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<journal-id journal-id-type="publisher-id">Front. Built Environ.</journal-id>
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<journal-title>Frontiers in Built Environment</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Built Environ.</abbrev-journal-title>
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<issn pub-type="epub">2297-3362</issn>
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<article-id pub-id-type="publisher-id">1753356</article-id>
<article-id pub-id-type="doi">10.3389/fbuil.2025.1753356</article-id>
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<subj-group subj-group-type="heading">
<subject>Original Research</subject>
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<title-group>
<article-title>Adaptive high-performance and multifunctional fa&#xe7;ade systems</article-title>
<alt-title alt-title-type="left-running-head">Matheou et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fbuil.2025.1753356">10.3389/fbuil.2025.1753356</ext-link>
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<name>
<surname>Matheou</surname>
<given-names>Maria</given-names>
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<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>&#x2020;</sup>
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<contrib contrib-type="author">
<name>
<surname>Phocas</surname>
<given-names>Marios C.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<contrib contrib-type="author">
<name>
<surname>Christoforou</surname>
<given-names>Eftychios G.</given-names>
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<xref ref-type="aff" rid="aff3">
<sup>3</sup>
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<contrib contrib-type="author">
<name>
<surname>M&#xfc;ller</surname>
<given-names>Andreas</given-names>
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<xref ref-type="aff" rid="aff4">
<sup>4</sup>
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<aff id="aff1">
<label>1</label>
<institution>Institute for Lightweight Structures and Conceptual Design, University of Stuttgart</institution>, <city>Stuttgart</city>, <country country="DE">Germany</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>Department of Architecture, University of Cyprus</institution>, <city>Nicosia</city>, <country country="CY">Cyprus</country>
</aff>
<aff id="aff3">
<label>3</label>
<institution>Department of Mechanical and Manufacturing Engineering, University of Cyprus</institution>, <city>Nicosia</city>, <country country="CY">Cyprus</country>
</aff>
<aff id="aff4">
<label>4</label>
<institution>Institute of Robotics, Johannes Kepler University</institution>, <city>Linz</city>, <country country="AT">Austria</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Maria Matheou, <email xlink:href="mailto:matheou.maria@ucy.ac.cy">matheou.maria@ucy.ac.cy</email>
</corresp>
<fn fn-type="equal" id="fn001">
<label>&#x2020;</label>
<p>
<bold>Present address:</bold> Maria Matheou, Department of Architecture, University of Cyprus, Nicosia, Cyprus</p>
</fn>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-01-28">
<day>28</day>
<month>01</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>11</volume>
<elocation-id>1753356</elocation-id>
<history>
<date date-type="received">
<day>24</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>28</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>30</day>
<month>12</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Matheou, Phocas, Christoforou and M&#xfc;ller.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Matheou, Phocas, Christoforou and M&#xfc;ller</copyright-holder>
<license>
<ali:license_ref start_date="2026-01-28">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>Adaptive, high-performance and multifunctional fa&#xe7;ades are recognized as key contributors to the EU&#x2019;s climate-neutral agenda, as outlined in Directive (EU) 2024/1275, the Renovation Wave, and Horizon Europe initiatives. These systems provide environmental control (daylight, shading), serve as an interface between indoor and outdoor environments and minimize reliance on heating, cooling and artificial lighting systems, enhancing energy efficiency and occupant comfort. In addressing this challenge, this paper presents the design and prototyping of three adaptive fa&#xe7;ade typologies aiming to combine a multifunctional role of controlling, redirecting and/or harvesting solar radiation. Designed through a performance-driven, integrated design methodology, aspects of morphology (system composition, geometrical characteristics), materiality and embedded actuation are discussed along with daylighting and irradiance analyses. To analyze their potential for visual comfort (daylight quality, glare, view to the outside) and solar harvesting, simulation studies were conducted for four distinct climatic conditions, corresponding to each case study using Climatestudio and Ladybug plug-ins for Grasshopper/Rhino 3D. Each fa&#xe7;ade is evaluated in its climatic context and the outcomes are synthesized through a cross-case comparative framework that links climate driver, performance objective, and actuation-feasible states. The first fa&#xe7;ade system uses a retroreflector&#x2019;s geometry to redirect solar radiation back toward its source, potentially reducing short-wave radiative loading near the fa&#xe7;ade by redirecting incident radiation toward the sky, while cable-driven actuation allows multiple folded states. The second system reinterprets static folding geometries, the so-called &#x201c;Hortenkachel&#x201d; into a kinetic shading system of translucent panels. The third prototype introduces rectangular photovoltaic modules supported by a cable net and strut framework facilitating solar tracking. All case examples are based on lightweight construction principles and mechanical simplicity in their kinematics. Prototypes complement the simulation studies and provide proof-of-concept validation for the kinematic behaviour of the adaptive high-performance fa&#xe7;ade systems. The novelty lies in (i) extending retroreflective optics into a kinetically reconfigurable fa&#xe7;ade for controlled solar-radiation redirection near the fa&#xe7;ade, and (ii) extracting transferable design principles across three typologies that refer to morphology, control logic, and multi-criteria performance (daylight, glare, view, radiation/energy). The reported fa&#xe7;ade states, performance ranges, and prototype strategies provide an archival benchmark for early-stage adaptive multifunctional fa&#xe7;ade design.</p>
</abstract>
<kwd-group>
<kwd>adaptive fa&#xe7;ades</kwd>
<kwd>architectural design</kwd>
<kwd>daylight performance</kwd>
<kwd>parametric workflow</kwd>
<kwd>reconfigurable structures</kwd>
<kwd>renewable energy</kwd>
<kwd>visual comfort</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. The project was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project-ID 279064222&#x2014;SFB 1244, and by the A.G. Leventis Foundation grant funded to the University of Cyprus, ABEPH 2022.</funding-statement>
</funding-group>
<counts>
<fig-count count="20"/>
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<ref-count count="41"/>
<page-count count="24"/>
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<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Sustainable Design and Construction</meta-value>
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</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>The origins of adaptive fa&#xe7;ades can be traced back to the 1960s, when sweeping societal shifts related to culture, technological advancement, and environmental awareness converged with the energy crisis of the 1970s, stimulated innovations in building envelope design (<xref ref-type="bibr" rid="B36">Moloney, 2011</xref>). During this period, cybernetic theory gained attention as a framework for conceiving the building envelope not as a static element but as an active, interactive system capable of responding dynamically to environmental stimuli and occupant needs (<xref ref-type="bibr" rid="B13">Fortmeyer and Linn, 2014</xref>; <xref ref-type="bibr" rid="B26">Kolarevic and Parlac, 2015</xref>). This theoretical foundation laid the groundwork for high-performance and multifunctional systems integrating active control mechanisms, sensors, and actuators to regulate multiple factors such as solar gain, thermal transmission, and daylight access (<xref ref-type="bibr" rid="B14">Fox and Kemp, 2016</xref>).</p>
<p>High-performance fa&#xe7;ades are building envelopes designed to optimize energy efficiency, indoor environmental quality and occupant comfort, while minimizing environmental impact and operational costs (<xref ref-type="bibr" rid="B1">Aksamija, 2013</xref>). In the EU context, such envelopes support the climate-neutral building agenda in Directive (EU) 2024/1275, the Renovation Wave and Horizon Europe. In parallel, the concept of multifunctionality in fa&#xe7;ades has become increasingly significant, emphasizing the integration of multiple environmental and energy-related functions within a single envelope component. These solutions combine thermal insulation, solar control, daylight control and renewable energy generation. Foundational fa&#xe7;ade-performance framing is given by <xref ref-type="bibr" rid="B38">Perino and Serra (2015)</xref> and <xref ref-type="bibr" rid="B12">Favoino (2015)</xref>, while <xref ref-type="bibr" rid="B34">Matin et al. (2018)</xref> and <xref ref-type="bibr" rid="B44">Shahin (2019)</xref> provide comparative overviews of responsive/adaptive fa&#xe7;ade technologies and high-performance envelope strategies; recent work further advances multifunctional adaptive concepts through integrated actuation and performance workflows (<xref ref-type="bibr" rid="B17">Gonzalez et al., 2023</xref>).</p>
<p>The integration of photovoltaic (PV) technology with shading systems marks a significant advancement in multifunctional fa&#xe7;ade design, particularly in the context of Building-Integrated Photovoltaics (BIPV) (<xref ref-type="bibr" rid="B49">Zhang et al., 2018</xref>). Photovoltaic-integrated shading devices (PVSDs) evolved as multifunctional components that simultaneously generate electricity and provide solar protection strategies (<xref ref-type="bibr" rid="B8">Corti et al., 2023</xref>). For instance, PV louvers and brise-soleil systems not only harvest solar energy but also regulate solar heat gain and daylight penetration inside buildings, optimizing thermal comfort and energy usage (<xref ref-type="bibr" rid="B29">Liang et al., 2024</xref>). Through simulation studies, the research in <xref ref-type="bibr" rid="B23">Jafari and Salavatian (2023)</xref> demonstrates that PVSDs designed with optimized configurations can achieve energy efficiency ratings of 35.54%, providing critical evidence of their dual functionality. The study shows how PVSDs regulate sunlight penetration while saving energy and producing electricity simultaneously, making it a practical application example.</p>
<p>Climate change pressures and decarbonization targets further accelerate the adoption of adaptive and energy-positive fa&#xe7;ades driven by PV integration and other environmental control strategies. More broadly, such adaptive fa&#xe7;ade strategies extend their influence from the building scale to the wider urban microclimate. Adaptive fa&#xe7;ades mitigate urban heat island (UHI) impacts through multiple mechanisms, including the use of shading devices to limit solar absorption, application of reflective and high albedo materials to reduce heat retention, and incorporation of green fa&#xe7;ades to promote evapotranspiration and cooling. By dynamically modulating solar heat gain and surface temperatures in response to weather and urban conditions, adaptive fa&#xe7;ades optimize their contribution to urban thermal comfort and reduce heat load at building and district scales (<xref ref-type="bibr" rid="B27">Koukelli et al., 2023</xref>; <xref ref-type="bibr" rid="B48">Yuan et al., 2022</xref>).</p>
<p>Both high-performance and multifunctional fa&#xe7;ade approaches promote dynamic response and multi-criteria optimization, thereby supporting a holistic and integrated strategy in contemporary fa&#xe7;ade design (<xref ref-type="bibr" rid="B16">Gallo and Romano, 2017</xref>). Interdisciplinary design is fundamental to the advancement of adaptive fa&#xe7;ades, as these systems are at the intersection of architecture, engineering, material sciences and building performance. Collaborative frameworks are crucial at every stage: from early conceptual design, where requirements, sustainability targets, and operational parameters are defined, to performance simulation and digital fabrication (<xref ref-type="bibr" rid="B46">Voigt et al., 2023</xref>; <xref ref-type="bibr" rid="B43">Schultz and Wang, 2022</xref>). Such approaches facilitate lifecycle-oriented thinking, ensuring that environmental, structural, and user-centric criteria are considered from material selection to post-occupancy evaluation (<xref ref-type="bibr" rid="B21">Hosseini et al., 2019</xref>).</p>
<p>Technically, adaptive fa&#xe7;ades depend on actuation to enable dynamic responses to environmental stimuli such as solar radiation, temperature, humidity, wind and user preferences. The strategic optimization of actuator type, placement, quantity, and control logic is key to achieving high performance, while maintaining reliability and cost-effectiveness. Actuation systems where motion is enabled through geometry, smart materials, or dual behavior (structural and kinetic) can achieve comparable performance to fully actuated mechanisms, while lowering weight, cost, and control complexity (<xref ref-type="bibr" rid="B28">Le et al., 2016</xref>).</p>
<p>However, the contribution of adaptive, multifunctional fa&#xe7;ades to both building-scale performance and urban thermal resilience remains underexplored. This paper addresses this gap by demonstrating a performance-driven, integrated design-and-prototyping workflow for adaptive, multifunctional fa&#xe7;ades and by extracting some generalizable insights through a structured cross-case synthesis. The objective is to clarify how fa&#xe7;ade morphology, materiality, and actuation strategy can be co-developed with environmental performance metrics to support design decision-making for adaptive envelopes.</p>
<p>Specifically, we (1) develop three lightweight adaptive fa&#xe7;ade typologies kinetic retroreflective shading (Dubai), kinetic Tri-fold reinterpretation of the Hortenkachel (Stuttgart), and a dual-axis BIPV shading device (Stockholm and Nicosia); (2) evaluate them using a coherent set of visual-comfort and solar-radiation metrics (illuminance, daylight provision and view categories per EN 17037, glare risk, and solar-radiation/energy indicators); and (3) synthesize trade-offs and climate suitability into transferable guidance on adaptivity scale, control complexity, and performance robustness. The reported actuation-feasible fa&#xe7;ade states and quantified performance outcomes provide archival benchmark material for future adaptive fa&#xe7;ade research and development.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Performance-driven, integrated design methodology</title>
