guidelines for thermal zone discretization of early de-
sign building energy models [BEM] we present an argument that cur-
rent zoning guidelines effectively recommend the use of a straight-
skeleton like subdivision. Based on this finding, our procedure accepts
an arbitrary building massing and subdivides each floor into core and
perimeter thermal zones. As a proof of concept the algorithm was im-
plemented as a plug-in for the parametric design environment
Grasshopper for Rhinoceros. A number of examples of various com-
plexities are shown to demonstrate its robustness and suitability for
automated multi-zone BEM generation.
Keywords: energy modeling, urban and schematic design, automatic
The earth’s urban population is expected to double by 2050, requiring the construction
and densification of hundreds of cities and neighborhoods [UN, 2012]. With 30-40% of the
world’s energy consumption coming from buildings and more than 60% of the increase in
building related CO2 emissions coming from developing countries [UNDP, 2010], creating
livable and energy efficient buildings and urban environments can thus be seen as the defining
planning challenge of our century. The use of tools for building energy use optimization is,
however, underutilized when it comes to understanding and predicting the energetic implica-
tions of schematic and urban design decisions. Computer-based building performance simula-
tion (BPS) tools have been developed since the early seventies to test drive different design
concepts during schematic design in order to ensure that individual buildings provide “high
comfort spaces” while having a “minimum environmental impact” [Hensen & Lamberts,
2011]. Yet, despite the improved usability of these tools, they tend to be mostly applied during
design-development or for demonstrating code compliance. As a direct result of this delayed
use of tools within the design process, a recent survey of energy modelers and architects by
Samuelson et al.  revealed that even in AEC (Architecture, Engineering, and Construc-
tion) firms which employ in-house energy models the results of simulations had in over 30%
of cases only “rarely” or “occasionally” an impact on design decisions. This finding is prob-
lematic since architects would benefit most from simulation-based feedback during the explo-
ration of rapidly changing design variants, as it is common practice in the early design stages.
Similarly, urban designers, a group that traditionally does not employ energy modeling tools,
would also greatly benefit from using energy simulations to inform site layout, massing stud-
ies and program distribution [Besserud & Hussey, 2011].
One of the reasons for the aforementioned delayed use of BPS in design is that the
generation of BEMs out of existing architectural or massing models currently involves multi-
ple manual steps and is therefore time and resource intensive [De Wilde, 1999][Mahdavi et
al., 2003][Ianni et al., 2013]. Applying current modeling practices to urban level projects that
involve multiple buildings therefore remains the exception and (if at all) is done using a com-
bination of spreadsheets with simulations of more generic building archetypes. Such a model-
ing approach is unsuitable for resolving details of urban microclimate and detailed neighbor-
hood planning. An alternative approach to the spreadsheet method would be to use already
available 3D models (that are produced anyhow e.g. for renderings or plan production) and
automatically convert them into energy models. Over the years, different groups have worked
on various aspects of this problem [van Treeck & Rank, 2007] [O’Donnell et al. 2013] [Pratt
et al. 2012] [Jones et al. 2013].
A key distinction between previous methods is the level of detail of the architectural
input model that is to be converted into a BEM. In 2007 van Treeck demonstrated how a full
3D Building Information Model (BIM) that includes interior walls and usage definitions can
be auto-translated into an energy model. The method presented performs a "dimensional re-
duction of 3D building models using graph theory" [van Treeck & Rank, 2007]. The algo-
rithm uses Boolean operations to decompose the input geometry and then performs surface
overlap tests to establish a connectivity network for a multi-zone energy model. Similarly,
O’Donnell et al.  worked on a semi-automated BIM to BEM conversion process im-
plementing automated space boundary identification. Pratt et al.  presented a geometric
modeling protocol and framework that included geometry correction and surface heuristics
that would allow the conversion of more traditional 3D CAD models with interior space sub-
divisions into BEMs. Later that same group refined this approach, presenting additional
methods for “cleaning up” real world architectural models by removing small holes, reducing
the number of interior surfaces and using a view-factor based method to identify zones and
their adjacencies [Jones et al. 2013].
