Automation of CAD models to BEM models for performance based goal-oriented
College of Environmental Design
Center for the Built Environment
College of Environmental Design
Department of Architecture
College of Environmental Design
Department of Architecture
aCorresponding author.†Current address: Department of Architecture. University of California,
Berkeley, 232 Wurster Hall #1800, Berkeley, CA 94720-1800, USA.
This work presents a new methodology to automate the derivation of Building Energy Models
(BEMs) from complex 3D Computer-Aided Design (CAD) geometry. The goal is to combine current
parametric modeling, digital fabrication, and computer graphics techniques to automatically generate
the geometric input of an energy model from any digital 3D model of a building. Such automation
facilitates the use and implementation of goal-oriented design methods that integrate energy
performance with other types of building performance models. In this work, mesh planarization
algorithms, which are currently used in computer graphics and in digital fabrication methods, are used
and adapted to automate and optimize the parsing of non-planar surfaces to EnergyPlus (E+), a
popular BEM engine. The proposed methodology facilitates the modeling of thermal zones with
double-curved envelopes, which is a time-consuming task that typically requires a high level of
expertise from the energy modeler. The proposed single, streamlined workflow generates digital
models that are suitable for both energy optimization and digital fabrication, thereby facilitating the
integration of two parallel design procedures at the core of an architectural design process. Through
this workflow, a single CAD model generates solutions that are energy efficient and feasibly
fabricated using digital techniques. This goal-oriented design workflow is applied in the study of
fritting pattern densities for three complex double-curved building geometries.
Keywords: generative design systems, goal-oriented design, energy optimization, digital interfaces
The recent rise of parametric, procedural, and algorithmic design processes may be partially attributed
to the development of new domain-specific programming languages for preexisting 3D modeling
software, such as Grasshopper for Rhinoceros [1, 2] and Dynamo for Revit . These processes
empower designers to more easily iterate and more deeply explore the resultant solution space for a
given design; however, studies show that human beings have limited abilities to assess large
alternative sets . Thus, it is common to complement parametric and/or procedural architectural
design with performance-based design using simulation software, which provides information about
the current design’s performance at any given point. Examples of such digital simulation tools
include: Radiance , a ray tracing-based software used for rendering and lighting, EnergyPlus , a
whole building energy simulation program, and SAP2000 , a simulation program for structural
analysis. However, the parallel use of both parametric and performance-based methods can lead to a
tiresome iterative cycle of model-simulate-evaluate-remodel. The inefficiencies of this cycle may
limit the depth of exploration within the design solution space.
Different types of Performance-based Generative Design Systems (PGDSs) have been proposed to
overcome these limitations. These systems directly apply the goal-oriented design method, in which
the designer establishes performance goals for a given design and allows the system to automatically
search that design’s solution space for the solution that best meets the desired objectives. PGDSs for
the built environment integrate three different modules: (i) a generative or parametric model that is
able to generate a multitude of design alternatives from a set of procedural rules or algorithmic
processes; (ii) a building performance simulation engine to assess the fitness of each design
alternative generated by the generative model; and (iii) a search mechanism or solver that
automatically steers the iteration process until it finds a solution, or set of design alternatives, whose
performance is closer to the pre-established goals. There are several PGDSs dedicated to the built
environment. These include: Audioptimization, a goal-oriented design system for acoustic design
proposed by Monks et al. ; EifForm, for structural design for structural design ; GENEARCH
[10,11,12], and GenOpt [13,14] for building energy performance, and more recent methods and
systems based on goal-oriented approaches such as the ones presented by Turrin et al. , Wright et
al. , Xu et al. , and Futrell et al. .
Recently, several modular programming tools with commercial optimization packages have emerged,
which facilitate the implementation of custom PGDSs for architectural design. For example, it is
possible to build the framework for an energy-based PGDS by coupling DIVA for Rhino  or
Ladybug/Honeybee  with Grasshopper functions and methods for parametric design, and any
Grasshopper-based evolutionary solver, such as Galapagos or Octopus . If Karamba  was used
instead of DIVA or Ladybug/Honeybee in this scenario, a framework for a structure-specific PGDS
would instead be developed.
Despite remarkable progress in the integration of several tools and modules used in goal-oriented
design methods, severe limitations persist in energy performance-based generative processes. These
limitations are primarily attributed to the geometric limitations of the energy simulation module used.