<p>A performance-driven, integrated design methodology for adaptive fa&#xe7;ades combines multidisciplinary criteria and quantifiable performance metrics to guide iterative design choices rather than prescribing fixed geometric solutions. <xref ref-type="bibr" rid="B5">Bedon et al. (2019)</xref> propose classification rules, performance indicators, and design methods that frame adaptive fa&#xe7;ades as systems mediating energy, daylight, and user comfort through adaptive behavior rather than static construction details. In line with this systems view, adaptive fa&#xe7;ades integrate passive and active components (sensing, actuation, control, and BIPV) and are commonly evaluated using performance-based indicators for energy and solar gains, power output, illuminance and daylight availability, glare probability, and occupant comfort (e.g., <xref ref-type="bibr" rid="B38">Perino and Serra, 2015</xref>; <xref ref-type="bibr" rid="B15">Galasiu and Veitch, 2006</xref>; <xref ref-type="bibr" rid="B42">Sadeghi et al., 2016</xref>; <xref ref-type="bibr" rid="B50">Zhang et al., 2022</xref>). To deal with trade-offs when integrating multifunctional fa&#xe7;ades, designers couple the assessment of photovoltaic yield, thermal performance, and visual comfort together in one simulation workflow (<xref ref-type="bibr" rid="B20">Hofer et al., 2016</xref>; <xref ref-type="bibr" rid="B35">Mesloub et al., 2020</xref>; <xref ref-type="bibr" rid="B6">Biloria et al., 2023</xref>). Consequently, performance-based processes in adaptive fa&#xe7;ade design set measurable design goals from early stages to enable trade-off analysis and multi-criteria decision-making, following decision-support and simulation-based frameworks (<xref ref-type="bibr" rid="B47">Voigt et al., 2023</xref>; <xref ref-type="bibr" rid="B3">Attia et al., 2012</xref>; <xref ref-type="bibr" rid="B37">Nabil and Mardaljevic, 2005</xref>). Practical constraints related to manufacturability, durability, and regulatory compliance are then incorporated to prevent high-performing, yet impractical solutions (<xref ref-type="bibr" rid="B50">Zhang et al., 2022</xref>; <xref ref-type="bibr" rid="B3">Attia et al., 2012</xref>; <xref ref-type="bibr" rid="B38">Perino and Serra, 2015</xref>).</p>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> illustrates the workflow of an interdisciplinary, integrated design process that is followed in this paper. The design elements including morphology, kinematics, construction and ecology inform performance verification, which includes static/structural, kinetic/operational, and daylight/visual comfort/solar radiation. Early decisions regarding parameters such as module size, array topology, depth, and degrees of freedom are coupled to the associated system kinematics and motion analysis. Mechanical detailing defines the constraints for feasible actuation and joints. Additionally, ecological criteria such as material, embodied impacts, energy efficiency serve as boundary conditions for the design process. A bidirectional loop between numerical simulation studies and scale-model prototyping follows for kinetic model validation. Performance assessment is based on corresponding guidelines set by EN 17037 operationalized through illuminance targets, daylight availability, discomfort-glare risk, and visual-environment metrics (EN 17037; <xref ref-type="bibr" rid="B40">Reinhart, 2014</xref>; <xref ref-type="bibr" rid="B41">Reinhart, 2018</xref>). The reference room material set (walls/ceiling/floor and glazing) was held constant across all cases investigated; only the fa&#xe7;ade-layer optical properties varied per typology (e.g., PV reflectance, translucent panel transmittance). In addition, the workplane sensor grid used a spacing of 0.60&#xa0;m, identical across all indoor studies following standards like EN 17037 and LEED.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Integrated design approach of adaptive kinetic fa&#xe7;ades. Source: <xref ref-type="bibr" rid="B33">Matheou and Phocas (2025)</xref>.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g001.tif">
<alt-text content-type="machine-generated">Flowchart illustrating interdisciplinary research in design and performance. The design section includes morphology, kinematics, construction, and ecology, with corresponding elements like structure, reconfiguration, and recyclability. The performance section covers static, kinetic, and daylight/solar radiation, emphasizing structural design, simplicity, adaptability, and illumination factors. Arrows indicate progression from state-of-the-art to simulation studies and scale models.</alt-text>
</graphic>
</fig>
<p>To improve comparability across the three developments, performance is assessed using a consistent metric set organized into: (i) indoor visual comfort (workplane illuminance and distribution; daylight provision and view categories per EN 17037; glare risk via annual glare probability/spatial glare indicators and selected point-in-time DGP checks), (ii) solar-radiation management (incident/reflected radiation, cumulative irradiance maps, and near-fa&#xe7;ade radiation redirection indicators), and (iii) solar-energy implications (annual incident radiation converted to transmitted solar heat gains where relevant). Unless otherwise stated, indoor simulations use the same reference office geometry and sensor-plane definition to enable cross-case interpretation. The performance metrics used in each case study are as follows:</p>
<p>Case 3.1 (Kinetic retroreflective, Dubai): reflection efficiency (ray redirection), cumulative irradiance (near-fa&#xe7;ade domain), workplane illuminance, EN 17037 daylight provision and view, annual glare probability.</p>
<p>Case 3.2 (Kinetic Tri-fold, Stuttgart): point-in-time illuminance (solstice-based), worst-case glare checks, EN 17037-based view assessment, parametric sensitivity to geometry (arrangement/coverage/shape).</p>
<p>Case 3.3 (Dual-axis PVSD, Stockholm and Nicosia): point-in-time illuminance and DGP at seasonal extrema, annual incident radiation and transmitted solar heat gains, annual spatial glare indicator (sDG) and comparative glare interpretation.</p>
<p>Point-in-time simulations are used where the research question requires rapid parametric exploration across many geometric variants and actuation states (e.g., arrangement, coverage, and shape studies). Running annual climate-based simulations for every parametric permutation and every reconfigurable state would be computationally prohibitive and would obscure early-stage design trends. To avoid overgeneralization, annual or climate-based metrics are applied selectively to the final actuation-feasible variants and to those cases where annual behavior is essential to the claim (e.g., annual glare exposure or annual solar gains). Representative dates (solstices/equinoxes) and hours (midday/afternoon) are selected to capture seasonal extrema of solar altitude/azimuth and to test known critical conditions for glare and solar load on south- and west-facing fa&#xe7;ades; in Dubai, peak-radiation hours during hot-season months are emphasized to reflect worst-case solar exposure.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>Conceptual design and experimental prototyping of kinetic fa&#xe7;ade systems</title>
<sec id="s3-1">
<label>3.1</label>
<title>Kinetic retroreflective fa&#xe7;ade system</title>
<sec id="s3-1-1">
<label>3.1.1</label>
<title>Design concept</title>
<p>The kinetic retroreflective fa&#xe7;ade system (<xref ref-type="bibr" rid="B25">Kip, 2023</xref>) addresses the complex challenge of balancing visual comfort parameters including illuminance, daylight availability, glare mitigation, and view to the outside, while simultaneously potentially reducing short-wave radiative loading near the fa&#xe7;ade by redirecting incident radiation toward the sky. The project&#x2019;s innovative approach centers on a kinetic retroreflective fa&#xe7;ade system that redirects incident solar radiation back toward the atmosphere, thereby avoiding problematic redirection into urban canyons that could exacerbate the urban heat island effect.</p>
<p>A cube corner retroreflector is an optical device that reflects incident electromagnetic radiation, particularly in the visible spectrum, predominantly back toward its source, maintaining this directional property largely independent of the device&#x2019;s orientation relative to the incident beam (<xref ref-type="bibr" rid="B18">Hansen and Madhu, 1972</xref>). <xref ref-type="fig" rid="F2">Figure 2</xref> illustrates this principle for August 21 at four time points (11:00, 12:00, 13:00 and 14:00). This unique characteristic has made retroreflectors indispensable in diverse applications, including road safety devices, bicycle spoke reflectors and radar systems (<xref ref-type="bibr" rid="B7">CIE, 2024</xref>). The extension of retroreflective concepts from static devices to kinetic architectural systems, however, introduces substantial technical challenges. These include the integration of actuation and control mechanisms, as well as the performance-based metrics (illuminance, glare etc.).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Retroreflector principle on August 21 at: <bold>(a)</bold> 11:00; <bold>(b)</bold> 12:00; <bold>(c)</bold> 13:00 and <bold>(d)</bold> 14:00. Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g002.tif">
<alt-text content-type="machine-generated">Four diagrams labeled a) through d) show a geometric shape with a red line and a yellow line intersecting and extending from it. The angles and orientations of the lines vary in each diagram, demonstrating different spatial arrangements.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-1-2">
<label>3.1.2</label>
<title>Methods of environmental performance analysis</title>
<p>Dubai, UAE, was selected as the case study location due to the recorded increase of 4&#xa0;&#xb0;C in average temperature between 2005 and 2019 (<xref ref-type="bibr" rid="B32">Mahanta and Samuel, 2020</xref>). Based on the global horizontal radiation map, the highest levels of solar radiation in Dubai occur between 11:00 and 14:00 during the months of May to August. Accordingly, the simulation studies for daylighting analysis were conducted for the hottest months on May 21, June 21, July 21 and August 21 using ClimateStudio plug-in (<xref ref-type="bibr" rid="B45">Solemma LLC, 2023</xref>) for Rhino3D/Grasshopper. Outdoor solar-radiation redirection and near-fa&#xe7;ade irradiance exposure (ray-tracing and cumulative irradiance analysis) was further evaluated using Ladybug plug-in and Honeybee Cumulative Irradiance Heat Maps (CIHM), respectively.</p>
<p>A preliminary comparative ray-tracing and cumulative irradiance analysis (<xref ref-type="bibr" rid="B27">Koukelli et al., 2023</xref>) was conducted to evaluate near-fa&#xe7;ade short-wave radiative performance of different fa&#xe7;ade configurations: baseline (glazed fa&#xe7;ade), horizontal louvers, biaxial rotation of quadratic panels (A1), monoaxial rotation of quadratic panels with a fixed horizontal axis set at 22.5&#xb0; (A2), and six types of basic trihedral corner reflectors (S1, S2, S3 and T1, T2, T3) (<xref ref-type="fig" rid="F3">Figure 3</xref>). The horizontal louvers were designed with a depth of 50&#xa0;cm and a spacing of 50&#xa0;cm. The square trihedral corner reflectors (S1, S2, S3) were analyzed in three distinct orientations facing the sky (<xref ref-type="fig" rid="F3">Figure 3E</xref>), each with length of 50&#xa0;cm and a row spacing of 50&#xa0;cm. Specifically, the panels were oriented with their reflective surfaces tilted toward the horizon at three different angles: (i) S1 with the V-shape positioned centered symmetrically, (ii) S2 with the V-shape rotated horizontally and toward the left, and (iii) S3 with the entire unit laterally toward the left. The triangular trihedral corner reflectors (T1&#x2013;T3) followed the same set of orientations. All retroreflector configurations were considered as fixed and did not track the sun path.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Case studies: <bold>(a)</bold> baseline (glazed fa&#xe7;ade); <bold>(b)</bold> horizontal louvres; <bold>(c)</bold> kinetic retroreflective fa&#xe7;ade system; <bold>(d)</bold> A1-biaxial (left) and A2-monoaxial quadrat fa&#xe7;ade module (right); <bold>(e)</bold> square trihedral corner reflectors: S1 (left), S2 (middle), S3 (right) and <bold>(f)</bold> triangular trihedral corner reflectors: T1 (left), T2 (middle), T3 (right). Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g003.tif">
<alt-text content-type="machine-generated">Illustration showing a sequence of geometric transformations. Panel a depicts a red and gray floor and wall with dimensions labeled. Panel b adds horizontal lines to the wall, followed by a grid in panel c. Panel d displays two parallel diagrams of a quadrilateral rotated along axes, one at a 22.5-degree angle. Panels e and f show two rows of polyhedral shapes resulting from the transformations.</alt-text>
</graphic>
</fig>
<p>To evaluate the near-fa&#xe7;ade outdoor radiative performance of the basic trihedral corner reflectors (A1, A2, A3, S1, S2, S3, T1, T2 and T3) relative to the baseline and horizontal louvres, the simulation environment modeled an outdoor test space of 10 &#xd7; 10&#xa0;m, with a 5 &#xd7; 4&#xa0;m south-facing fa&#xe7;ade and a corresponding sensor grid at ground level to capture radiation exposure. This analysis quantifies radiation redirection and near-fa&#xe7;ade cumulative irradiance within a 10 &#xd7; 10&#xa0;m domain; it does not include coupled urban microclimate modeling (e.g., airflow, long-wave exchange, or temperature fields). Therefore, outcomes are interpreted as potential near-fa&#xe7;ade radiative effects, not as direct quantification of urban heat island mitigation. The glazed fa&#xe7;ade was assigned by visible transmittance (Tvis) of 54.6% and high reflectivity (R:1, G:1, B:1), with a Solar Heat Gain Coefficient (SHGC) of 0.52. All the trihedral reflectors are considered as double face textile material with a high reflectance on the outer side and high absorbance on the inner side to prevent reflection from the glass to the fa&#xe7;ade modules. The key performance metric for this study is the reflection efficiency (R [%]), defined as the percentage of reflected rays (R<sub>p</sub>) with an angular deviation of 0&#xb0;&#x2013;45&#xb0; relative to incident rays, normalized to the total number of rays (R<sub>t</sub>). This metric ensures that solar radiation is redirected toward the sky rather than into the urban canyon, adjacent buildings, or pedestrian areas.</p>
<p>Following the cumulative irradiance analysis, illuminance analysis was conducted for all basic types (<xref ref-type="fig" rid="F4">Figure 4</xref>). As a next step, the best performing type was selected for further geometric investigations, such as size and depth gradation along the fa&#xe7;ade&#x2019;s height. An office model was considered for the daylighting analysis with 13.6&#xa0;m in length, 10.9&#xa0;m in width, and 4.0&#xa0;m in height, covering an area of approximately 115&#xa0;m<sup>2</sup> with south orientation (<xref ref-type="bibr" rid="B45">Solemma LLC, 2023</xref>). Lighting Materials (LM) have been assigned for walls, floor and ceiling, and glazing with a U-value of 0.82&#xa0;W/m<sup>2</sup>K and Visible Transmittance (Tvis) of 59%. Sensor points were placed 0.75&#xa0;m above the floor level to evaluate the work plane illuminance distribution. For visual comfort, metrics include illuminance (target range: 500&#x2013;1,000 lux for office spaces), daylight availability in accordance with EN 17037 (four compliance levels: Fail, Minimum, Medium, High), horizontal view angle analysis (14&#xb0;, 28&#xb0;, and 54&#xb0; thresholds for compliance levels) and annual glare probability. To ensure consistency across outdoor and indoor performance assessments, a cumulative irradiance analysis was conducted considering the geometrically improved reflector (T60-40).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Basic types of trihedral corner reflectors (S1, S2, S3 and T1, T2, T3) for the office model. Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g004.tif">
<alt-text content-type="machine-generated">Six 3D models of similar cuboid structures are labeled S1, S2, S3, T1, T2, and T3. Each model displays different internal configurations composed of geometric patterns, indicating varied structural designs.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-1-3">
<label>3.1.3</label>
<title>Simulation results</title>
