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1

Pottmann, Helmut, Michael Eigensatz, Amir Vaxman, and Johannes Wallner. "Architectural geometry." Computers & Graphics 47 (April 2015): 145–64. http://dx.doi.org/10.1016/j.cag.2014.11.002.

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2

Mark, Earl. "Reconstructing architectural geometry." Architectural Research Quarterly 3, no. 1 (March 1999): 65–76. http://dx.doi.org/10.1017/s1359135500001767.

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CAD systems provide convenient tools for the creation of simple geometry by direct manipulation on the computer screen. They work well enough for two-dimensional construction, but are often inadequate for creating doubly-curved three-dimensional surfaces. The solution proposed here is to use the in-built programming language provided in most CAD systems for direct creation of geometry. Developed for didactic purposes, the stunning reconstructions of Gothic vaults suggest a method of working likely to be of great value to the geometrically adventurous architect.
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3

Hassan, Soraya Masthura. "Prinsip Desain Geometri Arsitektur Tadao Ando." EMARA: Indonesian Journal of Architecture 3, no. 2 (December 15, 2017): 77–90. http://dx.doi.org/10.29080/emara.2017.3.2.77-90.

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Geometry has shown that the architecture was an expression of man and a basic principle that were always presented on an architectural work. The research was conducted through two steps with the first step was to identified the Tadao Ando’s geometry design principle through a content analysis approach. Based on the textual review, Tadao Ando's geometry design principle was tend to select the simple geometric forms as the embodiment of the building shapes. An user spatial experiences were created through inter space relationships and interactions with the surrounding environment through the geometry and shape processing and became the central to his architectural work creation. In other words, pure geometry concept was the instrument to presented all of those. The second step was to compared Tadao Ando's geometry design principles in the monistic architecture to the pluralistic architecture catagories using a precedent analysis approach. The comparisons toward the geometrical principles were more complex and quite varied geometric shapes in pluralistic architecture while simple geometric shapes can be found in the monistic architecture,as well as interlinked circular paths in pluralistic architecture which shaped by the ‘direction wall’ rather than a simple circulation path in the monistic architecture, and the wall-formed angle was a multiple of 15° in monistic architecture but varying angles in the pluralistic architecture.
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4

Hassan, Soraya Masthura. "Prinsip Desain Geometri Arsitektur Tadao Ando." EMARA: Indonesian Journal of Architecture 3, no. 2 (December 15, 2017): 77–90. http://dx.doi.org/10.29080/emara.v3i2.152.

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Geometry has shown that the architecture was an expression of man and a basic principle that were always presented on an architectural work. The research was conducted through two steps with the first step was to identified the Tadao Ando’s geometry design principle through a content analysis approach. Based on the textual review, Tadao Ando's geometry design principle was tend to select the simple geometric forms as the embodiment of the building shapes. An user spatial experiences were created through inter space relationships and interactions with the surrounding environment through the geometry and shape processing and became the central to his architectural work creation. In other words, pure geometry concept was the instrument to presented all of those. The second step was to compared Tadao Ando's geometry design principles in the monistic architecture to the pluralistic architecture catagories using a precedent analysis approach. The comparisons toward the geometrical principles were more complex and quite varied geometric shapes in pluralistic architecture while simple geometric shapes can be found in the monistic architecture,as well as interlinked circular paths in pluralistic architecture which shaped by the ‘direction wall’ rather than a simple circulation path in the monistic architecture, and the wall-formed angle was a multiple of 15° in monistic architecture but varying angles in the pluralistic architecture.
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5

Ahmadzadeh Siyahrood, Sanaz, Arghavan Ebrahimi, Javad Ghiasvand, and Mohammadjavad Mahdavinejad. "THE FACTORS CONTRIBUTING IN SPIRITUALITY DEFINITION OF IRANIAN MOSQUES." Journal of Islamic Architecture 5, no. 4 (December 21, 2019): 198–208. http://dx.doi.org/10.18860/jia.v5i4.5254.