All of these studies assumed that a detailed BIM or CAD model of a building with
defined interior spaces is available for conversion into BEM. Typically such models are avail-
able later in the design process. The studies further tended to convert each room in the archi-
tectural model into a new thermal zone. In contrast to these previous efforts, this paper is
mainly concerned with the conversion of more abstract massing models into BEM. Within the
context of this paper a massing model is a geometric representation that approximates the
shape of a building and that does per se not contain any information about the interior subdi-
vision of a building such as floors and walls (Figure 1). This "empty hull" is then paired with
Figure 1: Massing model and its typical modeling styles in urban and schematic design.!
a) Building envelope b) Buildings as stacked floor volumes
a vague idea on how the interior can be used programmatically, how the building could be
materialized and how the facade might look like, e.g. a mixed use building, office-residential,
heavy construction with punched window facade. A thermal simulation, however, requires
more specific inputs, windows have to be modeled explicitly and the building volumes need
to be discretized more finely into thermal zones. Thus, two essential steps are required to
convert massing models into BEMs automatically. During step one, the building volume, rep-
resented by poly-surfaces, has to be converted into multi-zone thermal model geometry, in-
volving a discretization into multiple sub-volumes to represent floors and zones and geomet-
rically articulated facades. In the second step, parameters have to be assigned to the individual
zones including information such as materiality, space usage and space conditioning.
This manuscript is mainly concerned with the first step, i.e. the automated conversion
of an architectural massing model as defined above into a meaningful multi-zone BEM geom-
etry that can be used by a whole building energy modeling program such as EnergyPlus,
TRNSYS and others [Crawley et al., 2000] [Klein, 1979] [ESRU, 2005]. The next paragraph
reviews current guidelines for generating multi-zone thermal energy models of buildings and
lays the foundation for the following methodology of our auto-zoning procedure.
2. Early design multi-zone energy models
For decades modelers have implemented multi-zone thermal models to simulate ener-
gy use of a building. It is therefore somewhat surprising that there exists relatively little scien-
tifically backed advice as to how an “early design variant” should be broken up into discrete,
thermal zones. According to the literature [Hirsch, 2010] [BEMBOOK, 2014] a thermal zone
should roughly correlate with the spatial subdivision of a building into rooms and spaces. To
simplify the simulation and also the HVAC system layout, multiple rooms may be joined to-
gether in one zone if they share similar load profiles. However, the floor plan that would pro-
vide a basis for such a room subdivision is usually unknown during the schematic design
stage. ASHRAE 90.1 Appendix G hence provides a brief guideline for this case stating that
the floor plan should be divided into a “core” and “perimeter" region. The perimeter is de-
fined as the space along the facade with a depth of five meters. Further, the perimeter should
be subdivided by orientation and spaces with glazed exterior surfaces with more than one ori-
entation should be subdivided proportionally. The leftover region in the center of the floor
plate forms the “core” [ANSI/ASHRAE/IESNA, 2007]. 90.1 Appendix G provides no binding
guidance of how the boundary between different zones should be modeled.
The original motivation for breaking a building into thermal zones is that simulation
programs treat all zones as a node within a thermal network that represent a perfectly mixed
air volume. So, the theory goes that if one for example models a larger building as a single
thermal zone than heat surplus that may occur during the winter near a south facing space
may be absorbed by a space to the north that is underserved by solar gains. As a consequence
the predicted energy demand decreases due to a balancing between loads, gains and absorp-
tion/dampening capacities of a space [Smith et al. 2011]. Figure 2 compares various multi-
zone thermal models of the same floor to a single zone model assuming low and high internal
loads. The figure shows that annual loads for heating and cooling may differ by up to 13%
and 14% for low and high internal loads, respectively. As expected, the Appendix G method
yields higher and thus more conservative annual loads than the single zone simulation.
As mentioned earlier, the 90.1 Appendix G guideline does not specify how to take in-
ter-zone heat and mass transfer into account. Figure 3 reveals the magnitude of this effect by
comparing annual loads for the building from Figure 2 divided according to Appendix G but
with interior zone boundaries being either adiabatic and step by step adding conduction, solar
radiation and different levels of air mixing. As one would expect, adding these different inter-
zone heat flows successively bring the Appendix G solution closer to the single zone solution.