For example, although EnergyPlus (E+) is a state-of-the-art Building Energy Modeler (BEM), its
modeling features and geometry protocols are very limited relative to those of a typical 3D CAD
software. Shape convexity and planarity are the most significant geometric limitations in E+. All
surfaces must be planar and convex, triangular or quadrilateral. Mesh triangulation can avoid these
limitations, but it can lead to others. For example, mesh triangulation may result in the exponential
increase of simulation time, especially if the triangulation result is a dense mesh. The simulation time
increment is related to view factor calculations necessary for simulating radiant heat transfer;
therefore, it is difficult to simulate a thermal zone with any type of curved and/or double-curved
surfaces in E+. Such geometric limitations force the designer to manually oversimplify the design's
geometry whenever an energy simulation is needed. Although energy modeling experts have
streamlined the manual simplification of model geometry, there are inevitable consequences of this
approach: (i) the geometric gap between the energy model and any other model, which simultaneously
confuses the relationship between geometric features and energy performance and hinders the
integration of building energy performance considerations in the multi-objective optimization process
[23, 24]; (ii) the loss of accuracy, which is more relevant if the building uses passive solar design
strategies and has an envelope with a significant amount of self-shaded surface area; (iii) the loss of
complex parametric modeling as a tool in goal-oriented design, as manual adjustment of an inherently
automated process compromises the value of the automation.
2. Goals and envisioned solution
This work proposes an automatic and robust method of deriving BEM from fully parametric building
models, thus providing a method to efficiently and accurately generate parametric energy models
during a goal-oriented design process. Automatically deriving BEMs from their
parametric/architectural counterparts allows designers to directly use energy-based generative design
processes without the use of intermediary simplified models. This will facilitate the integration of
building energy performance in multi-objective PGDS, which are generative design systems that have
more than one performance objective . For example, a multi-objective PGDS might optimize a
design for both structural and energy performance. The proposed automation will also reduce the
current gap between the different model representations of the same design, thereby strengthening the
relationship between them. For example, if the relationship between the BEM and the parametric
model is bidirectional, visualizing the impact of design changes for energy performance optimization
during the goal-oriented design workflow becomes a trivial task.
To achieve the goal of deriving a thermal model from a 3D model of a design, the proposed method
combines current techniques used in digital fabrication and remeshing with energy modeling ones.
Thus, mesh planarization algorithms will be used to generate discrete meshes from double curved
Non-Uniform Ratio Basis Spline (NURBS) surfaces. The resultant meshes may be easily exported to
E+. Applying such algorithms minimizes the differences among the geometries of the parametric
model, the digital fabrication model, and the energy simulation model. In this way, one model can
directly inform the next.
Because mesh planarization algorithms are also used in digital fabrication, the envisioned goal-
oriented design approach focuses both on energy performance and on construction feasibility. In this
particular study, the approach is applied to the study of glass fritting patterns for the envelope of all-
glass thermal zones with curved and complex envelopes. The theme of a complex curved all-glass
building was selected because it presents at the same time construction obstacles, where planar glass
panels are desirable due to cost constrains, and a difficult thermal problem. In this test case, the
algorithms search for appropriate shading frit patterns, and adapt the emergent forms within pre-
defined boundaries and rules until buildable forms are identified (e.g., maximum glass panel size and
deviation from the original surface). The proposed integration of mesh planarization methods with
energy performance-based design is illustrated in Figure 1.
Figure 1 – Workflow diagram of the proposed energy based generative design system. From an initial surface, a
mesh based on planar quad meshes is produced both for fabrication and energy simulation. The Genetic
Algorithm (GA) search process will optimize the fritting density of the fabrication model glass panels.
In the proposed workflow, planarization algorithms, available in Kangaroo Grasshopper’s add-on
package, process an initial freeform geometry. The result is a mesh composed of planar quads with
constraints applied to their maximum dimensions. Each planar quad corresponds to a planar glass
panel with maximum size of a standard double glass panel: 3x3 m. This model corresponds both to a
model, where all the glass panels are ready for digital fabrication, and a geometry model that can be
directly fed to E+ and Radiance by assigning specific E+ and Radiance materials to each panel.
Radiance is used to map solar radiation on the building envelope and, in turn, clusters facade panels
by the amount of radiation they receive. The proposed workflow uses Honeybee as the E+ interface
and DIVA for Grasshopper as the interface for Radiance. A Genetic Algorithm (GA) controls the frit
density assigned to each panel cluster. In this way, the GA searches for the best fritting densities for
each solar exposure. Finally, when the GA converges, the resultant frit pattern is remapped on the
digital fabrication model. Through this loop, a single architectural geometric representation is
informed by two parameters: construction and energy consumption.