<p>As shown in <xref ref-type="table" rid="T1">Table 1</xref>, S1 and S3 exhibit reflectance performance exceeding 80%, with S1 reaching an average of 88% over the examined hours and S3 achieving 81% over the same period. The triangular trihedral corner reflector variants (T1, T2, T3) generally maintain high reflectance, with the T2 and T3 reaching overall performance above 75% for the majority of the time. CIHM values indicate that the radiation load decreases slightly (<xref ref-type="table" rid="T2">Table 2</xref>). On average, values are reduced by approximately 0.4&#xa0;kWh/m<sup>2</sup> compared to a glass fa&#xe7;ade without shading, showing that all reflector types reduce reflected radiation toward the urban canyon. This effect arises because all fa&#xe7;ade types are oriented roughly orthogonally to the fa&#xe7;ade, which limits direct reflection of solar radiation toward the ground. Among the variants, the greatest reduction in reflected radiation is achieved by T3, with reductions of 42.9% on May 21 and June 21% and 50.0% on July 21 and August 21, and was therefore selected for the daylighting analysis.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Ray trace analysis on May 21, June 21, July 21 and August 21 for S1, S2, S3 and T1, T2, T3 in Dubai.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" align="center">Simulated condition (date and time)</th>
<th align="center">S1 [%]</th>
<th align="center">S2 [%]</th>
<th align="center">S3 [%]</th>
<th align="center">T1 [%]</th>
<th align="center">T2 [%]</th>
<th align="center">T3 [%]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">May 21</td>
<td align="center">11:00</td>
<td align="center">88.00</td>
<td align="center">86.30</td>
<td align="center">75.80</td>
<td align="center">85.10</td>
<td align="center">91.60</td>
<td align="center">75.60</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">88.50</td>
<td align="center">100.00</td>
<td align="center">94.50</td>
<td align="center">64.00</td>
<td align="center">100.00</td>
<td align="center">98.40</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">72.00</td>
<td align="center">91.70</td>
<td align="center">82.70</td>
<td align="center">60.70</td>
<td align="center">95.30</td>
<td align="center">89.50</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">80.90</td>
<td align="center">18.50</td>
<td align="center">100.00</td>
<td align="center">82.90</td>
<td align="center">24.50</td>
<td align="center">99.10</td>
</tr>
<tr>
<td rowspan="4" align="center">June 21</td>
<td align="center">11:00</td>
<td align="center">82.20</td>
<td align="center">74.80</td>
<td align="center">75.00</td>
<td align="center">87.20</td>
<td align="center">79.60</td>
<td align="center">67.50</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">88.00</td>
<td align="center">88.50</td>
<td align="center">94.50</td>
<td align="center">60.50</td>
<td align="center">94.90</td>
<td align="center">95.40</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">74.40</td>
<td align="center">84.50</td>
<td align="center">84.50</td>
<td align="center">58.50</td>
<td align="center">90.70</td>
<td align="center">89.40</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">77.50</td>
<td align="center">21.40</td>
<td align="center">93.80</td>
<td align="center">85.70</td>
<td align="center">46.00</td>
<td align="center">92.90</td>
</tr>
<tr>
<td rowspan="4" align="center">July 21</td>
<td align="center">11:00</td>
<td align="center">85.30</td>
<td align="center">82.90</td>
<td align="center">72.70</td>
<td align="center">85.20</td>
<td align="center">90.60</td>
<td align="center">68.90</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">87.70</td>
<td align="center">97.50</td>
<td align="center">88.10</td>
<td align="center">65.50</td>
<td align="center">98.10</td>
<td align="center">97.30</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">80.60</td>
<td align="center">94.50</td>
<td align="center">88.40</td>
<td align="center">61.20</td>
<td align="center">97.20</td>
<td align="center">93.20</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">83.60</td>
<td align="center">81.70</td>
<td align="center">71.20</td>
<td align="center">83.70</td>
<td align="center">88.40</td>
<td align="center">53.70</td>
</tr>
<tr>
<td rowspan="4" align="center">August 21</td>
<td align="center">11:00</td>
<td align="center">86.80</td>
<td align="center">15.10</td>
<td align="center">71.50</td>
<td align="center">95.40</td>
<td align="center">34.70</td>
<td align="center">75.40</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">92.30</td>
<td align="center">100.00</td>
<td align="center">91.60</td>
<td align="center">95.40</td>
<td align="center">99.90</td>
<td align="center">96.30</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">85.71</td>
<td align="center">100.00</td>
<td align="center">84.30</td>
<td align="center">87.00</td>
<td align="center">99.40</td>
<td align="center">97.80</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">80.60</td>
<td align="center">23.90</td>
<td align="center">69.30</td>
<td align="center">92.90</td>
<td align="center">32.60</td>
<td align="center">64.40</td>
</tr>
<tr>
<td colspan="2" align="center">Overall performance</td>
<td align="center">88.00</td>
<td align="center">69.00</td>
<td align="center">81.00</td>
<td align="center">69.00</td>
<td align="center">75.00</td>
<td align="center">75.00</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: M. Kip.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Results of the cumulative irradiance heat map in Dubai.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Fa&#xe7;ade type</th>
<th align="center">Date</th>
<th align="center">CR [kWh/m<sup>2</sup>]</th>
<th align="center">D&#x26;D [kWh/m<sup>2</sup>]</th>
<th align="center">RR [kWh/m<sup>2</sup>]</th>
<th align="center">Reduction [%]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Baseline (glazed Fa&#xe7;ade)</td>
<td align="center">May 21</td>
<td align="center">8.0</td>
<td align="center">7.3</td>
<td align="center">0.7</td>
<td align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">7.1</td>
<td align="center">6.4</td>
<td align="center">0.7</td>
<td align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.3</td>
<td align="center">6.7</td>
<td align="center">0.6</td>
<td align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.9</td>
<td align="center">6.3</td>
<td align="center">0.6</td>
<td align="left">&#x200b;</td>
</tr>
<tr>
<td rowspan="4" align="center">Horizontal louvers</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.2</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.9</td>
<td align="center">6.4</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.1</td>
<td align="center">6.6</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.7</td>
<td align="center">6.2</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td rowspan="4" align="center">A1</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.3</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">7.0</td>
<td align="center">6.4</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.2</td>
<td align="center">6.7</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.6</td>
<td align="center">6.2</td>
<td align="center">0.4</td>
<td align="center">&#x2212;33.3</td>
</tr>
<tr>
<td rowspan="4" align="center">A2</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.3</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">7.0</td>
<td align="center">6.5</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.2</td>
<td align="center">6.7</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.5</td>
<td align="center">6.2</td>
<td align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
<tr>
<td rowspan="4" align="center">S1</td>
<td align="center">May 21</td>
<td align="center">7.7</td>
<td align="center">7.2</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.7</td>
<td align="center">6.2</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">6.9</td>
<td align="center">6.5</td>
<td align="center">0.4</td>
<td align="center">&#x2212;33.3</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.5</td>
<td align="center">6.1</td>
<td align="center">0.4</td>
<td align="center">&#x2212;33.3</td>
</tr>
<tr>
<td rowspan="4" align="center">S2</td>
<td align="center">May 21</td>
<td align="center">7.7</td>
<td align="center">7.1</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.9</td>
<td align="center">6.3</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.0</td>
<td align="center">6.6</td>
<td align="center">0.4</td>
<td align="center">&#x2212;33.3</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.6</td>
<td align="center">6.1</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td rowspan="4" align="center">S3</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.2</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.9</td>
<td align="center">6.3</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.1</td>
<td align="center">6.6</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.7</td>
<td align="center">6.2</td>
<td align="center">0.5</td>
<td align="center">&#x2212;167</td>
</tr>
<tr>
<td rowspan="4" align="center">T1</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.3</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.9</td>
<td align="center">6.5</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.1</td>
<td align="center">6.8</td>
<td align="center">0.4</td>
<td align="center">&#x2212;33.3</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.8</td>
<td align="center">6.3</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td rowspan="4" align="center">T2</td>
<td align="center">May 21</td>
<td align="center">7.9</td>
<td align="center">7.4</td>
<td align="center">0.6</td>
<td align="center">&#x2212;14.3</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">7.0</td>
<td align="center">6.5</td>
<td align="center">0.5</td>
<td align="center">&#x2212;28.6</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.1</td>
<td align="center">6.8</td>
<td align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.8</td>
<td align="center">6.3</td>
<td align="center">0.5</td>
<td align="center">&#x2212;16.7</td>
</tr>
<tr>
<td rowspan="4" align="center">T3</td>
<td align="center">May 21</td>
<td align="center">7.8</td>
<td align="center">7.4</td>
<td align="center">0.4</td>
<td align="center">&#x2212;42.9</td>
</tr>
<tr>
<td align="center">June 21</td>
<td align="center">6.9</td>
<td align="center">6.5</td>
<td align="center">0.4</td>
<td align="center">&#x2212;42.9</td>
</tr>
<tr>
<td align="center">July 21</td>
<td align="center">7.1</td>
<td align="center">6.8</td>
<td align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
<tr>
<td align="center">August 21</td>
<td align="center">6.8</td>
<td align="center">6.3</td>
<td align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>CR, cumulative radiation; D&#x26;D, direct and diffuse radiation; RR, reflected radiation.</p>
</fn>
<fn>
<p>Source: M. Kip.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The illuminance levels were within the acceptable range (<xref ref-type="table" rid="T3">Table 3</xref>); however the results revealed a pronounced gradient, with high values near the fa&#xe7;ade, and much lower values toward the rear of the room, indicating insufficient light uniformity. To address this issue, further variations of T3 were analysed considering two different fa&#xe7;ade module sizes (60&#xa0;cm and 80&#xa0;cm) and depth gradient from 80&#xa0;cm at the top row to 40&#xa0;cm at the bottom row (T60-40 and T80-40) to allow more daylight admission by decreasing the depth.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Illuminance mean values of S1, S2, S3 and T1, T2, T3 in Dubai.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" align="center">Simulated condition (date and time)</th>
<th align="center">S1 [lux]</th>
<th align="center">S2 [lux]</th>
<th align="center">S3 [lux]</th>
<th align="center">T1 [lux]</th>
<th align="center">T2 [lux]</th>
<th align="center">T3 [lux]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">May 21</td>
<td align="center">11:00</td>
<td align="center">409</td>
<td align="center">196</td>
<td align="center">255</td>
<td align="center">451</td>
<td align="center">367</td>
<td align="center">276</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">548</td>
<td align="center">249</td>
<td align="center">333</td>
<td align="center">632</td>
<td align="center">495</td>
<td align="center">364</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">552</td>
<td align="center">227</td>
<td align="center">310</td>
<td align="center">609</td>
<td align="center">428</td>
<td align="center">333</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">510</td>
<td align="center">306</td>
<td align="center">293</td>
<td align="center">590</td>
<td align="center">382</td>
<td align="center">309</td>
</tr>
<tr>
<td rowspan="4" align="center">June 21</td>
<td align="center">11:00</td>
<td align="center">349</td>
<td align="center">185</td>
<td align="center">237</td>
<td align="center">407</td>
<td align="center">352</td>
<td align="center">261</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">532</td>
<td align="center">257</td>
<td align="center">343</td>
<td align="center">633</td>
<td align="center">521</td>
<td align="center">382</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">512</td>
<td align="center">228</td>
<td align="center">304</td>
<td align="center">584</td>
<td align="center">440</td>
<td align="center">335</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">472</td>
<td align="center">200</td>
<td align="center">282</td>
<td align="center">550</td>
<td align="center">374</td>
<td align="center">299</td>
</tr>
<tr>
<td rowspan="4" align="center">July 21</td>
<td align="center">11:00</td>
<td align="center">392</td>
<td align="center">189</td>
<td align="center">246</td>
<td align="center">435</td>
<td align="center">358</td>
<td align="center">265</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">505</td>
<td align="center">234</td>
<td align="center">309</td>
<td align="center">582</td>
<td align="center">458</td>
<td align="center">340</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">553</td>
<td align="center">233</td>
<td align="center">314</td>
<td align="center">618</td>
<td align="center">447</td>
<td align="center">336</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">515</td>
<td align="center">208</td>
<td align="center">299</td>
<td align="center">589</td>
<td align="center">386</td>
<td align="center">312</td>
</tr>
<tr>
<td rowspan="4" align="center">August 21</td>
<td align="center">11:00</td>
<td align="center">514</td>
<td align="center">201</td>
<td align="center">278</td>
<td align="center">555</td>
<td align="center">372</td>
<td align="center">295</td>
</tr>
<tr>
<td align="center">12:00</td>
<td align="center">563</td>
<td align="center">222</td>
<td align="center">312</td>
<td align="center">619</td>
<td align="center">415</td>
<td align="center">326</td>
</tr>
<tr>
<td align="center">13:00</td>
<td align="center">637</td>
<td align="center">229</td>
<td align="center">326</td>
<td align="center">679</td>
<td align="center">420</td>
<td align="center">335</td>
</tr>
<tr>
<td align="center">14:00</td>
<td align="center">633</td>
<td align="center">218</td>
<td align="center">325</td>
<td align="center">706</td>
<td align="center">402</td>
<td align="center">332</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: M. Kip.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The illuminance levels for T60-40 range between 456 lux, 482 lux, 428 lux and 404 lux, while for T80-40 range, between 438 lux, 465 lux, 412 lux, and 386 lux in May 21, June 21, July 21 and August 21, respectively. Overall, these deviations are small and can be considered negligible in terms of illuminance performance. The analysis of light uniformity further indicated that improvements were only marginal and not sufficient to achieve a fully satisfactory distribution, leading to the conclusion that reflectors are not suitable to function as light shelves. The variation T60-40 was selected for further investigation on daylight availability, glare, and view, instead of T80-40 due to the size.</p>