While ASHRAE 90.1 does not give recommendations on and leaves it up to the modeler to
provide accurate assumptions, we conclude this mini experiment by grouping the heat and
mass transfer into three useful architectural scenarios (floor-plan-typologies) that can be im-
plemented as presets in the following energy modeling workflow. The “individual office sce-
nario” only considers conduction heat transfer between the zones. The “open plan” scenario
can consider radiation exchange and inter-zone air-mixing. The “small building” scenario al-
lows to simulate lumped zones.
The previous paragraphs confirm the relevance of current practice to divide a building
into multiple thermal zones and identify 90.1 Appendix G as the only existing guideline ad-
vising on discretizing a building volume into thermal zones. This paper proposes a method to
carry out this step automatically. Several existing design tools also have auto-zoning methods
implemented. Autodesk Vasari [Autodesk, 2013] is a commercially available schematic de-
sign tool for architects, can automatically split up a building massing into perimeter and core
zones. Details of the zoning algorithm and its implementation have not been publicly re-
leased. Similarly, Reinhart et al.  introduced software for multi-zone energy model pro-
duction. The software is, however, limited to simple and strictly orthogonal shapes and adja-
cencies to neighboring buildings are not recognized. In the following section a general algo-
rithm is described that overcomes these limitations.
Figure 3: Comparison of a perimeter and core subdivision with different inter-zonal
heat and mass transfer scenarios versus a single zone simulation and their correlation
with architectural floor plan typologies.
Figure 2: Comparison of subdivision schemata for two extreme internal load scenarios.
The presented research builds on three tools for simulation and geometric modeling:
EnergyPlus, the McNeel Rhino Platform and Archsim Energy Modeling for Grasshopper. En-
ergyPlus is a whole building energy simulation program that can model building related ener-
gy flows in a sub hourly time resolution [EERE, 2013]. It is validated thoroughly and it is dis-
tributed free of charge. This makes it one of the most accessible professional energy simula-
tion tools available and thus is the simulation environment of choice. McNeel Rhinoceros is a
CAD modeling software that can create, edit, analyze, and translate curves, surfaces, and
solids. McNeel offers extensive support for plug-in development with the RhinoCommon
SDK. This research relies heavily on this basic geometric modeling ecosystem [McNeel,
2013]. Rhino was also chosen due to its popularity among architects and urban planners.
Archsim Energy Modeling for Grasshopper is a user and programming interface for energy
model production. It features a thermal model class library containing abstract definitions for
zones, faces, materials, etc. and can translate those into a simulation engine specific syntax.
Archsim supports EnergyPlus and the TRNSYS. Given a set of geometry and parameters it
constructs multi-zone thermal models and writes out the simulation input file [Dogan, 2013].
For rapid energy model production two essential capabilities are added to the above toolset:
•Automated geometry production: The massing model input geometry has to be divided
into sub-volumes representing the floors, perimeter and core zones of a building.
•Efficient parameter assignment: The produced geometry has to be paired with additional
information such materiality, loads, schedules and HVAC settings to generate a complete
In the following section the automated geometry production workflow is explained in
detail. Methods for efficient parameter assignment are introduced afterwards. We then present
three test cases that show the robustness of the algorithm and its feasibility for an ArchSim/
EnergyPlus modeling workflow.
Automated Geometry Production
Input: Based on the authors experience from practice and teaching, urban and
schematic design processes mainly produce two types of input geometry. In the earliest
stages, the buildings are modeled as a single volume. This form of representation helps the
designer to understand basic morphologic features such as the massing and the proportions of
a design. It usually originates from a 2D drawing that is extruded. Another very common rep-
resentation involves “stacking” floor-volumes. This adds a notion of “scale” since it immedi-
ately allows one to read floor heights from the model. It is also popular since it is inline with
the architectural design process, thinking of distributing program and densities. The following
algorithm can work with both styles (Figure 1). If “Case A” is encountered one volume is in-
terpreted as one building envelope. For “Case B”, the algorithm requires the user to group the
volumes if they belong to the same building. For "Case A" the algorithm begins with a floor
to floor subdivision of the envelope based on a floor height that is specified by the user. The
floor to floor distance can be given as array to take into account varying floor heights. For
"Case B" the floor subdivision procedure is skipped. Starting point for all following steps is a
“Building” that consists of a list of sub volumes for each floor.