3. Related Work
Recent development in energy modeling has improved the automation of thermal zoning in BEMs
[26, 27, 28, 29, 30, 31]; however, such improvements have been limited to simple geometry. Already
faceted geometries are the most complex cases found in the literature. A review of existing modeling
approaches finds that the parsing of curved surfaces from a CAD or BIM model to a BEM is limited
to standard triangulation algorithms, which allow only limited control and do not follow energy
modeling best practices. Such approaches are found in Ladybug/Honeybee and Green Building Studio
In fact, although possible, perfectly curved forms are relatively rare in architectural design. In most
cases, the curved surfaces that are built are faceted approximations. The infrequency of perfectly
curved structures is typically attributed to their high construction costs, particularly for steel and glass
construction. The only exceptions to this are certain types of concrete building technologies (e.g.;
concrete elements that use metal or polymer based frameworks). Thus, it is reasonable to think that
the modeling problem in goal-oriented design for energy performance could be addressed as a
construction problem where the planarity of the elements is desirable. This is a common research
topic in architectural geometry and digital fabrication [32, 33, 34, 35].
In its search of construction approaches for double-curved geometry based on planar elements, recent
research in digital fabrication applies developments in mathematics around quadmesh quasi-
planarization [36, 37]. To obtain a planar quadrilateral subdivision of any given surface, quasi-
isothermic remeshing algorithms are used to transform a given mesh into a S-isothermic quadrilateral
mesh. A quadrilateral mesh is S-isothermic if: (i) all the quadrilaterals are planar, (ii) all faces have
incircles, and (iii) the incircles of adjacent quadrilaterals touch. Figure 3 illustrates the concept of a
quadrilateral mesh and how the quasi-isothermic algorithm remeshes a given mesh into a planar quad
mesh. Sechelmann et al., describes in more depth the algorithmic approach to create S-isothermic
quadrilateral meshes in .
Figure 2. Left: incircles of a non S-isothermic quad mesh. In order to be S-isothermic the incircles of adjacent
meshes need to touch. This produces the same ratio on both sides of the edge ij; cot(βi/2)/cot(βj/2) . Right:
examples of S-isothermic quad meshes generated by the algorithm proposed by .
Figure 3 shows a pavilion that used a similar planarization approach; however, this example departs
from the concept of S-isothermic in-circles through periodic conformal maps [37, 38]. Conformal
maps can extend the panelization from quad planar panels to hexagonal ones. Because these
algorithms can remesh an original surface into a set of planar and convex panels, while
simultaneously controlling how the remeshing is done, the resultant geometry can be simulated in E+
if assigned a proper E+ construction assembly to it.
Figure 3. The Landesgartenschau Exhibition Hall was designed and constructed resorting to surface discrete
planarization algorithms. 
The proposed goal-oriented design system was applied to a case study composed of three glass
pavilions in order to test and validate the approach. The tested pavilions were variations of a semi-
ellipsoid with a 30 m primary axis, a 15 m secondary axis, and a 7.5m height. In each case, the
primary axis was oriented due North-South. The poles of this base geometry were cut to provide two
entrances on the North and South ends. This constitutes solution A. Solution B is a deformation of
solution A, in which the section along the primary axis was rescaled to create a “peanut” shape to
promote self-shading and to create a different solar radiation pattern. As discussed in section 1, a
different irradiance distribution not only affects the overall energy consumption of the solutions but
also the optimized frit pattern/density on the envelope. Solution C is the result of the deformation of
the main meridians of the ellipsoid, which were varied for the same reasons as solution B. Figure 4
shows the initial NURBS geometry of all the solutions of the case study. Table 1 reports the floor
area, surface area, volume, and form factor (surface to volume ratio) of each pavilion.
Figure 4. The base semi-ellipsoid and the three pavilions derived from it.
Floor Area (m2)
Surface area (m2)
Table 1. Floor area, volume, surface area, and form factor of each solution.
Although the workflow proposed in section 2 could be applied to any complex building shape, it was
only tested in these three scenarios due to the prototypal nature of this work. The goal was to perform
a set of initial tests that verifies the efficacy of the proposed method. Thus, the three t scenarios
represent different degrees within a range of potential geometric complexity for the same type of
building. Although they share the same archetypal form, the surface-to-volume ratios (form factors),
solar radiation distributions, and self-shading patterns are unique for each solution. Solution A
presents a surface of revolution of a simple arc, with a homogeneous, gradient-based solar radiation
distribution and with the smallest form factor of the three examples. The double curvature of solution
B’s revolution profile increases its form factor while introducing more variation in solar radiation
distribution and self-shading patterns. Finally, solution C presents a higher level of geometric
complexity while maintaining the same form factor. Its meridional section varies along the revolution
path, which generates a double curved surface that is difficult to discretize in planar quad meshes.