<p>The T60-40 variation with fully open modules achieves the minimum daylight availability threshold of 100 lux across 95% of the floor area, while an improved daylight level is expected when the modules are folded (<xref ref-type="fig" rid="F5">Figure 5</xref>). In terms of view analysis, the proportion classified as &#x201c;failing&#x201d; is limited to 7.3% at 1.20&#xa0;m and 4.0% at 1.70&#xa0;m (<xref ref-type="fig" rid="F5">Figures 5C,D</xref>). By contrast, 91.5% (1.20&#xa0;m) and 93.9% (1.70&#xa0;m) of the area fall within the highest category &#x201c;High.&#x201d; Therefore, it can be concluded that the T60-40 variant ensures a consistently good view to the outside. The red areas in <xref ref-type="fig" rid="F5">Figure 5E</xref> indicate 1.6% of views with disturbing glare, occurring between October and February from 16:00 to 18:00.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>S60-40 in Dubai: <bold>(a)</bold> illuminance; <bold>(b)</bold> daylight availability; <bold>(c)</bold> view analysis at eye height 1.20&#xa0;m; <bold>(d)</bold> view analysis at eye height 1.70&#xa0;m; <bold>(e)</bold> annual share of disturbing glare. Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g005.tif">
<alt-text content-type="machine-generated">Five-panel diagram showing different simulations of a square grid within a mechanical structure. Panel a) shows a blue gradient, b) is solid yellow, c) exhibits a mix of blue and grey patches, d) shows a sparse blue and grey pattern, and e) depicts a grid with varying red and yellow densities.</alt-text>
</graphic>
</fig>
<p>Following the improvement of indoor daylighting conditions through adjustments to the geometrical characteristics of the fa&#xe7;ade module, a further analysis of the cumulative irradiance map was conducted comparing the baseline with T60-40. As shown in <xref ref-type="table" rid="T4">Table 4</xref>, reflected radiation is reduced by 42.9% on May 21 and June 21 and by 50% on July 21 and August 21, behaving the same as T3 (<xref ref-type="table" rid="T2">Table 2</xref>). A visual assessment further confirms that radiation decreases significantly in the immediate vicinity of the fa&#xe7;ade, where red discolorations shift to yellow and, in some cases, even to blue (<xref ref-type="table" rid="T4">Table 4</xref>). At greater distances from the fa&#xe7;ade, however, no major changes are observed.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Cumulative irradiance heat map for the baseline and the S60-40 in Dubai.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Simulated condition</th>
<th colspan="2" align="center">Baseline</th>
<th colspan="2" align="center">S60-40</th>
<th rowspan="2" align="center">Reduction [%]</th>
</tr>
<tr>
<th align="center">CR [kWh/m<sup>2</sup>] (1)</th>
<th align="center">D&#x26;D [kWh/m<sup>2</sup>] (2)</th>
<th align="center">CR [kWh/m<sup>2</sup>] (1)</th>
<th align="center">D&#x26;D [kWh/m<sup>2</sup>] (2)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">May 21</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx1.tif">
<alt-text content-type="machine-generated">Red plaid pattern with intersecting horizontal and vertical dark red lines, creating a grid-like design on an orange-tinted background.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx2.tif">
<alt-text content-type="machine-generated">Abstract image featuring a vibrant grid pattern of intersecting horizontal and vertical lines over a gradient background. The top of the image shows a transition from blue to yellow, while the majority is a deep orange.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx3.tif">
<alt-text content-type="machine-generated">Bright red plaid pattern with intersecting dark lines forming a grid. The top edge features a sawtooth-like white trim.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx4.tif">
<alt-text content-type="machine-generated">Colorful abstract illustration featuring a grid pattern in vibrant red tones with intersecting black lines. The top section transitions from blue to yellow, creating a gradient effect.</alt-text>
</inline-graphic>
</td>
<td rowspan="2" align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">8.0</td>
<td align="center">7.3</td>
<td align="center">7.8</td>
<td align="center">7.4</td>
</tr>
<tr>
<td align="center">RR [kWh/m<sup>2</sup>] (1)&#x2013;(2)</td>
<td colspan="2" align="center">0.7</td>
<td colspan="2" align="center">0.4</td>
<td align="center">&#x2212;42.9</td>
</tr>
<tr>
<td rowspan="2" align="center">June 21</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx5.tif">
<alt-text content-type="machine-generated">A grid pattern with intersecting orange, red, and yellow lines creating a plaid-like design. The background has a vibrant, warm palette with variations in line intensity and thickness.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx6.tif">
<alt-text content-type="machine-generated">Abstract graphic art featuring a grid of intersecting black lines over a gradient background transitioning from purple at the top to orange and yellow at the bottom, resembling a sunset.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx7.tif">
<alt-text content-type="machine-generated">Abstract pattern featuring a grid overlaying a vibrant orange background with shades of yellow and hints of blue at the top. The grid consists of intersecting red and black lines creating a plaid-like effect.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx8.tif">
<alt-text content-type="machine-generated">Colorful grid pattern with horizontal and vertical lines over a gradient background transitioning from purple at the top to orange at the bottom. The top edge features a zigzag pattern.</alt-text>
</inline-graphic>
</td>
<td rowspan="2" align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">7.1</td>
<td align="center">6.4</td>
<td align="center">6.9</td>
<td align="center">6.5</td>
</tr>
<tr>
<td align="center">RR [kWh/m<sup>2</sup>] (1)&#x2013;(2)</td>
<td colspan="2" align="center">0.7</td>
<td colspan="2" align="center">0.4</td>
<td align="center">&#x2212;42.9</td>
</tr>
<tr>
<td rowspan="2" align="center">July 21</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx9.tif">
<alt-text content-type="machine-generated">Red and orange plaid pattern featuring intersecting vertical and horizontal lines, creating a grid-like appearance with varying shades and intensity, giving a vibrant, textured look.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx10.tif">
<alt-text content-type="machine-generated">A grid pattern with intersecting horizontal and vertical lines, featuring a gradient background transitioning from blue at the top to orange at the bottom.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx11.tif">
<alt-text content-type="machine-generated">Grid pattern with intersecting red and black lines on an orange background. The top section has triangular white shapes with blue peaks, resembling a stylized city skyline.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx12.tif">
<alt-text content-type="machine-generated">Abstract pattern featuring a grid of orange and red colors with blue and white accents at the top. The pattern is densely packed with intersecting horizontal and vertical lines, creating a vibrant, warm appearance.</alt-text>
</inline-graphic>
</td>
<td rowspan="2" align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">7.3</td>
<td align="center">6.7</td>
<td align="center">7.1</td>
<td align="center">6.8</td>
</tr>
<tr>
<td align="center">RR [kWh/m<sup>2</sup>] (1)&#x2013;(2)</td>
<td colspan="2" align="center">0.6</td>
<td colspan="2" align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
<tr>
<td rowspan="2" align="center">August 21</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx13.tif">
<alt-text content-type="machine-generated">A vibrant plaid pattern with horizontal and vertical lines creating a grid. The color transitions from bright red at the top to orange and yellow toward the bottom, creating a gradient effect.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx14.tif">
<alt-text content-type="machine-generated">A grid pattern with intersecting horizontal and vertical lines in various colors, creating a plaid effect. The top part features blue and pink hues, transitioning to yellow and orange towards the bottom.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx15.tif">
<alt-text content-type="machine-generated">Colorful woven textile pattern featuring intersecting red, yellow, and black lines. The background is predominantly yellow, with a plaid-like design, creating a vibrant and intricate visual effect.</alt-text>
</inline-graphic>
</td>
<td align="center">
<inline-graphic xlink:href="fbuil-11-1753356-fx16.tif">
<alt-text content-type="machine-generated">Plaid pattern with intersecting red, yellow, and black lines on a yellow background. The top features a white scalloped border.</alt-text>
</inline-graphic>
</td>
<td rowspan="2" align="left">&#x200b;</td>
</tr>
<tr>
<td align="center">6.9</td>
<td align="center">6.3</td>
<td align="center">6.8</td>
<td align="center">6.3</td>
</tr>
<tr>
<td align="center">RR [kWh/m<sup>2</sup>] (1)&#x2013;(2)</td>
<td colspan="2" align="center">0.6</td>
<td colspan="2" align="center">0.3</td>
<td align="center">&#x2212;50.0</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>CR, cumulative radiation; D&#x26;D, direct and diffuse radiation; RR, reflected radiation.</p>
</fn>
<fn>
<p>Source: M. Kip.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s3-1-4">
<label>3.1.4</label>
<title>Fa&#xe7;ade construction, actuation and prototyping</title>
<p>The system comprises seven rows of triangular trihedral corner reflectors (74 units) with a height of 45&#xa0;cm and a width of 90&#xa0;cm supported by a cable net system. To follow the daylighting performance criteria, the modules in the top row have a depth of 60&#xa0;cm, while those in the bottom row measure 40&#xa0;cm. The wings of the modules are connected to an elastic steel sheet at an angle of 45&#xb0;, and to ensure optimal bending capacity of the elastic steel sheet, a clearance of 50&#xa0;mm is maintained between the folding axis of the bar and the attached wing. Each module can be folded or unfolded (<xref ref-type="fig" rid="F6">Figure 6</xref>) via two running cables. Since cable-driven actuation occurs horizontally in rows, individual rows can also be controlled independently. This enables, for example, the selective closure of rows at eye level to maintain outward visibility, following a clustered actuation strategy. A double-sided textile membrane is integrated into the wings&#x2019; frame, featuring high reflectance on the interior surface and high absorption on the exterior surface.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Indoor visualization with unfolded (left) and folded (right) trihedral corner reflectors and birds&#x2019; eye view with unfolded (left) and folded (right) trihedral corner reflectors. Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g006.tif">
<alt-text content-type="machine-generated">Interior and exterior views of a building with unique geometric fa&#xE7;ades. The top images show an office with desks facing an intricate triangular lattice, casting patterns inside. The bottom images display the building&#x27;s exterior with similar geometric panels, providing a decorative and functional sunshade. Tall modern towers are visible in the background against a clear blue sky.</alt-text>
</graphic>
</fig>
<p>To experimentally assess the kinetic behaviour of the fa&#xe7;ade modules, a 1:3 scale prototype was fabricated to verify the kinetic behavior of the proposed system (<xref ref-type="fig" rid="F7">Figure 7</xref>). The black elements were printed from Polyethylene Terephthalate Glycol (PETG) filament, while the elastic steel sheet was represented by an elastic joint fabricated from Thermoplastic Polyurethane (TPU) filament. The prototype provided insights into the actuation mechanism of the wings. By pulling the cables, the wings could be folded with minimal applied force; upon release, the wings returned to their initial position, demonstrating the elastic restoring capacity of the system.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Prototype in 1:3 scale with the stepwise reconfiguration. Source: M. Kip.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g007.tif">
<alt-text content-type="machine-generated">A sequence of four images shows a black table-top stand with a structure resembling an inverted cone or funnel. In the first image, two hands pull cords connected to the structure, causing it to expand. In the following images, the structure appears more expanded, with increased tension on the cords, demonstrating a mechanical adjustment or transformation.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s3-2">
<label>3.2</label>
<title>Kinetic tri-fold fa&#xe7;ade system</title>
<sec id="s3-2-1">
<label>3.2.1</label>
<title>Design concept</title>
<p>The design project, developed by Jiuyuan Liu, Simon G&#xf6;bel and Tobias Steiger, introduces an adaptive kinetic fa&#xe7;ade system inspired by the Hortenkachel geometry, originally designed by Helmut Rhode and later developed by Egon Eiermann. The Hortenkachel is a distinctive fa&#xe7;ade system used in the Horten department stores, consisting 50 &#xd7; 50&#xa0;cm tiles, initially made of ceramic and later of aluminum, each featuring a stylized &#x201c;H&#x201d; for Horten. The system comprises two main components: (a) the egg-crate frame of individual wings, and (b) the wings within the frame. Its application to the reference office model is illustrated in <xref ref-type="fig" rid="F8">Figure 8</xref>. Technically, the original Hortenkachel was not conceived as a shading device. Therefore, the objective of this study was first to identify and optimize the geometric parameters of the Hortenkachel for solar shading aligned with user controllability (<xref ref-type="fig" rid="F9">Figure 9a</xref>), and then to design a lightweight kinetic shading system using recyclable materials and a minimal number of actuators through module clustering.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Hortenkachel applied to the reference office model. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g008.tif">
<alt-text content-type="machine-generated">Three-dimensional diagram of a rectangular structure with a detailed section showing a grid-like pattern. The inset emphasizes a close-up of the grid, composed of blue squares with internal pink triangular shapes. Dimensions of fifty centimeters by fifty centimeters are noted. Color coding indicates &#x22;egg crate&#x22; in blue and &#x22;wings&#x22; in pink.</alt-text>
</graphic>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Hortenkachel deconstruction: <bold>(a)</bold> hortenkachel; <bold>(b)</bold> egg-crate system; <bold>(c)</bold> wings; <bold>(d)</bold> Tri-fold: additional side wings. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g009.tif">
<alt-text content-type="machine-generated">Diagram showing the process of folding a sheet into an origami pattern. Panel a) shows a flat sheet with arrows indicating initial folds. Panel b) presents additional folding steps with directional arrows. Panel c) illustrates further folding into a triangular shape. Panel d) displays the final compact, multi-layered structure.</alt-text>
</graphic>
</fig>
<p>Initially, the egg-crate system was analysed without the wings, however, this configuration lacked flexibility (<xref ref-type="fig" rid="F9">Figure 9b</xref>). Subsequently, various wing geometries were explored, testing different arrangements, sizes, coverages, shapes, and depths. When applied without the egg-crate frame, the wings alone failed to meet the target illuminance levels, particularly during winter at 12:00, when the low solar altitude allowed direct sunlight to penetrate the office room (<xref ref-type="fig" rid="F9">Figure 9c</xref>). These limitations highlighted the need for a new system capable of both shading and flexibility. To address this, a single-axis Tri-fold system was developed (<xref ref-type="fig" rid="F9">Figure 9d</xref>), combining modules with the primary Hortenkachel wings and additional translucent side wings to control glare and regulate indoor illuminance, while preserving outward visibility and user adaptability (<xref ref-type="fig" rid="F10">Figure 10</xref>).</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Outdoor (left) and indoor visualization (right) of the single-axis Tri-fold fa&#xe7;ade system. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g010.tif">