Subdivision: The next step is to subdivide the floor volumes into thermal zones. For a
limited number of cases the perimeter and core zone subdivision, as described by the previ-
ously mentioned ASHRAE 90.1 Appendix G guideline, is a trivial and fast operation. The
core region can be found by offsetting the outer edge of the floor plan. Then a simple search
for the closest point from the outer polygon vertices to the inner ones can already yield the
desired subdivision. This is shown in Figure 4a. When the search function returns pointers to
the inner vertices, the lists of points that make up a zone outline can be constructed, even if
edges of the offset polygon collapse. For more complicated cases the above mentioned ap-
proach fails. Figure 4b shows a convex floor plan with a core region that retreated completely
from the left part of the polygon due to a series of collapsing edges during the offset. It subdi-
vides parts that have good “core visibility” as intended but leaves the entire left half undivid-
ed. Now, an ear-clipping method [Meisters, 1975], [ElGindy et al., 1993] could divide the rest
into convex regions. However, with a certain thickness of the remaining polygon-tip it might
be desirable to split the tip into single sided zones instead of a lumped region with access to
multiple cardinal directions.
This would require a splitting axis somewhere along the medial axis [Preparata, 1977]
of the polygon. A medial axis approximation is shown in Figure 4c. The medial axis however,
does not consist of straight line segments and instead can involve parabolic curves. This is not
desirable since the final output of the algorithm are 3D thermal zones that should ideally con-
sist of as few as possible planar surfaces. Very similar to the medial axis but involving just
straight lines is the "straight skeleton" that was first described by Aichholzer et al.  and
extensively discussed [Aichholzer & Aurenhammer, 1996], [Barequet et al., 2003]. The
straight skeleton of a polygon as shown in Figure 4d divides the polygon into cells for each
outer edge and is thus fulfilling the requirement of splitting perimeter zones by orientation. In
order to obtain a core and a valid thermal zone subdivision a couple of simple steps have to be
added. In a second step the algorithm produces the core region by performing an offset of the
outer and hole polygons. Then the core overlap is removed from each skeleton cell by a 2D
boolean difference operation. Due to limitations of the radiation distribution algorithm of En-
ergyPlus and TRNSYS the thermal zones have to be strictly convex spaces. Thus, the result-
ing perimeter and core zones have to be further subdivided if they are concave. Various poly-
gon partitioning techniques exists for this task and have been described in detail [O’Rourke,
1998]. Since the resulting perimeter regions are guaranteed to be hole-free, a simple split at
each concave vertex perpendicular to the longest exterior edge of the polygon delivers the de-
sired result. The core regions however, can consist of polygons with holes. One simple exam-
ple is a donut-shape floor plate with a circular core region. Here, a triangulation and a subse-
quent diagonal-removal procedure is used to obtain strictly convex zones [Hertel &
Mehlhorn, 1983]. The result of the previous steps is a set of 2D regions for the perimeter and
the core of each floor plate. Pseudo code that briefly summarizes the previously described
steps is given below.
The implementation of a robust straight skeleton algorithm that can handle complex
polygons is not a trivial task. The presented algorithm uses a ported and slightly improved
a) Perimeter split b) Failure c) Medial axis d) Straight skeleton (with a concave cell)
version of an implementation that has been provided by Petr Felkel and has been extensively
described by Felkel & Obdrzalek . For both the offset and the Boolean operations the
algorithm rely on the polygon clipping library “Clipper” by Johnson .
Form 2D regions to 3D zones: The 2D core and perimeter cells have to be further
processed to obtain the final 3D volumes that represent a thermal zone. The simplest approach
is to extrude the cells by the floor height. This however, is only possible if the facades of the
initial envelope are vertical. In order to avoid this limitation the algorithm uses the previously
generated or provided floor volumes. Analogous to cutting styrofoam blocks with a hot wire
the algorithm computes vertical clipping planes along the 2D perimeter and core regions
while skipping outer edges and then cuts out the zones from each floor volume. Pseudo code
is given on the next page.