Finally, the workflow was implemented as an integrated dynamic model (IDM) . An integrated
dynamic model can be defined as a combination of a design tool, a visual programming language
(VPL), and a building performance simulation software (BPS). The IDM paradigm was selected
because it provides valid feedback, it is extremely flexible to accommodate rapid design changes, and
it allows the user to have full control on every step of the process . Thus, the Rhino CAD platform
environment was selected because it offers a wide range of tools that fully support the implementation
of IMDs, namely: (1) dedicated modeling tools, (2) a well developed and known VPL, Grasshopper,
which can be extended by other high-level languages such as Python, and (3) several interfaces to
EnergyPlus and Radiance, such as DIVA and Honeybee. This CAD platform was also important in
the implementation of the proposed workflow because it provides several add-ons for mesh
manipulation, such as Kangaroo , and several evolutionary solvers such as Galapagos and
Each solution was panelized and planarized using Kangaroo Physics 2.0 , a dynamic physics
simulator for Grasshopper that uses the planarization algorithms discussed in section 3. The number
and size of the glass panels (quadmeshes) was controlled by a small grasshopper script that divides
the original surface along its width (u) and length (v), directions and informs the user about the
dimensions of the largest and smallest glass panel. After this step, the NURBS surface was
transformed into a mesh and planarized using Kangaroo 2.0. Finally, the planarity of each panel was
tested by a grasshopper procedure made specifically for such a test. If the planarity test returns “true”
for all quad mesh panels it validates Kangaroo's remeshing settings, and the energy simulation can be
run. Figure 5 illustrates both the original surfaces and the resulting planar quad meshes computed by
Kangaroo, which constitute both the construction/fabrication model for the glass panels and the
geometric model for E+. Figure 6 shows the output from both the panel sizing algorithm and the
planarity test of a non-optimized quad mesh composed of 120 panels.
Figure 5. Original surfaces and the resulting S-isothermic planar quad meshes. The processed meshes are ready
to be fed to E+.
Figure 6. Left: the design system informs the user about the location and the dimensions of the biggest (orange)
and smallest (purple) glass panel. In this way, the user can assess if the surface rationalization is feasible from a
construction point of view. Right: planarity test of an intermediary step of the planarization process. The red
color flags non-planar quadmeshes, while the green color indicates planar ones.
The fritting density of the glass panels was modeled as an E+ shading object; thus, every panel had a
scalable centered opaque shading object. By scaling every shading object, it was possible to infer the
fritting percentage applied to each glass panel. This was the only simplification used to reduce
simulation time without compromising accuracy. The system then reprocessed the simplified shades
back to the digital fabrication model as fritting patterns through a dedicated set of scripted functions
that allows the user to control the size and shape of the frit pattern. Figure 7 shows the energy model
with shading objects equivalent to a fritting density of 60% and their translation to a possible fritting
pattern within the digital fabrication model.
Figure 7. E+ shading objects (60% shading ratio) and their remapping to a possible glass fritting pattern.
4.2 Simulation and optimization process
In the reported test case, the energy and solar radiation simulations were performed with E+ and
Radiance using the climate file of Logan International Airport, Boston, USA. Although a cold
climate, Boston experiences hot and humid summers; thus, it provides a useful climate to test both
winter and summer conditions. Summer thermal performance was of particular importance because
the proposed system aims for the optimization of shading, a passive cooling strategy.
The material used for the envelope was triple low-e glazing with argon. This type of glazing was
chosen for its high thermal performance, specifically its low thermal conductivity (U-factor). The
frame and structure of the glass was modeled as aluminum. Finally, the ground floor was modeled as
a heavyweight concrete slab. Before running a whole building energy simulation with E+, a solar
radiation analysis with Radiance was conducted for each panel. A sensor node was placed in the area
centroid of each panel. The value registered by the sensor node was remapped into a color that was
applied to the corresponding panel quad mesh. The panels were then clustered according to their
irradiance values. The grouping of the panels is based on solar radiation similarity. Table 2, shows the
five groups of panels that were generated for each design alternative according with their irradiance
range. This clustering process avoids panel-by-panel optimization, minimizing the number of design
variables controlled by the GA. Although this strategy constrains the design solution space it
facilitates the search process without losing too much granularity. Finally, Grasshopper’s Galapagos
standard GA controlled the shading fraction of each cluster aiming towards the minimization of the
overall energy consumption. Figure 8 shows the annual solar radiation on the envelope of each
pavilion and illustrates how the panels were clustered in groups of similar solar irradiance (SR).