<alt-text content-type="machine-generated">A modern architectural installation features a geometric frosted glass wall in a snowy forest setting at sunset. The interior view shows a person standing near chairs and a table, with sunlight casting shadows through the patterned glass.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2-2">
<label>3.2.2</label>
<title>Methods of daylighting performance analysis</title>
<p>A comparative parametric analysis was conducted between the baseline (glazed fa&#xe7;ade), the original Hortenkachel, various static geometric configurations, static Tri-fold modules (50% openness) and an adaptive scenario featuring single-axis Tri-fold modules (50 &#xd7; 50&#xa0;cm module size arranged horizontally) to assess their influence on daylight performance. The parametric analysis examined three types with side wings arranged: (a) mixed; (b) vertical; and (c) horizontal (<xref ref-type="fig" rid="F11">Figures 11a&#x2013;c</xref>), where the mixed type combines both alignments, meaning that one module is vertically positioned and the adjacent module, horizontally positioned. Four module sizes were subsequently analyzed: (a) 25&#xa0;cm; (b) 50&#xa0;cm; (c) 75&#xa0;cm; and (d) 100&#xa0;cm (<xref ref-type="fig" rid="F11">Figure 11d</xref>), this was followed by four coverage and shape variations: (a) fa&#xe7;ade coverage of 50%; (b) fa&#xe7;ade coverage of 75%; (c) low mid-point; and (d) high mid-point (<xref ref-type="fig" rid="F11">Figure 11e</xref>). In the sun-tracking scenario (<xref ref-type="fig" rid="F12">Figure 12</xref>), the Tri-Fold modules dynamically track the sun&#x2019;s position and configure their openness.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Fa&#xe7;ade arrangements with side-wings grey-colored: <bold>(a)</bold> mixed; <bold>(b)</bold> vertical; <bold>(c)</bold> horizontal; <bold>(d)</bold> size variations: module 25&#xa0;cm, 50&#xa0;cm, 75&#xa0;cm, and 100&#xa0;cm; <bold>(e)</bold> coverage and shape variations: 50% covered (left); 75% covered; low mid-point; high mid-point (right). Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g011.tif">
<alt-text content-type="machine-generated">Five geometric designs labeled a to e, each featuring a grid of triangles. Labeled a to e, configurations vary in size and shading patterns, with triangles arranged to form intricate, symmetrical designs. Each row presents a different arrangement or scale.</alt-text>
</graphic>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Tri-fold module tracking the solar altitude on the summer and winter solstices at 12:00 and 15:00. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g012.tif">
<alt-text content-type="machine-generated">Diagrams illustrating sun angles and shadow directions on a building for specific times and dates: December 21 at 12 PM and 3 PM, and June 21 at 12 PM and 3 PM. Orange arrows indicate sun directions, with circular grids representing the horizon and building orientation.</alt-text>
</graphic>
</fig>
<p>Daylighting simulations were performed for the summer and winter solstices at 12:00 and 15:00 in Stuttgart, Germany, using the office reference model described in <xref ref-type="sec" rid="s3-1-2">Section 3.1.2</xref>, with south- and west-facing glazed fa&#xe7;ades. The analysis was conducted in Rhinoceros 3D and ClimateStudio under CIE clear sky conditions through point-in-time simulations. Opaque wood was assigned to the primary wings and polycarbonate with 30% light transmittance to the side wings.</p>
</sec>
<sec id="s3-2-3">
<label>3.2.3</label>
<title>Simulation results</title>
<p>A comparative analysis of the baseline, the Hortenkachel, the three arrangements (mixed, vertical and horizontal) and the single-axis Tri-fold system, shows significant differences in daylighting performance (<xref ref-type="table" rid="T5">Table 5</xref>). The baseline produces the highest illuminance levels (5363 lux in winter at 12:00), exceeding the target range (500&#x2013;1000 lux). The Hortenkachel reduces illuminance however, the system is structurally complex for integrating adaptive feature, as it combines an egg-crate framework with additional wings, increasing material and fabrication cost. While the mixed and the vertical arrangement perform well on the winter and summer solstices at 12:00 and 15:00, mixed arrangements complicate actuation for clustering because adjacent modules have different orientations (vertical-horizontal), and vertical arrangements can lead to intolerable glare, especially in winter when the solar altitude is low. For this reason, subsequent simulations focused on the horizontal arrangement, in which the primary wings that face the sun are opaque, and the secondary wings are translucent to diffuse incoming radiation. The module-size variation had no significant effect on illuminance; however, the illuminance levels remain low and further improvement is essential. Therefore, a 50&#xa0;cm module was selected as a balance between performance and human scale (<xref ref-type="table" rid="T6">Table 6</xref>). Coverage and shape studies showed that cases with high and low mid-points performed better overall, while 50% coverage yielded lower illuminance, because fully open modules already provide effective protection for south- and west-oriented surfaces (<xref ref-type="table" rid="T7">Table 7</xref>). The adaptive scenario addresses this limitation by employing a kinetic shading system that tracks the solar&#x2019;s altitude to dynamically regulate illuminance. However, modules with high and low mid-points pose greater control challenges due to their asymmetrical geometry and non-uniform kinetic behavior.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Illuminance mean values by arrangement in Stuttgart.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Location</th>
<th colspan="2" align="center">Simulated condition (date and time)</th>
<th align="center">Baseline [lux]</th>
<th align="center">Hortenkachel [lux]</th>
<th align="center">Mixed [lux]</th>
<th align="center">Vertical [lux]</th>
<th align="center">Horizontal [lux]</th>
<th align="center">Single-axis tri-fold [lux]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Stuttgart</td>
<td rowspan="2" align="center">June 21</td>
<td align="center">12:00</td>
<td align="center">2530</td>
<td align="center">529</td>
<td align="center">361</td>
<td align="center">421</td>
<td align="center">320</td>
<td align="center">905</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">2433</td>
<td align="center">589</td>
<td align="center">384</td>
<td align="center">399</td>
<td align="center">484</td>
<td align="center">699</td>
</tr>
<tr>
<td rowspan="2" align="center">December 21</td>
<td align="center">12:00</td>
<td align="center">5363</td>
<td align="center">1516</td>
<td align="center">664</td>
<td align="center">842</td>
<td align="center">650</td>
<td align="center">687</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">1772</td>
<td align="center">524</td>
<td align="center">247</td>
<td align="center">250</td>
<td align="center">255</td>
<td align="center">559</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: J. liu, S. G&#xf6;bel and T. steiger.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Illuminance mean values by size in Stuttgart.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Location</th>
<th colspan="2" align="center">Simulated condition (date and time)</th>
<th align="center">Module size 25&#xa0;cm [lux]</th>
<th align="center">Module size 50&#xa0;cm [lux]</th>
<th align="center">Module size 75&#xa0;cm [lux]</th>
<th align="center">Module size 100&#xa0;cm [lux]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Stuttgart</td>
<td rowspan="2" align="center">June 21</td>
<td align="center">12:00</td>
<td align="center">357</td>
<td align="center">361</td>
<td align="center">370</td>
<td align="center">470</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">358</td>
<td align="center">384</td>
<td align="center">396</td>
<td align="center">373</td>
</tr>
<tr>
<td rowspan="2" align="center">December 21</td>
<td align="center">12:00</td>
<td align="center">928</td>
<td align="center">664</td>
<td align="center">605</td>
<td align="center">790</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">234</td>
<td align="center">247</td>
<td align="center">244</td>
<td align="center">237</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: J. liu, S. G&#xf6;bel and T. Steiger.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Illuminance mean values by coverage and shape variations in Stuttgart.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Location</th>
<th colspan="2" align="center">Simulated Condition (date and time)</th>
<th align="center">50% [lux]</th>
<th align="center">75% [lux]</th>
<th align="center">Low mid-point [lux]</th>
<th align="center">High mid-point [lux]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Stuttgart</td>
<td rowspan="2" align="center">June 21</td>
<td align="center">12:00</td>
<td align="center">320</td>
<td align="center">255</td>
<td align="center">432</td>
<td align="center">635</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">484</td>
<td align="center">312</td>
<td align="center">534</td>
<td align="center">671</td>
</tr>
<tr>
<td rowspan="2" align="center">December 21</td>
<td align="center">12:00</td>
<td align="center">650</td>
<td align="center">424</td>
<td align="center">820</td>
<td align="center">840</td>
</tr>
<tr>
<td align="center">15:00</td>
<td align="center">255</td>
<td align="center">151</td>
<td align="center">321</td>
<td align="center">310</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: J. liu, S. G&#xf6;bel and T. steiger.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Following the parametric analysis on illuminance regarding the arrangements, size, coverage and shape variations, another comparative study was conducted for the baseline, static Tri-fold and single-axis Tri-fold. The Tri-fold solar&#x2019;s altitude tracking mechanism maintains indoor illuminance within the target range, achieving a mean value of 905 lux on the summer solstice at 12:00, outperforming both the baseline (2530 lux) and the static Tri-fold (1158 lux) (<xref ref-type="fig" rid="F13">Figure 13</xref>). Glare analysis was conducted for the worst-case scenario in winter solstice at 12:00 presenting intolerable glare for the baseline and the static Tri-fold (<xref ref-type="fig" rid="F13">Figure 13</xref>). The single-axis Tri-fold (altitude-responsive) system demonstrates robust daylight- and glare-control behavior under seasonal variations. In summer, when the sun is higher, the modules open to permit daylight and preserve outward views while preventing glare; in winter, when the solar altitude is lower, the modules remain closed to block direct sunlight and avoid visual discomfort. View analysis (<xref ref-type="fig" rid="F13">Figure 13</xref>) following EN 17037 confirms that while views towards the southern sun are occasionally obstructed for glare control in winter at 12:00, west-facing views remain accessible, reflecting the system&#x2019;s adaptive and occupant-centered design. Gray zones indicate no access to views; dark blue indicates minimal access; turquoise indicates moderate access; and green indicates full access to views.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Baseline (left); static Tri-fold (middle); single-axis Tri-fold (left): <bold>(a)</bold> illuminance mean values on the summer solstice at 12:00; <bold>(b)</bold> glare probability (DGP) on the winter solstice at 12:00 (worst-case scenario); <bold>(c)</bold> view analysis on the summer solstice at 12:00 (left and middle) and on the winter solstice at 12:00 (left). Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g013.tif">
<alt-text content-type="machine-generated">Three groups of images labeled a, b, and c. Group a shows three heat maps with blue to red gradients indicating varying intensities. Group b features three grids of circles with varying densities and colors. Group c consists of three contour maps with blue to gray shading, illustrating different degrees of a certain variable.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2-4">
<label>3.2.4</label>
<title>Fa&#xe7;ade construction, actuation and prototyping</title>
<p>In the daylighting analysis, vertical zoning plays a crucial role in achieving optimal visual comfort. Inspired by the classical blind mechanism, the proposed adaptive shading system, Tri-fold, operates through a single actuator controlling six modules per zone (<xref ref-type="fig" rid="F14">Figure 14</xref>). The actuator engages by pulling a string connected to the lower edges of the modules, causing them to fold upward in an origami-like motion. Upon release, gravity restores the modules to their original closed position. Across the entire fa&#xe7;ade, a total of 33 actuators is distributed to generate various shading patterns responsive to the sun&#x2019;s position and user preferences. The side wings of the modules are supported by an aluminum frame, while the joints between the elements are made of elastic 3D-printed TPU, enabling the characteristic foldable, origami-inspired transformation of each module (<xref ref-type="fig" rid="F15">Figure 15</xref>). A 1:2 scale prototype was built to experimentally demonstrate the kinematics of the system.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Cable-driven actuation method, modules clustering and module reconfiguration with 100%, 75% and 50% openness. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g014.tif">
<alt-text content-type="machine-generated">Diagram showing an expandable structure with actuators, motors, and pulling strings. The left side illustrates the vertical arrangement of components. The center and right sections show horizontal frames, with varying expansion percentages at 100, 75, and 50 percent. Wooden panels and metal crisscross patterns are visible.</alt-text>
</graphic>
</fig>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>Prototype in 1:2 scale. Source: J. Liu, S. G&#xf6;bel and T. Steiger.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g015.tif">
<alt-text content-type="machine-generated">A grid of ten images showing various stages of a folding geometric paper model. Each model is framed by wooden sticks, displaying different transformations of triangular and diamond-shaped patterns. The designs transition from fully expanded to partially collapsed configurations.</alt-text>
</graphic>
</fig>
<p>In real-world applications, TPU-based compliant mechanisms could be substituted with pneumatic joints which offer higher durability, scalability, and reliable performance under repeated actuation. Additionally, since the proposed system responds dynamically to the solar altitude, solar thin-film photovoltaic panels could be integrated on the primary upper wings to generate renewable energy while providing shading.</p>
</sec>
</sec>
<sec id="s3-3">
<label>3.3</label>
<title>Dual-axis photovoltaic shading device</title>
<sec id="s3-3-1">
<label>3.3.1</label>
<title>Design concept</title>
<p>An adaptive unitized building envelope system incorporating thin-film photovoltaic PV modules was developed as part of a research project conducted at the University of Cyprus. The system integrates lightweight PV modules mounted on aluminum support plates and is designed for seamless application on both new and existing building fa&#xe7;ades. A key feature of the prototype is its minimal use of actuators, which are strategically positioned outside the main structural body. The configuration reduces the number of active components within the movable structure, thereby simplifying control and minimizing mechanical complexity.</p>