Adjacency: In urban scenes it is quite common that buildings touch each other and
not every face of the envelope is a facade with outward facing windows. In such a case the
algorithm needs to identify such faces in order to assign the correct boundary conditions and
materials later. Additionally, the zoning should also react to inter-building partition walls to
avoid building a perimeter zone there. In order to detect adjacencies the algorithm uses Arch-
sim EM's adjacency graph building functionality. Archsim relies on congruent faces with op-
posing face normal in order to find a connection. It provides a recursive face splitting algo-
rithm to handle geometry that has touching surfaces with non-congruent surfaces. With the
adjacencies identified, the zoning procedure can now build adjacency aware core and perime-
ter regions. Adjacencies are handled by joining the neighboring floor plans into a single plate
before core and perimeter region offsets are computed. Considering the possibility that floor
plans are not always at matching Z-coordinates, the closest floor plan in the neighboring
building is used. The offset regions are then trimmed back to the buildings original size, re-
sulting in a core region that now touches the adjacent wall element. However, his procedure is
not always straight forward: In an extreme case where the core offset in the neighboring
building completely collapses and "retreats" back into only one building, undesirable core
geometry can be produced.
Input. A set F of poly-lines in a plane representing the outlines of a ﬂoor plan.!
Output. A list of doubly connected edges describing the cellular core and perimeter subdivision
1. Compute the straight skeleton S(F) and store the resulting skeleton cells in a list
2. Compute an inward offset O(F) of the input poly-lines F.!
3. O(F) describes the core region(s)
5. DO obtain c
6. IF p
7. split c
9. append c
10. Split RCORE
11. append LCC
12. RETURN TDZ(F)
Automatic window/shading modeling: After the zone geometry is modeled, we have
to further articulate the facades. The user can specify orientation dependent window to wall
ratios that are then used to model the window surfaces on all outward facing zone surfaces.
This can be done by duplicating and then scaling the windows parent surface. Alternatively,
standard Grasshopper modeling capabilities can be used to implement more elaborate facade
design patterns such as punched hole facades with multiple small openings or simple horizon-
tal window stripes. Manual intervention is also possible.
In addition the algorithm producing the zone geometry the user needs to be presented
with an efficient way to assign essential simulation parameters, such as materiality of the
building elements, usage patterns and control strategies in form of schedules as well as the
internal loads, to each zone. Regarding usage patterns and loads for various space types, early
design simulations often rely on standards as they are defined in the “SIA Merkblatt
2024” [SIA, 2006]. Thus, parameter templates for the various zone types that exist in the
model can easily be defined. These zone types however, are distributed throughout the entire
model and thus a diverse type-mix might exist within one building. Consequently, a parameter
definition via a building-template seems inadequate. Since selecting each and every zone in-
dividually to assign the appropriate template is also not an option, a more general method that
can assign zone templates throughout the various buildings is required. In our workflow,
analogous to the architectural zoning in a master plan, the user defines large 2D or 3D regions
to assign parameters to the individual thermal zones. To define a 2D region a closed curve,
surface or image map can be used. Alternatively, 3D regions that are modeled by large closed
volumes allow better control over the vertical distribution of the zone templates. Each region
carries settings for perimeter and core and a simple point containment test is performed on the
geometric centroid of each zone to assign the parameters. This allows the user to create com-
plicated mixed-use scenarios with a minimal amount of effort.
Testing the algorithm
Algorithm THREEDIMENSIONALZONEGEOMETRY(TDZ(F) , V)!
Input. A set of planar zoning cells TDZ(F) and the corresponding ﬂoor volume V.!
Output. A list of closed volumes representing the thermal zone geometry for core and perimeter
2. IF cp
3. Create an extrusion of c
4. Append E(c
6. Duplicate V as V
8. IF e is an interior edge!
9. Trim V
10. Append V
11. RETURN ZG(TDZ(F), V)
In order to test the algorithms planar zoning functionality we tested various floor plan
outlines with varying complexity (Figure 5). Starting with a simple rectangle we continue by
adding convex and non-convex holes. We then use our algorithm for one building of the
massing model from Figure 1 and run a multi-zone energy simulation in the Boston climate to
test the feasibility of our automated zoning algorithm within an ArchSim and EnergyPlus
workflow (Figure 6). Simulation results for one building are visualized by false coloring the
zone geometry for heating, cooling and lighting energy demand (Figure 7). While test case in
Figure 6 only requires a simple extrusion after we have obtained the 2D zoning due to its ver-
tical facades, we show the discretization of a complex 3D massing model with sloped facades
that requires the “wire cutting” approach in Figure 8.