417 - 661
661 - 905
905 - 1148
1148 - 1392
1392 - 1636
593 - 804
804 - 1015
1015 - 1225
1225 - 1436
1436 - 1647
830 - 987
987 - 1143
1143 - 1230
1230 - 1456
1456 - 1613
Table 2. Clusters of glass panels per solution and their irradiance range (kWh/m2).
After clustering the glass panels by solar radiation, a whole building energy assessment was
performed with E+. The main simulation assumptions and settings used were: (i) simplified variable
air volume (VAV) HVAC system to calculate sensible cooling and heating loads and energy
consumption for space conditioning; (ii) heating setpoint set to 20 Cº and cooling setpoint set to 26
Cº; (iii) infiltration rate of 0.3 air changes per hour (ACH), which represents an airtight building; (iv)
a power density for light fixtures of 11.4 W/m2 (a typical value for fluorescent bulbs); and finally (vi)
an illuminance setpoint of 300 lux to control the dimmable lighting system used in the model.
Figure 8. Up: annual solar radiation mapped in the envelope of the three pavilions. Down: the five glass panel
clusters based on the annual irradiance of Boston, MA.
Three main energy uses were considered and reported: heating, cooling, and lighting. Equipment
loads were excluded because they do not depend on environmental factors or on building envelope
characteristics but on the type of equipment used and occupancy schedules. The total energy
consumption reported is the sum of hourly heating, cooling, and lighting energy consumption. Due to
the differences in area and in volume between the different alternatives, Energy Use Intensity (EUI)
per area unit (EUI - kWh/m2), and per volume unit, (EUI(v) - kWh/m3), were the energy metrics used
to assess results. Finally, the performance-based design exploration included two main tasks:
1) An annual parametric study of different shading conditions – Before setting an automatic
optimization procedure for shading/fritting density, three different shading ratios were annually
simulated in order to better understand the baseline energy profile of the three pavilions. The different
shading alternatives were: (i) no shading (base case); (ii) 40% evenly distributed shading; and (iii) a
shading gradient that is distributed according with solar radiation (SR) measurements (Table 3):
0 to 20% of
20 to 40% of
40 to 60% of
60 to 80% of
80 to 100% of
% of shading
Table 3. Gradient shading alternative - percentage of shading/glass fritting according to solar radiation.
By simulating different forms with similar areas and volumes, we can assess how form affects solar
irradiation and total energy consumption, as well as the impact of different shading schemes in the
overall energy profile of each case.
2) Optimization of shading/fritting percentage for cooling energy consumption – Because shading is a
cooling strategy, an optimization cycle was performed, which was informed by the lessons learned in
the parametric study. The summer period considered for the optimization was May 20th to September
21st, including thus the end of the mid-season and the whole summer.
Results are grouped in the two sections: (i) Parametric study of different shading conditions; and (ii)
Optimization of shading/fritting percentage for cooling energy consumption.
5.1 Parametric study of different shading conditions
Figures 8, 9, and 10 illustrate the annual solar radiation analysis for Boston, and the three different
shading strategies applied for each solution in this analysis stage. The solar radiation analysis
presented in Figure 8 shows how different forms present different distributions. These differences
directly result from the geometric differences in tilt, angle, and self-shading patterns among the three
tested forms. Thus, although these tested forms derive from the same archetypical geometry, their
annual irradiance distributions are sufficiently diverse to result in mutually unique shading patterns.
Figure 9 illustrates the resultant shading pattern given a desired homogeneous shading factor of 40%
per panel. In contrast, Figure 10 shows the shading pattern given a gradient shading strategy based on
solar radiation values, where incident radiation acts as an attractor/repeller that controls the amount of
shading for each cluster of panels.