<p>The unitized structural system comprises a primary frame of aluminum profiles, within which a pre-tensioned cable net serves as the main supporting mechanism. This cable net carries a secondary assembly consisting of aluminum struts, interconnected via continuous cables on both the front and rear sides of the system. The PV modules are rigidly attached to the front-facing struts, ensuring that any rotational movement of the struts results in a synchronized reorientation of the PV panels. The system allows for bi-axial movement, with the struts capable of rotating within both the vertical and horizontal planes. These rotations are actuated by controlled adjustments in the relative lengths of the continuous cables, enabling the PV modules to track the motion of the sun in two degrees of freedom. This capability allows for real-time adaptation to the sun&#x2019;s position, maximizing energy capture throughout the day. <xref ref-type="fig" rid="F16">Figure 16</xref> illustrates a small-scale prototype of the system in its initial configuration, where the struts are aligned horizontally, and the PV modules are oriented vertically. The overall dimensions of the prototype unit in actual scale are 540&#xa0;cm in width and 365&#xa0;cm in height. The assembly houses 20&#xa0;PV modules, each measuring 66&#xa0;cm in width and 50&#xa0;cm in height. Due to the rigid connection between each module and its corresponding strut, any change in the strut&#x2019;s orientation directly adjusts the PV panel&#x2019;s inclination, thereby enabling uniform angular realignment relative to incident sunlight.</p>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Prototype system in 1:10 scale. Source: <xref ref-type="bibr" rid="B39">Phocas et al. (2024)</xref>.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g016.tif">
<alt-text content-type="machine-generated">Wooden frame with a grid of square tiles connected by strings and red pulley mechanisms. The setup likely illustrates a mechanical or structural concept.</alt-text>
</graphic>
</fig>
<p>For synchronized movement, all cables within a plane (either horizontal or vertical) can be actuated in parallel, allowing the PV modules to reorient simultaneously and uniformly in response to changing solar angles. The continuous secondary cables are routed through a pulley system that includes a pair of counter-rotating pulleys at one end and a guiding pulley at the midpoint. This arrangement is driven by a single rotational actuator, such as a stepper motor, connected to the axis that links the paired pulleys within each row of cables. Importantly, only two actuators are employed in total, both mounted on the stationary aluminum frame and mechanically decoupled from the lightweight, movable system body. This approach maintains the low self-weight of the main structural components, ensuring efficient operation without compromising structural balance or dynamic response.</p>
</sec>
<sec id="s3-3-2">
<label>3.3.2</label>
<title>Methods of daylighting performance analysis</title>
<p>Following the initial evaluation of the dual-axis BIPV system (<xref ref-type="bibr" rid="B39">Phocas et al., 2024</xref>), which primarily targeted maximizing PV efficiency, while reducing the mechanical complexity (associated with dual-axis tracking), a supplementary daylighting and solar irradiance analysis was conducted.</p>
<p>Daylighting simulations were carried out in ClimateStudio for a CIE clear-sky condition in two distinct climatic contexts, Nicosia, Cyprus and Stockholm, Sweden, on March 20, June 21, September 22 and December 21&#xa0;at 12:00, using the office reference model described in <xref ref-type="sec" rid="s3-1-2">Section 3.1.2</xref>. To complement the spacing distance between the PV modules, an opaque material with a reflectance of 28% was assigned to the panels. The analysis on illuminance and glare focused on the fixed position, average optimum (static and optimized position for maximum PV power output) and sun-tracking positions for the four selected point-in-times (<xref ref-type="fig" rid="F17">Figure 17</xref>). This step enables a combined evaluation of energy generation and indoor daylight quality, clarifying to what extent the dual-axis BIPV system can be redesigned to provide both high solar-energy yield and adequate daylighting and shading performance.</p>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>PVSD applied in an office model: <bold>(a)</bold> fixed position; <bold>(b)</bold> average optimum in Nicosia (left) and in Stockholm (right); <bold>(c)</bold> sun-tracking at 12:00 on March 20, June 21, September 22 and December 21 in Nicosia (from left to right); <bold>(d)</bold> sun-tracking at 12:00 on March 20, June 21, September 22 and December 21 in Stockholm (from left to right). Source: Authors.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g017.tif">
<alt-text content-type="machine-generated">Four sets of rectangular 3D grids, labeled a) to d), each with variations in the arrangement of dark blue and gray squares on a white block, depict changes in structure.</alt-text>
</graphic>
</fig>
<p>The transmitted solar heat gain was conducted for four fa&#xe7;ade types: (a) baseline, (b) fixed vertically positioned PV, (c) average optimum for Stockholm and Nicosia (fixed position), and (d) an orientation optimized for 21 June and then applied to the entire year. The fixed vertically positioned PV and the average optimum were chosen in a previous irradiance analysis and photovoltaic system power (<xref ref-type="bibr" rid="B39">Phocas et al., 2024</xref>). The third configuration was defined by first determining the fa&#xe7;ade orientation that minimizes incident solar radiation for summer solstice (June 21, 12:00) and subsequently applying this single orientation to the annual simulation. This scenario reflects a summer-driven control concept and allows a direct comparison with the two other single-state strategies (vertical and annual average optimum), without introducing hourly tracking. It also quantifies the annual effect of maintaining a summer-protective fa&#xe7;ade state even during periods when passive solar gains would be desirable.</p>
<p>Annual incident solar radiation on the fa&#xe7;ade, obtained from ClimateStudio, was converted into transmitted solar heat gains using the common fenestration formulation:<disp-formula id="equ1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>solar</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>incident</mml:mtext>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>S</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>G</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>where <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>incident</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the solar radiation incident on the glazing <inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>kWh</mml:mtext>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#xb7;</mml:mo>
<mml:mtext>yr</mml:mtext>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>G</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the solar heat gain coefficient of the glazing (0.52 in this study), and <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the glazed area (31.5&#xa0;m<sup>2</sup>). This approach is consistent with the solar gain calculation methods in (<xref ref-type="bibr" rid="B2">ASHRAE, 2021</xref>) and with the definition of total solar energy transmittance in EN 410 and ISO 15099.</p>
</sec>
<sec id="s3-3-3">
<label>3.3.3</label>
<title>Simulation results</title>
<p>The mean illuminance values for the fixed position, average optimum and the sun-tracking system in Stockholm and in Nicosia are shown in <xref ref-type="table" rid="T8">Table 8</xref>. In Stockholm, the sun-tracking system shows a consistently lower mean illuminance than the fixed vertical position during periods of low solar altitude, with 34.9% lower (1875 vs. 2878 lux) on March 20, 29.2% lower (1992 vs. 2813 lux) on September 22, and 11.1% (786 vs. 884 lux) on December 21. The reduction is smallest on June 21 (0.36%), because the high solar altitude minimizes the kinetic feature of tracking. A comparable pattern is observed in Nicosia with the sun-tracking system, 2.5% lower (546 vs. 560 lux) on March 20, 5.0% lower (529 vs. 557 lux) on 22 September, 9.5% lower (2595 vs. 2868 lux) on 21 December and 11.6% (501 vs. 449 lux) on June 21. These results indicate that dual-axis sun tracking is most effective, in terms of differentiation from a fixed vertical system, when the solar altitude is low. In winter the difference diminishes, because the very low solar altitude combined with relatively large panel spacing allows more daylight penetration even in the fixed case.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>Illuminance mean values of the fixed position, average optimum and the sun-tracking system in Stockholm and Nicosia.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Location</th>
<th align="center">Simulated Condition (date and time)</th>
<th align="center">Fixed position [lux]</th>
<th align="center">Average optimum 60/-9 [lux]</th>
<th align="center">Average optimum 44/-11 [lux]</th>
<th align="center">Sun-tracking system [lux]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Stockholm</td>
<td align="center">March 20 12:00</td>
<td align="center">2878</td>
<td align="left">&#x200b;</td>
<td align="center">2513</td>
<td align="center">1875</td>
</tr>
<tr>
<td align="center">June 21 12:00</td>
<td align="center">562</td>
<td align="left">&#x200b;</td>
<td align="center">546</td>
<td align="center">560</td>
</tr>
<tr>
<td align="center">September 22 12:00</td>
<td align="center">2813</td>
<td align="left">&#x200b;</td>
<td align="center">2439</td>
<td align="center">1992</td>
</tr>
<tr>
<td align="center">December 21 12:00</td>
<td align="center">884</td>
<td align="left">&#x200b;</td>
<td align="center">867</td>
<td align="center">786</td>
</tr>
<tr>
<td rowspan="4" align="center">Nicosia</td>
<td align="center">March 20 12:00</td>
<td align="center">560</td>
<td align="center">572</td>
<td align="left">&#x200b;</td>
<td align="center">546</td>
</tr>
<tr>
<td align="center">June 21 12:00</td>
<td align="center">449</td>
<td align="center">507</td>
<td align="left">&#x200b;</td>
<td align="center">501</td>
</tr>
<tr>
<td align="center">September 22 12:00</td>
<td align="center">557</td>
<td align="center">573</td>
<td align="left">&#x200b;</td>
<td align="center">529</td>
</tr>
<tr>
<td align="center">December 21 12:00</td>
<td align="center">2868</td>
<td align="center">2967</td>
<td align="left">&#x200b;</td>
<td align="center">2595</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The annual solar irradiation is 833&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Stockholm and 1019&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Nicosia, which corresponds (with the simulated SHGC of 0.52) to 433.2&#xa0;kWh/m<sup>2</sup>&#xb7;yr and 529.9&#xa0;kWh/m<sup>2</sup>&#xb7;yr of transmitted solar gains, respectively (<xref ref-type="table" rid="T9">Table 9</xref>). For the actual fa&#xe7;ade area of 31.5&#xa0;m<sup>2</sup>, this equals about 13.6&#xa0;MWh/yr in Stockholm and 16.7&#xa0;MWh/yr in Nicosia, confirming the expected effect of climate, with the Mediterranean location offering higher annual solar availability. The fixed vertical PV reduces annual gains by about one-third in both locations. In Stockholm, transmitted gains drop from 433.2&#xa0;kWh/m<sup>2</sup>&#xb7;yr to 282.4&#xa0;kWh/m<sup>2</sup>&#xb7;yr (34.8% reduction), which for 31.5&#xa0;m<sup>2</sup> equals 8.9&#xa0;MWh/yr, i.e., a reduction of roughly 4.75&#xa0;MWh/yr compared to the baseline. In Nicosia, the same configuration reduces transmitted gains from 529.9&#xa0;kWh/m<sup>2</sup>&#xb7;yr to 348.9&#xa0;kWh/m<sup>2</sup>&#xb7;yr (34.2%), or from 16.7&#xa0;MWh/yr to about 11.0&#xa0;MWh/yr for the whole fa&#xe7;ade, a reduction of about 5.7&#xa0;MWh/yr.</p>
<table-wrap id="T9" position="float">
<label>TABLE 9</label>
<caption>
<p>Transmitted solar heat gain values of the baseline, fixed position, adaptive optimum and the solstice-derived fixed.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Location</th>
<th align="center">Fa&#xe7;ade Configuration</th>
<th align="center">Transmitted per m<sup>2</sup> [kWh/m<sup>2</sup>&#xb7;yr]</th>
<th align="center">Total for 31.5&#xa0;m<sup>2</sup> [MWh/yr]</th>
<th align="center">Absolute reduction vs. baseline [kWh/yr]</th>
<th align="center">Reduction vs. baseline [%]</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="center">Stockholm</td>
<td align="center">Baseline</td>
<td align="center">433.2</td>
<td align="center">13.6</td>
<td align="center">&#x2013;</td>
<td align="center">&#x2013;</td>
</tr>
<tr>
<td align="center">Fixed</td>
<td align="center">282.4</td>
<td align="center">8.9</td>
<td align="center">4.8</td>
<td align="center">34.8</td>
</tr>
<tr>
<td align="center">Average optimum</td>
<td align="center">251.2</td>
<td align="center">7.9</td>
<td align="center">5.7</td>
<td align="center">42.0</td>
</tr>
<tr>
<td align="center">Solstice-derived fixed</td>
<td align="center">254.8</td>
<td align="center">8.0</td>
<td align="center">5.6</td>
<td align="center">41.2</td>
</tr>
<tr>
<td rowspan="4" align="center">Nicosia</td>
<td align="center">Baseline</td>
<td align="center">529.9</td>
<td align="center">16.7</td>
<td align="center">&#x2013;</td>
<td align="center">&#x2013;</td>
</tr>
<tr>
<td align="center">Fixed</td>
<td align="center">348.9</td>
<td align="center">11</td>
<td align="center">5.7</td>
<td align="center">34.2</td>
</tr>
<tr>
<td align="center">Average optimum</td>
<td align="center">329.2</td>
<td align="center">10.4</td>
<td align="center">6.3</td>
<td align="center">37.9</td>
</tr>
<tr>
<td align="center">Solstice-derived fixed</td>
<td align="center">329.7</td>
<td align="center">10.4</td>
<td align="center">6.3</td>
<td align="center">37.8</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The average optimum fixed orientation achieves the lowest gains overall: 251.2&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Stockholm (42.0% reduction), which is 7.9&#xa0;MWh/yr for 31.5&#xa0;m<sup>2</sup>, and 329.2&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Nicosia (37.9% reduction), which is 10.37&#xa0;MWh/yr. The solstice-derived fixed orientation (i.e., fa&#xe7;ade position defined for 21 June and applied unchanged to the annual simulation) yields very similar results: 254.8&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Stockholm (41.2% reduction) and 329.7&#xa0;kWh/m<sup>2</sup>&#xb7;yr in Nicosia (37.8% reduction), corresponding to about 8.0&#xa0;MWh/yr and 10.38&#xa0;MWh/yr for the full fa&#xe7;ade, respectively. This is relevant for designs that require strong solar protection in summer, but prevent over-shade in winter, when passive solar gains are desirable. It should be noted that the solstice-derived fixed orientation does not represent a continuously sun-tracking fa&#xe7;ade. A system that updates its position hourly or seasonally would be able to align the fa&#xe7;ade more closely with the incident solar vector and thus further reduce incident (and transmitted) solar gains during high-load periods. The present case therefore represents a conservative, single-state approximation of a summer-driven control strategy.</p>