In Figure 5 the zoning result of our algorithm is shown for floor plan geometry of
varying complexity. The offsetting procedure has defined the core and perimeter regions, both
visualized in a dark and light gray. The core region completely disappeared from regions that
are thinner than two times the offset distance as marked by red circles in the figure. The
perimeter cells that further subdivide the perimeter region into single sided zones were de-
fined by the straight skeleton procedure and are visualized by black outlines around each cell.
The green circles mark additional cell splits into strictly convex zones as described earlier.
The darker core regions are also subdivided into strictly convex zones. The blue circle high-
lights a region where some diagonals could not be removed and thus resulting in very narrow/
Figure 5: Various zoning test cases of varying complexity. !
Light grey represent the perimeter and dark grey the core.
In Figure 6, the ArchSim EM, EnergyPlus workflow integration is demonstrated. 11b
shows the 3d geometry of perimeter (medium gray) and core (dark grey) zones as well as the
window geometry (light gray). 11c shows only the inner surfaces of the model. The image
validates that all interior heat transfer surfaces have been recognized as such by ArchSim EM
and illustrates the complexity of the connectivity graph of the thermal model. The overall
model complexity is outlined in Table 1. The shown building consists of 118 zones that in to-
tal consist of 877 faces such as roof- , partition-, facade- and window surfaces. Figure 7
shows exemplarily how the EnergyPlus simulation results can be visualized. The zone geome-
try is false-colored according to the cumulative annual energy use intensity for heating a),
Figure 6: Detailed model visualization: !
a) Input volume !
b) Zone and window geometry!
c) Surface connectivity
Figure 7: False colored zones to visualize EUI[J]:!
Table 1: Model complexity (for partial model as shown in Figure 6)
Number of zones
Number of opaque surfaces
Number of glazed surface
Table 2: Runtimes [s] (for partial model as shown in Figure 6)
cooling b) and lighting c). In Table 2 the computational cost of each step is listed for the ex-
ample model of Figure 6.
In Figure 8 the 3D decomposition of a high-rise massing with sloped facade surfaces
is shown. The input geometry is split into floor volumes before the inner subdivision is com-
puted. The figure visualizes this by rendering the generated partition walls. Finally the
perimeter zones and windows are shown. Note the triangular surfaces that appear along the
edges of the massing where vertical zone partition wall meet the sloped facade surfaces.
The current manuscript serves the purpose of describing a general and flexible multi-
zone energy model production algorithm that can be used by others. It is our hope that the in-
troduced procedure can simplify and accelerate BPS in early design significantly and that it
can integrate smoothly into workflows already used by design and planning teams. In Figure
5 our procedure proved its robustness with complicated geometry. It strictly follows the cur-
rent convention for zoning early design variants as defined in the previously mentioned
ASHRAE 90.1 guideline. The straight skeleton of a polygon per se follows the rule to parti-
tion the affiliation of a space to a facade proportionally. This fact is particularly useful for the
zone subdivision of more complicated floor plans since coming up with a “correct” subdivi-
sion manually can easily become a time consuming and non-trivial task. As shown in Figure
5c moving the courtyard of a simple rectangular shape off-center can already produce com-
plex space affiliations that are not directly obvious.
The convex partitioning of the core can occasionally lead to very long and narrow
zones due to the character of HertelMehlhorn based procedure which first triangulates and
then removes unnecessary diagonals to obtain convexity. To avoid this, the implementation of
a more elaborate splitting mechanism is planned for the future.
Another future goal is to compare simulation results generated with the multi-zone
discretization algorithm against an altogether different urban modeling approach which is
based on abstracting an arbitrary neighborhood massing that consists of hundreds of buildings
into a meaningful group of “typical” two zone thermal models [Dogan & Reinhart 2013]. The
approach has been implemented into a fully automated procedure that makes informed simpli-
fications based on micro-climatic boundary conditions and internal loads. The methodology
Figure 8: Complex massing: Input, floor subdivision, inner subdivision and facade.
offers easy multi-building energy model management and drastically reduced simulation
complexity and runtimes and thus facilitates rapid early design evaluation and optimization.
A general algorithm for creating multi-zone building energy models for urban and
schematic design massing models is introduced. The algorithm can handle complex building
shapes and may facilitate and accelerate building energy modeling in early design.
We would like to thank Transsolar Energietechnik GmbH Munich for productive discussions
and partial funding of the research project.
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