Figure 9. 40% homogeneous shading distribution across the three design alternatives modeled with E+ shading
Table 4 reports both the EUI and EUI(v) of each solution. Figures 11 and 12 shows a bar chart that
compares the energy performance of each of the tested design alternatives in terms of EUI (kWh/m2)
and EUI(v) (kWh/m3). As shown in the graphs, solution A requires the most heating energy, which
can be attributed to this form’s small solar exposure on its north facade. Solutions A and B have
similar irradiance distributions on their north facades; however, solution B compensates for the
associated heat losses via two south-facing areas that receive high solar gains. Solution C has the
lowest heating energy consumption of the three test cases. This can be attributed to this form’s more
uniform solar radiation distribution, which reduces the contrast between heat losses and gains. In all
cases, shading is effective in reducing cooling loads, but it also increases the heating demands. The
gradient shading solution is the most effective in reducing cooling energy consumption, which
supports the intuition that the panels that need more shade are the ones that receive more solar
radiation. Lighting energy consumption varies slightly among the three scenarios; however, these
differences are insignificant relative to those of the space conditioning end-uses. This is explained by
the consistently high amount of glazing across all solutions and each solution’s success in blocking
direct sun while still allowing diffuse light, which minimizes lighting energy needs with relative
Figure 10. The gradient shading solution modeled with E+ shading objects.
EUI - kWh/m2
EUI(v) - kWh/m3
Table 4. EUI and EUI(v) of each solution.
Figure 11. Annual EUI (kWh/m2) of the different design alternatives.
Figure 12. Annual EUI(v) (kWh/m3) of the different design alternatives.
Figures 11 and 12 show that the significant reduction of cooling energy consumption provided by the
gradient solution does not compensate in terms of heating in solution A. From this more holistic
perspective, the 40% homogeneous shading solution is slightly more efficient, as indicated by its
lower EUI and EUI(v).
Regarding solution B energy profile, the gradient shading scheme is the most energy efficient solution
overall. It reports an improvement of 11% when compared to the no shading scheme. This is because
the difference between heating and cooling loads in the unshaded case is smaller than in solution A.
Like solution A, the heating demand is higher for the shaded conditions than for the base case, but
unlike solution A, the reduction in cooling demand is sufficiently compensates for the higher heating
loads. Finally, solution C shows a similar profile to solution B but is less efficient.
This parametric study shows that providing a fixed shading system to a specific all-glass building
geometry can be effective year-round, even in a climate like Boston. Even in solution A, the
experiment shows that with a homogeneous 40% shading ratio we can improve the overall energy
consumption. This supports the choice to run the optimization cycle only for the summer period in
order to find the best shading strategy.
5.2 Optimization of shading/fritting percentage for cooling energy consumption
Two fully automated search procedures were conducted using Galapagos’ standard GA. The first,
Opt#1, was conducted without any restrictions to the parameters that control the amount of shading
for each group of panels receiving the same irradiance range. The second, Opt#2, was conducted with
some constraints assigned to those parameters, which aimed to promote a gradient shading pattern or
at least to minimize shading to panels that receive less solar radiation. In order to optimize the shading
strategy the optimization was constrained to end of spring, May 20th, to the end of summer,
Figures 13 and 14 show the results of Opt#1. Figure 14 shows the remapping of shading ratio,
presented in Figure 13, to a frit pattern. The Opt#1 solution is counterintuitive because it provides
more shading to the panels that receive less solar radiation. To reduce cooling loads, the GA blocks
the panels with the largest area, except the ones that are more exposed to the sun. Nevertheless, this
simulation indicates that the GA probably found a local minimum and that the process needed more
Figures 15 and 16 show the results of Opt#2. Figure 16 presents the frit pattern of the shading
percentage shown in Figure 15. With the extra guidance provided by the constraints, the GA found a
more expectable solution that places the higher shading ratio in the areas that report higher irradiance
Table 5, figures 17, and 18, compare the energy performance of each design solution for no shading
(baseline), Opt#1, and Opt#2 for the time period under study. The charts show that Opt#2 is extremely
effective in solution A, slightly effective in solution B and not as effective as Opt#1 in solution C.
However, the results of solution A and B show that steering the optimization process through
constraints on the parametric model based on initial analysis can lead to better results that are more
energy efficient and closer to the designer’s intents. In summary, the GA was able to find more
efficient shading strategies that could improve the energy performance of the all glazing pavilions in
the summer period.
Figure 13. Opt#1 shading solution with E+ shading objects.
Figure 14. Opt#1 shading ratio remapped as a fritting pattern. Shading ratio label indicates the average.
Figure 15. Opt#2 shading solution with E+ shading objects.
Figure 16. Left: Opt#2 shading ratio remapped as a fritting pattern. Shading ratio label indicates the average.
Right: Examples of fritting patterns generated with the remapping algorithm. All of the three options has the
same shading ratio, 70%.