<p>In Stockholm, the three investigated PV positioning strategies (fixed, average optimum, and sun-tracking) show that reorienting the system alone cannot eliminate glare for certain low solar altitudes. At 12:30 on March 20 all configurations reach Daylight Glare Probability (DGP) 1.00, and on December 21 the values remain clearly uncomfortable (0.79&#x2013;0.81), indicating that the combination of low solar altitude and view direction creates inherently critical situations (<xref ref-type="table" rid="T10">Tables 10</xref>&#x2013;<xref ref-type="table" rid="T12">12</xref>). When glare is evaluated over space and time, however, the average optimum configuration performs best (sDG &#x3d; 15.1%) compared to the fixed position (19.1%) and the sun-tracking (<xref ref-type="fig" rid="F18">Figure 18</xref>). This means that, relative to the fixed case, the average optimum reduces the share of views experiencing disturbing glare over the year by about 21%, while the sun-tracking case still achieves a reduction of roughly 16%. In high-latitude locations, even a limited-state adaptive fa&#xe7;ade (fixed &#x2018;average-optimum&#x2019; or seasonal state), rather than continuous sun tracking, is more effective for visual comfort than a static vertical fa&#xe7;ade.</p>
<table-wrap id="T10" position="float">
<label>TABLE 10</label>
<caption>
<p>Daylight glare probability (DGP) of the fixed system at 12:30 on March 20, June 21, September 22, and December 21 in Stockholm.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Stockholm</th>
<th colspan="4" align="center">Fixed</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">1.00</td>
<td align="center">0.49</td>
<td align="center">0.50</td>
<td align="center">0.79</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx17.tif">
<alt-text content-type="machine-generated">A grid-like structure with bright red sections contrasted against gray, casting intricate shadows on the floor. The design features vertical and horizontal lines creating a geometric pattern with both light and shadow elements.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx18.tif">
<alt-text content-type="machine-generated">Abstract graphic featuring a grid-like pattern with bright red vertical and horizontal sections overlaying a dark background. Squares within the grid host smaller gray rectangles, creating a balanced composition of contrasting colors and shapes.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx19.tif">
<alt-text content-type="machine-generated">Interior architectural view featuring large vertical panels with red patterns and geometric designs. The panels allow light to cast shadows and reflections on the floor, creating a dynamic visual effect.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx20.tif">
<alt-text content-type="machine-generated">Interior view through large windows with bright red light sections on the upper part of the panes. A building facade with numerous windows is visible in the background.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T11" position="float">
<label>TABLE 11</label>
<caption>
<p>Daylight glare probability (DGP) of the average optimum system at 12:30 on March 20, June 21, September 22, and December 21 in Stockholm.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Stockholm</th>
<th colspan="4" align="center">Average optimum</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">1.00</td>
<td align="center">0.50</td>
<td align="center">0.53</td>
<td align="center">0.80</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx21.tif">
<alt-text content-type="machine-generated">Interior of a modern building with large windows featuring a geometric pattern of alternating red and gray sections. The pattern continues onto the walls and the floor, creating a dynamic and interconnected design.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx22.tif">
<alt-text content-type="machine-generated">Abstract digital artwork featuring a grid-like pattern with red and gray geometric shapes. Rectangular columns divide the image vertically, creating a multi-layered appearance with a perspective depth effect.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx23.tif">
<alt-text content-type="machine-generated">A row of vertical rectangular panels with alternating red and gray geometric patterns, some resembling plus signs, viewed from the interior of a space with a gray floor.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx24.tif">
<alt-text content-type="machine-generated">A series of tall, narrow windows in a dark room, with bright red geometric patterns visible outside, casting reflections onto the interior surfaces. The patterns resemble abstract shapes or symbols against a dark backdrop.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T12" position="float">
<label>TABLE 12</label>
<caption>
<p>Daylight glare probability (DGP) of the sun-tracking system at 12:30 on March 20, June 21, September 22, and December 21 in Stockholm.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Stockholm</th>
<th colspan="4" align="center">Sun-tracking</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">1.00</td>
<td align="center">0.49</td>
<td align="center">0.53</td>
<td align="center">0.81</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx25.tif">
<alt-text content-type="machine-generated">Interior view of a building with large windows. The floor has a grid-like pattern with alternating light and dark squares. The windows are framed by thick vertical beams, and the ceiling features a bright red geometric design.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx26.tif">
<alt-text content-type="machine-generated">Simulation of a 3D room with walls and floor in bright red, featuring an array of gray panels arranged vertically and horizontally. The panels are uniformly distributed across the space.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx27.tif">
<alt-text content-type="machine-generated">A row of vertical glass panels with a geometric design is partially highlighted in red. The red sections form a pattern near the top of the panels, contrasting with the surrounding gray and black grid-like pattern.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx28.tif">
<alt-text content-type="machine-generated">View from inside a building through large floor-to-ceiling windows. The upper sections of the windows are highlighted in bright red, contrasting with the dark interior and visible building exterior.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<fig id="F18" position="float">
<label>FIGURE 18</label>
<caption>
<p>Spatial Disturbing Glare (sDG) for the PVSD fa&#xe7;ade in Stockholm: <bold>(a)</bold> fixed position; <bold>(b)</bold> average optimum; <bold>(c&#x2013;f)</bold> PVSD fixed to the sun-tracking position on: <bold>(c)</bold> March 20; <bold>(d)</bold> June 21; <bold>(e)</bold> September 21, and <bold>(f)</bold> December 21. Source: Authors.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g018.tif">
<alt-text content-type="machine-generated">Six diagrams labeled a to f show seating arrangements with color-coded distribution. Each diagram has a value labeled &#x22;sDG&#x22; indicating some form of density or gradient. Red, orange, and grey colors are used to represent different levels, suggesting a concentration or intensity shift across the seating. Blue rectangles at the bottom indicate possible entrances or factors influencing the seating.</alt-text>
</graphic>
</fig>
<p>In Nicosia, the same set of configurations results in generally lower glare levels. The fixed position already yields a relatively low annual value (sDG &#x3d; 11.5%) and only moderate DGP values for the four representative dates (0.42&#x2013;0.54), which implies that a static configuration is sufficient to maintain acceptable visual comfort for most of the year (<xref ref-type="fig" rid="F19">Figure 19</xref>). By contrast, the more sun-facing &#x201c;average optimum&#x201d; and the sun-tracking drive the winter case (21 December, 12:30) up to DGP &#x3d; 1.00, without providing a clear annual advantage (sDG remains around 11%&#x2013;12%) (<xref ref-type="table" rid="T13">Tables 13</xref>&#x2013;<xref ref-type="table" rid="T15">15</xref>). In this low-latitude, high-irradiance context, orienting the PV surface toward the solar vector increases exposure to direct high-luminance sources during the short low-solar-altitude periods, without yielding any compensatory gains in annual spatial glare.</p>
<fig id="F19" position="float">
<label>FIGURE 19</label>
<caption>
<p>Spatial Disturbing Glare (sDG) for the PVSD fa&#xe7;ade in Nicosia <bold>(a)</bold> fixed position; <bold>(b)</bold> average optimum; <bold>(c&#x2013;f)</bold> PVSD fixed to the sun-tracking position on: <bold>(c)</bold> March 20; <bold>(d)</bold> June 21; <bold>(e)</bold> September 21, and <bold>(f)</bold> December 21. Source: Authors.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g019.tif">
<alt-text content-type="machine-generated">Six graphical panels labeled a to f depict grid-like seating arrangements with varying seat availability and density represented by colors. Panel a shows sDG=11.5, b has sDG=11.6, c has 10.9, d shows 11.7, e displays 12.5, and f has 12.0. Colored gradients range from gray to yellow and red, indicating different levels of occupancy or engagement in the lower seat rows. Blue arrows are placed below each grid, suggesting directional influence or movement.</alt-text>
</graphic>
</fig>
<table-wrap id="T13" position="float">
<label>TABLE 13</label>
<caption>
<p>Daylight glare probability (DGP) of the fixed system at 12:30 on March 20, June 21, September 22, and December 21 in Nicosia.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Nicosia</th>
<th colspan="4" align="center">Fixed</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">0.51</td>
<td align="center">0.42</td>
<td align="center">0.49</td>
<td align="center">0.54</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx29.tif">
<alt-text content-type="machine-generated">Computer-generated illustration highlighting window locations in a building with red overlays. The windows are arranged in a grid pattern across multiple vertical sections, creating a structured architectural design.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx30.tif">
<alt-text content-type="machine-generated">A row of windows set against a bright red background, segmented by vertical black bars. Each window appears to have a repetitive square pattern with similar spacing. The overall effect is vivid and geometric.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx31.tif">
<alt-text content-type="machine-generated">Abstract graphic featuring a pattern of bright red rectangles with gray squares inside, arranged in rows and columns. The design creates a grid-like structure with vertical and horizontal lines intersecting throughout. The background and borders are in darker shades, enhancing the contrast.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx32.tif">
<alt-text content-type="machine-generated">A room with tall columns, casting shadows on a patterned floor. Bright red sections highlight parts of the columns and walls, creating a contrast with the grey tones.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T14" position="float">
<label>TABLE 14</label>
<caption>
<p>Daylight glare probability (DGP) of the average optimum system at 12:30 on March 20, June 21, September 22, and December 21 in Nicosia.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Nicosia</th>
<th colspan="4" align="center">Average optimum</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">0.56</td>
<td align="center">0.47</td>
<td align="center">0.58</td>
<td align="center">1.00</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx33.tif">
<alt-text content-type="machine-generated">Computer-generated illustration of a red-highlighted interior space with multiple vertical and horizontal panels. The panels are arranged in a symmetrical pattern against a dark background.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx34.tif">
<alt-text content-type="machine-generated">Illustration of a grid or matrix composed of a series of red panels arranged vertically, separated by dark lines. Each panel features gray, block-like shapes aligned horizontally, evenly spaced within the red segments.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx35.tif">
<alt-text content-type="machine-generated">Illustration of a wall with vertical panels casting shadows. Bright red background with dark gray panels arrayed in several rows and columns, creating a grid-like pattern with shadowing effects on the ground.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx36.tif">
<alt-text content-type="machine-generated">A digital rendering shows a space with vertical support beams and rectangular elements. Red, gray, and black colors dominate the scene, with red backgrounds and shadows projected on the floor.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T15" position="float">
<label>TABLE 15</label>
<caption>
<p>Daylight glare probability (DGP) of the sun-tracking system at 12:30 on March 20, June 21, September 22, and December 21 in Nicosia.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Nicosia</th>
<th colspan="4" align="center">Sun-tracking</th>
</tr>
<tr>
<th align="center">March 20 at 12:30</th>
<th align="center">June 21 at 12:30</th>
<th align="center">September 22 at 12:30</th>
<th align="center">December 21 at 12:30</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">DGP</td>
<td align="center">0.53</td>
<td align="center">0.45</td>
<td align="center">0.53</td>
<td align="center">1.00</td>
</tr>
<tr>
<td align="center">Radiance render</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx37.tif">
<alt-text content-type="machine-generated">Abstract graphic featuring a series of vertical red panels with gray, rectangular shapes. The panels are aligned in rows within a dark space, creating a stark contrast and an illusion of depth.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx38.tif">
<alt-text content-type="machine-generated">A 3D render of a bright red surface divided into nine sections, each with two protruding gray brackets. The background and edges are shaded in dark gray, creating a contrast.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx39.tif">
<alt-text content-type="machine-generated">A 3D architectural rendering of a room with a grid of floating, rectangular panels. The room is predominantly red, with gray panels and vertical gray lines dividing the space. Shadows are cast on the floor.</alt-text>
</inline-graphic>
</td>
<td align="left">
<inline-graphic xlink:href="fbuil-11-1753356-fx40.tif">
<alt-text content-type="machine-generated">Architectural design featuring a grid-like window structure with a pattern of alternating red and gray panels. The interior displays a shadowed floor with geometric shapes formed by window light patterns.</alt-text>
</inline-graphic>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>A further factor that helps explain the observed DGP peaks is the spacing between PV elements. Because the array is not fully continuous, the inter-panel gaps act as apertures through which direct sunlight can penetrate when the solar altitude and azimuth align with these openings. At those moments the gap, rather than the PV surface, becomes the dominant bright element in the field of view, leading to high point-in-time DGP even though a PVSD is present. This effect is more easily triggered in low-altitude locations (such as in Stockholm in spring and winter), but it can also appear in Nicosia in December when the sun is lower. Consequently, spacing should be treated as a glare-relevant design parameter reduced or supplemented by a secondary glare layer to block these beam paths.</p>
<p>Comparing the two climates, Stockholm benefits most from the static average-optimum PV orientation (the yearly energy-based position), because it reduces annual spatial disturbing glare by about 21% compared to the fixed position. Nicosia, by contrast, is already well served by a fixed configuration, and additional solar-oriented positions mainly penalize the few winter hours when direct sun can enter through panel gaps. This shows that PV/fa&#xe7;ade control rules should be climate-specific: in higher latitudes the aim is to balance solar access and glare over many potentially problematic sun positions, whereas in Mediterranean conditions the priority is to shield the space from a small number of low-sun situations that sun-tracking and PV spacing would otherwise expose.</p>
</sec>
<sec id="s3-3-4">
<label>3.3.4</label>
<title>Fa&#xe7;ade construction, actuation and prototyping</title>
<p>The design of the structural components, control elements, and their interconnections follows a modular assembly logic, enabling both interchangeability of parts and facilitating straightforward assembly and disassembly processes. This modular approach supports flexibility in prototyping and potential scalability for real-world applications. In addition, a critical aspect influencing the control strategy is the configuration of the secondary cable system and its anchorage to the aluminum frame. The routing and termination points of these cables directly impact the number of actuators required for achieving the system&#x2019;s adaptive motion. As such, the cable layout has been optimized to support transformability with minimal actuation, reinforcing the overall design goal of mechanical and control efficiency.</p>
<p>The primary design objectives include: (1) minimizing the number of actuators necessary to achieve the desired adaptability of the envelope, and (2) ensuring that the integration of control components does not interfere with the structural or gravitational behavior of the lightweight system. To this end, the actuators and associated mechanisms are deliberately decoupled from the movable body, allowing for a self-weight neutral control integration. An overview of the structural and kinematic configuration of the system is presented in <xref ref-type="fig" rid="F20">Figure 20</xref>. Detailed investigations into the kinematic behavior, load-deformation response, and comparative energy performance of the integrated photovoltaic modules are provided in (<xref ref-type="bibr" rid="B39">Phocas et al., 2024</xref>).</p>
<fig id="F20" position="float">
<label>FIGURE 20</label>
<caption>
<p>Structural system with control components. Source: <xref ref-type="bibr" rid="B39">Phocas et al. (2024)</xref>.</p>
</caption>
<graphic xlink:href="fbuil-11-1753356-g020.tif">
<alt-text content-type="machine-generated">Diagram of a mechanical grid structure featuring multiple square panels arranged in rows and columns. Red pulleys are attached at intersections, with green motors at one side, and yellow axes of rotation running vertically and horizontally, indicating movement and operation points.</alt-text>
</graphic>
</fig>
</sec>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Cross-case synthesis, applicability and limits</title>
<p>
<xref ref-type="table" rid="T16">Table 16</xref> presents the three developments into a comparable framework, clarifying how climate drivers and dominant objectives determine the appropriate adaptivity scale and control logic. The retroreflective fa&#xe7;ade targets near-fa&#xe7;ade radiation redirection in a hot, high-irradiance context with row-level reconfiguration, whereas the Tri-fold system addresses glare/illuminance regulation in a temperate climate using zonal actuation, and the PVSD balances gains, glare, and PV orientation at the fa&#xe7;ade assembly scale across two climates. <xref ref-type="table" rid="T16">Table 16</xref> complements this by aligning each case&#x2019;s metric bundle with its objective and by making the main trade-offs explicit: (i) the retroreflective concept is effective for near-fa&#xe7;ade short-wave radiation management, yet its outcomes remain domain- and distance-dependent and should not be interpreted as coupled urban microclimate prediction; (ii) the Tri-fold device demonstrates that expressive, pattern-based shading can remain performance-robust when its motion logic is driven by climate-relevant conditions, while the point-in-time emphasis motivates targeted annual validation for final actuation-feasible states; and (iii) the PVSD highlights that energy-oriented orientations can reduce transmitted gains substantially, but glare sensitivity is often governed by panel spacing and edge conditions, meaning that geometric detailing (overlap/staggering/secondary glare layer) may be as important as tracking strategy.</p>
<table-wrap id="T16" position="float">
<label>TABLE 16</label>
<caption>
<p>Cross-case synthesis: design intent and implementation, assessment, key outcomes, and trade-offs.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Typology</th>
<th rowspan="2" align="center">Primary objectives</th>
<th align="center">Adaptivity scale</th>
<th rowspan="2" align="center">Metrics</th>
<th rowspan="2" align="center">Headline results</th>
<th rowspan="2" align="center">Main trade-offs/limits</th>
<th rowspan="2" align="center">Applicability</th>
</tr>
<tr>
<th align="center">Control</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">Kinetic retroreflective shading</td>
<td rowspan="2" align="center">Reduce reflected solar exposure near fa&#xe7;ade, maintain indoor comfort</td>
<td align="center">Row-level (modules coupled per row)</td>
<td rowspan="2" align="center">Ray-tracing and cumulative irradiance (near-fa&#xe7;ade), illuminance, EN 17037 daylight/view, annual glare probability</td>
<td rowspan="2" align="center">Reflection efficiency up to 88% (S1); near-fa&#xe7;ade cumulative irradiance reduced by 0.4&#xa0;kWh/m<sup>2</sup> vs. baseline; reduced reflected radiation toward canyon by 43%&#x2013;50%, EN 17037&#xa0;min daylight met (100 lux over 95% area); disturbing glare 1.6%</td>
<td rowspan="2" align="center">Not coupled microclimate/UHI model; effect depends on domain and distance, reflector not effective as light shelf, full-scale control/actuation not validated</td>
<td rowspan="2" align="center">Dense, high-irradiance urban contexts where radiation redirection and glare/daylight balance matter</td>
</tr>
<tr>
<td align="center">Discrete folding states</td>
</tr>
<tr>
<td rowspan="2" align="center">Kinetic tri-fold</td>
<td rowspan="2" align="center">Regulate illuminance, reduce glare, preserve view</td>
<td align="center">Zone-level (modules coupled per vertical zone)</td>
<td rowspan="2" align="center">Point-in-time illuminance and glare, EN 17037 view, parametric geometry exploration</td>
<td rowspan="2" align="center">Winter noon baseline 5363 lux, altitude-tracking tri-fold achieves mean 905 lux (summer solstice 12:00) vs. baseline 2530 lux and static tri-fold 1158 lux, glare risk reduced in closed state</td>
<td rowspan="2" align="center">Point-in-time emphasis, prototype scaling/actuation fidelity, higher control complexity for mixed arrangements</td>
<td rowspan="2" align="center">Temperate climates with seasonal glare peaks, offices needing simple single-axis actuation</td>
</tr>
<tr>
<td align="center">Single-axis altitude-responsive tracking</td>
</tr>
<tr>
<td rowspan="2" align="center">Dual-axis PVSD</td>
<td rowspan="2" align="center">Balance solar gains, glare, PV orientation</td>
<td align="center">Fa&#xe7;ade-wide (fully synchronized array)</td>
<td rowspan="2" align="center">Annual transmitted gains, point-in-time DGP, annual spatial glare indicator (sDG)</td>
<td rowspan="2" align="center">Baseline annual gains: 433.2 (Stockholm)/529.9&#xa0;kWh/m<sup>2</sup>&#xb7;yr (Nicosia); &#x201c;average-optimum&#x201d; reduces by 42% (to 251.2) and 37.9% (to 329.2); Stockholm sDG improves 19.1%&#x2013;15.1% (21% reduction)</td>
<td rowspan="2" align="center">Inter-panel gaps can trigger glare, tracking guaranteed glare improvement</td>
<td rowspan="2" align="center">High latitudes benefit from static optimized states, mediterranean needs protection at critical low-sun hours</td>
</tr>
<tr>
<td align="center">Fixed vs. static &#x201c;average-optimum&#x201d; vs. tracking (dual-axis)</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Source: Authors.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Beyond indoor solar-gain reduction, the retroreflective configuration illustrates how a fa&#xe7;ade can be configured to manage the directionality of reflected radiation toward the exterior environment, potentially reducing re-radiation or reflected loading within an urban canyon while preserving interior visual conditions. The design intention is therefore not a single-objective reduction of incident radiation, but a redistribution strategy compatible with architectural integration and acceptable daylight levels. Its main weak point is that the demonstrated benefits are specific to near-fa&#xe7;ade short-wave radiative effects and depend on the evaluated spatial domain and distance from the fa&#xe7;ade; therefore, conclusions should remain bounded to radiation redirection unless coupled microclimate modeling is performed. The Tri-fold kinetic shading system further confirms that once a fa&#xe7;ade is made responsive, it can be steered to maintain illuminance within a target range while suppressing seasonal or orientation-driven glare peaks. This is relevant because it indicates that geometrically expressive, pattern-based devices can still perform robustly when evaluated against performance criteria, provided that their actuation logic is informed by climate-relevant simulations rather than purely geometric intent.</p>
<p>For the PVSD, the cross-climate comparison in <xref ref-type="table" rid="T16">Table 16</xref> clarifies that &#x201c;optimal&#x201d; orientations are climate-dependent: in Stockholm, a static, energy-based &#x201c;average optimum&#x201d; orientation can mitigate low-sun glare compared to the reference fixed position, whereas in Nicosia where baseline glare levels are already low more sun-facing orientations do not necessarily improve annual glare conditions and can trigger high point-in-time DGP values in winter. This indicates that Mediterranean conditions may require protecting only a few critical low-sun hours rather than maximizing sun exposure. Across both locations, spacing between PV elements emerges as a glare-relevant parameter: panel gaps act as apertures for direct beam penetration and are responsible for glare peaks, implying that PV arrays should be detailed with overlap, staggering, or secondary glare layers when used as view-facing adaptive shading.</p>
<p>Across the three adaptive fa&#xe7;ade systems, a recurring design intention is to achieve transformability through lightweight construction and a minimum, strategically placed number of actuators. In the retroreflective fa&#xe7;ade, horizontal cable-driven rows enable stepwise reconfiguration; in the Tri-fold system, one actuator governs a vertical zone of modules; and in the dual-axis PV shading system, only two actuators mounted on the fixed frame drive synchronized bi-axial motion of all panels. This clustered actuation discretizes the fa&#xe7;ade&#x2019;s admissible configurations. Two implications follow: first, performance evaluation should prioritize actuation-feasible states (e.g., baseline, fixed, average optimum, tracking) rather than purely geometric optima; second, a small set of robust states can offer a better performance-to-complexity ratio than continuous tracking, particularly when glare peaks are driven by a few critical low-sun hours. Embedding actuation concept early in the integrated design workflow becomes critical: module depth gradients, row/zone subdivision, and cable routing should be defined together with climatic simulations so that the fa&#xe7;ade meets illuminance targets and glare limits with minimal actuators and without adding mass to moving parts. In other words, performance assessment (illuminance, sDG, DGP) and actuation/geometry detailing (panel spacing, overlap, feasible poses) must be co-developed, because small geometric choices such as inter-panel gaps can negate glare benefits achieved through orientation alone.</p>
<p>The outdoor ray-tracing and cumulative irradiance analyses quantify near-fa&#xe7;ade short-wave exposure/redirection within a defined domain (10 &#xd7; 10&#xa0;m), and therefore indicate radiative proxies rather than coupled microclimate outcomes (air temperature, wind, long-wave exchange). A full sensitivity study of optical properties (reflectance/transmittance) was outside scope; values were fixed to representative materials and should be tested parametrically in future work. Likewise, scaled prototypes validate kinematics and assembly logic but do not replicate full-scale stiffness, friction, tolerances, actuator forces, and material optical properties; performance claims therefore rely primarily on the simulation results summarized in <xref ref-type="table" rid="T16">Table 16</xref>, while prototypes support feasibility.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<label>5</label>
<title>Conclusion</title>
<p>This study demonstrates that adaptive fa&#xe7;ades should be assessed through a multi-criteria lens, where illuminance, daylight availability, glare control, and solar/energy performance are evaluated concurrently. Across three typologies and four climatic contexts, the results show that performance outcomes and referred control strategies are strongly climate- and objective-dependent, as synthesized in <xref ref-type="table" rid="T16">Table 16</xref>.</p>
<p>Quantitatively, the retroreflective system reaches reflection efficiency values up to 88% and reduces near-fa&#xe7;ade cumulative irradiance by approximately 0.4&#xa0;kWh/m<sup>2</sup> relative to the unshaded baseline; the refined configuration reduces reflected radiation toward the canyon by 43%&#x2013;50% at the evaluated peak-season points while maintaining EN 17037 minimum daylight provision (100 lux over 95% of the floor area) with disturbing glare limited to 1.6%. The Tri-fold system reduces extreme winter-noon illuminance from 5363 lux (baseline) and demonstrates altitude-responsive regulation, reaching approximately 905 lux at summer-solstice noon versus 2530 lux (baseline) and 1158 lux (static Tri-fold). For the PVSD, the static &#x201c;average-optimum&#x201d; orientation reduces annual transmitted gains by up to 42% (Stockholm) and improves annual spatial disturbing glare from 19.1% to 15.1%, confirming that robust fixed states can outperform increased control complexity under certain climatic conditions.</p>
<p>The findings further indicate that adaptive fa&#xe7;ade development benefits from evaluating actuation-feasible states and integrating motion logic early in the design workflow, since geometric details such as inter-panel gaps can dominate glare performance. Future work should extend validation through full-scale prototypes and, where outdoor thermal claims are central, couple near-fa&#xe7;ade radiative analyses with urban microclimate modelling while addressing standardization, lifecycle performance, and economic feasibility to support wider architectural adoption.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>MM: Writing &#x2013; original draft, Writing &#x2013; review and editing. MP: Writing &#x2013; original draft, Writing &#x2013; review and editing. EC: Writing &#x2013; review and editing, Writing &#x2013; original draft. AM: Writing &#x2013; review and editing, Writing &#x2013; original draft.</p>
</sec>
<ack>
<title>Acknowledgements</title>
<p>The authors acknowledge the work of Jiuyuan Liu, Simon G&#xf6;bel, and Tobias Steiger for their commitment in the design studio &#x201c;Smart Shade&#x201d; held at ILEK in the winter semester 2022/23 supervised by MM, the fruitful collaboration with Matthias Kip during his Master&#x2019;s thesis, and the contribution of Weifeng He to the daylighting analysis.</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<fn-group>
<fn fn-type="custom" custom-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1799376/overview">Tomasz Cholewa</ext-link>, Lublin University of Technology, Poland</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/865105/overview">Yorgos Spanodimitriou</ext-link>, University of Campania Luigi Vanvitelli, Italy</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3316533/overview">Feray Maden</ext-link>, Ya&#x15f;ar University, T&#xfc;rkiye</p>
</fn>
</fn-group>
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