Table 5. EUI and EUI(v) of each solution for no shading, Opt#1, and Opt#2.
Figure 17. EUI (kWh/m2) of the different design alternatives of the optimization experiment.
Figure 18. EUI (kWh/m2) of Solution A for no shading, Opt#1, and Opt#2 alternatives.
The parametric study tested three shading scenarios for each of the three solutions: no shading, 40%
homogeneous shading for the glass panels, and a gradient shading approach based on solar radiation
incident upon the building envelope. The goal was to test the efficacy of a shading strategy based on a
fritting pattern in Boston, Massachusetts over one year. Boston experiences all seasons. The summers
are warm to hot and humid, with periods that can exceed 32 ºC, while winters are cold, with freezing
temperatures from November through the end of March. Typically, Boston’s climate is heating-
dominated, but because it also experiences hot and humid summers, cooling loads are relevant in this
period. That is why shading is an important passive strategy for a whole glass pavilion in this climate.
The annual parametric simulations show two different patterns. Table 4, Figure 11, and Figure 12,
show that heating loads clearly dominate solution A, while in solutions B and C, the difference
between heating and cooling loads is much smaller. There are several reasons for this, but it seems
that the relationship between surface area and volume plays a relevant role. Because it has the largest
volume of the three, solution A has the largest volume of air to heat; simultaneously, it has the largest
surface area of the three solutions, which means that it has the most envelope heat loss. The result is
significantly higher heating than cooling loads.
Because solution A does not have self-shading and has more exposed surface area, it also requires a
higher percentage fritting in the glass panels in the gradient shading scenario. This eventually blocks
desired solar heat gains in the winter, which also contributes to the relatively high heating loads. That
is why the gradient shading scenario is the only one where shading is unfavorable. The volumes and
surface areas of solutions B and C are smaller; therefore, they require a smaller heating load and
experience less heat dissipation than does solution A. Self-shading and/or a more even distribution of
solar radiation on the envelopes of solutions B and C help distribute a more balanced frit pattern in the
gradient shading scenario. This experiment also demonstrates that the optimization of individualized
fritting patterns in glass panels requires a geometrically accurate energy model.
Table 6 shows the percentage of improvement of EUI by adding shading to the glass pavilions. It is
clear that shading is a beneficial a passive strategy year round for an all-glass pavilion in Boston.
Even solution A sees a small benefit from 40% homogeneous shading in its glass panels, which
indicates that shading can be an effective passive design strategy to reduce energy consumption in
cases with a large exposed surface area. The table also shows that deriving a shading pattern based on
solar radiation distributions can be more efficient than using homogeneous shading factors. These
results reinforced the need of the second set of tests that aimed to optimize the glass fritting in each
% of improvement
(Base case: No shading)
% of improvement
(Base case: 40% homogeneous
Table 6. Percentage of improvement in energy consumption of the parametric study of different shading
conditions. The percentage of improvement was calculated for: (1) 40% homogeneous shading and the gradient
shading against no shading; (2) gradient shading against 40% homogenous shading.
Because shading is a passive cooling strategy, the goal of the second set of tests was to determine the
efficacy of glass fritting as a cooling strategy. Thus, the optimization was constrained to the warm
months in Boston. As previously described in section 5.2, two optimization procedures were
performed in the second set of tests. The first, Opt#1, was conducted without constraining the amount
of shading for each group of panels receiving the same range of solar radiation. Figure 13 shows that
the shading optimization prioritizes the area size of the panel clusters instead of the amount of solar
radiation incident upon the building envelope. To test if the strategy adopted by the GA in Opt#1 was
optimal, a second optimization procedure was conducted that imposed a more direct relationship
between incident solar radiation and the amount of fritting.
% of improvement
(Base case: No shading)
% of improvement
(Base case: Opt#1)
Table 7. Percentage of improvement of energy consumption in the optimization study. The percentage of
improvement was calculated for: (1) Opt#1 and Opt#2 against no shading; (2) Opt#2 against Opt#1.
Table 7 compares both Opt#1 and Opt#2 to a non-shaded base case, as well as to each other. The
automated search procedure provided by the GA was able to considerably reduce the overall energy
consumption of the non-shaded base cases. As expected, the optimization produced a high
improvement in solution A in both optimization procedures. This is related to the fact that solution A
has the largest surface area and, consequently, the most exposed envelope of the three scenarios.
Comparing the two optimization strategies, constraining the search procedure to promote a gradient
shading pattern based on the solar radiation distribution yields better results in solutions A and B. In
solution A, Opt#2 was able to find a solution that is 18% better than the Opt#1. In the case of solution
C, Opt#2 found a worst solution than Opt#1. This indicates that the success of steering the search by
imposing Opt#2 constraints is closely related to the amount of exposed surface area. Thus, the poor
performance of Opt#2 in solution C could be related to that scenario’s lower solar radiation variance,
which makes this option a less suitable candidate for a gradient-based shading approach.
This work proposed a new, goal-oriented design approach, which integrates multiple 3D
representations of a building into a single parametric model that may be optimized for multiple
parameters, including energy efficiency. The proposed approach uses planarization methods, which
have been developed and applied in digital fabrication, to overcome the limitations of energy
modeling of curved and double curved geometries. This allows to automatically generate the
geometry of an energy model from a complex 3D CAD model, thus, avoiding time consuming
manual modeling tasks that are incompatible with fully automated optimization workflows.
Because the planarization algorithms are accessible, the user can directly specify how the
discretization of the original surfaces is performed, therefore controlling the degree of detail of the
energy model. The proposed approach also minimizes the gap between construction model and
thermal model by using the geometry of the first as an input to the second. Only the shades are
modeled differently for energy simulation. To solve this discrepancy, a dedicated algorithm remaps
the most thermally effective shade into a fritting pattern. Synchronized or shared models in
performance-based generative systems improve and streamline the feedback between energy
simulation and architectural design. In this way, energy simulation can easily inform the construction
model and vice-versa.
The use of planarization algorithms to optimize an original free form also indicates a high potential
for model integration in multi-objective goal-oriented design methods, where the automated search
process aims to simultaneously optimize different aspects of a single design.
The results showed the usefulness of goal-oriented methods to fully understand the complex trade-offs
associated with energy-related problems in buildings. Unexpected results from these methods could
inform the design process with new perspectives and different solutions to solve specific design
problems. The two optimization procedures showed how an accurate geometry can be important in
energy optimization workflows. Optimizing the fritting density of different glass panel clusters of the
same building envelope requires a detailed energy model that can simulate self shading and variable
solar radiation distribution patterns. This is hard to incorporate in the typical oversimplified box-based
energy models. The optimization experiments also showed that in some cases steering the
optimization process, by constraining certain design parameters, can improve the quality of the search
procedure. Finally, the experiments also showed how the energy performance approach can actually
inform the physical and aesthetic properties of the building envelope with different densities of
In sum, the generative-design system prototype proved to be:
• Robust – it was able to automatically translate a diversity of double-curved building
geometries to E+.
• Adaptable – by allowing the user to control the generation of the BEM model and steer the
optimization process through the use of constraints.
• Reliable – it found energy efficient passive solutions that resulted in percentages of
improvement of almost 70%.
The limitations of the proposed methodology are mostly related with simulation computational time.
There is direct correlation between the number of panels and simulation time, meaning that the higher
the number of panels, the higher the simulation computational cost due mostly to view factor
calculations for E+ radiant heat transfer computation. Another limitation is related with steering the
GA search procedure. The Opt#1 experiment shows that the GA probably got stuck in a local
minimum. This problem can be related with the type of GA used, Galapagos standard GA. In future
work, it will be worthy to test more sophisticated and robust GAs, such as SPEA2  commonly
used for multi-objective problems.
In order to further develop the proposed methodology, future work should focus on:
1) Test the GA results against a problem with a known optimal value - this step would
measure and validate the search mechanism accuracy.
2) Comparing different evolutionary solvers - this would inform the methodology about the
trade-offs between speed and quality of several search mechanisms, thus helping in the
selection and the setting of the parameters of the most suitable evolutionary solver.
3) Extend the proposed methodology to multi-zone models. Due to the prototypal nature of
this work only single zone models of a specific building type were tested. Extending the work
to more complex multi-zone models of different building types would improve the
methodology regarding its applicability and generalization.
4) Modeling the fritting panels as Bidirectional Scattering Distribution Function (BSDF)
based materials – this would improve accuracy and simulation time.
5) Adding more details to the fabrication model, such as structure and variable thicknesses –
to test how flexible is the method to contemplate more building design disciplines and their
respective representational models.
6) Extending the methodology to multi-objective optimization generative design systems
where, for example, structural optimization and construction cost are contemplated.
Work presented in this paper was partially financed by the Portuguese Science and Technology
Foundation (FCT) through the PhD scholarship SFRH/BD/98658/2013. The authors would
like to thank Sara Tepfer for her precious collaboration and help.
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