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Islamic mosques in Iran, similar to other Islamic nations, are reflections of visual beauties and typical examples of symbolic integration and relationship with strong beliefs and geometry. Scrutiny of these relationships provides a broader and profound perception of the design paradigm of these sacred masterpieces, which not only have been responding to the functional aspect of holy places but also represent an aesthetic model of architectural geometric perfection. This paper aims to survey this paradigm with a focus on its basic concepts and geometric origins; in this regard, it seeks to address the ensuing questions: what are the fundamental ideas in the design of mosques? How and which methods were used have been reflected in the architecture of mosques? How has the geometry assisted the architecture of mosques? What is the geometry role in the accomplishment of those basic concepts? To this end, after stating the fundamental concepts and dominant ideology in the design of mosques and the progress factors of Islamic architecture, their architectural features, spatial organization, and relations with geometry had been examined. The research hypothesis is that monotheism and divine unity are the original concepts of the architecture of mosques and this type of architectural design tries with the help of a range of abstract arts, symbolic materials, various methods, and science of geometry symbolize these ideas to create a sacred atmosphere and place which could be an intermediate spot for the human to achieve that divinity and unity.
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6

Bellone, T., F. Fiermonte, and L. Mussio. "THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-5/W1 (May 16, 2017): 623–30. http://dx.doi.org/10.5194/isprs-archives-xlii-5-w1-623-2017.

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Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. <br><br> Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,…) those most frequently employed in architectural design are: <br> &amp;ndash; Euclidean Geometry <br> &amp;ndash; Projective Geometry <br> &amp;ndash; The non-Euclidean geometries. <br><br> Entire architectural periods are linked to specific types of geometry. <br><br> Euclidean geometry, for example, was the basis for architectural styles from Antiquity through to the Romanesque period. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture.
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7

Chang, Wei. "Application of Tessellation in Architectural Geometry Design." E3S Web of Conferences 38 (2018): 03015. http://dx.doi.org/10.1051/e3sconf/20183803015.

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Tessellation plays a significant role in architectural geometry design, which is widely used both through history of architecture and in modern architectural design with the help of computer technology. Tessellation has been found since the birth of civilization. In terms of dimensions, there are two- dimensional tessellations and three-dimensional tessellations; in terms of symmetry, there are periodic tessellations and aperiodic tessellations. Besides, some special types of tessellations such as Voronoi Tessellation and Delaunay Triangles are also included. Both Geometry and Crystallography, the latter of which is the basic theory of three-dimensional tessellations, need to be studied. In history, tessellation was applied into skins or decorations in architecture. The development of Computer technology enables tessellation to be more powerful, as seen in surface control, surface display and structure design, etc. Therefore, research on the application of tessellation in architectural geometry design is of great necessity in architecture studies.
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8

Pottman, Helmut, Andreas Asperl, Michael Hoffer, Axel Killian, and Andre Brown. "Book Review: Architectural Geometry." International Journal of Architectural Computing 6, no. 2 (June 2008): 215–16. http://dx.doi.org/10.1260/147807708785850131.

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9

Yi, Zhong, and Cheng Zhi Yuan. "Mathematical Analysis on Helicoids Architectural Form." Advanced Materials Research 790 (September 2013): 273–77. http://dx.doi.org/10.4028/www.scientific.net/amr.790.273.

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In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.
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10

Carpo, Mario. "Drawing with Numbers: Geometry and Numeracy in Early Modern Architectural Design." Journal of the Society of Architectural Historians 62, no. 4 (December 1, 2003): 448–69. http://dx.doi.org/10.2307/3592497.

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Precision in building was pursued and achieved well before the rise of modern science and technology. This fact applies to the classical tradition as well as to medieval architecture, and is particularly evident in architectural drawings and design from the Italian Renaissance onward. In this essay, I trace the shift from geometry-the primary tool for quantification in classical architecture- to numeracy that characterizes Renaissance architectural theory and practice. I also address some more general aspects of the relation between technologies of quantification and the making of architectural forms.
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11

Pottmann, Helmut. "Architectural Geometry as Design Knowledge." Architectural Design 80, no. 4 (July 8, 2010): 72–77. http://dx.doi.org/10.1002/ad.1109.

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12

Ediz, Özgür, and Gülen Çağdaş. "A Computational Architectural Design Model Based on Fractals." Open House International 32, no. 2 (June 1, 2007): 36–45. http://dx.doi.org/10.1108/ohi-02-2007-b0005.

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Digital design technologies play a significant role in assisting the designer through conceptual architectural design. Computer supported design systems can generate various images at the early design phase and can contribute to seeking alternative architectural forms. Currently, different design approaches are being employed in the formation of architectural products. Examples of architecture that produce unusual forms are often encountered within unique conceptual approaches. The development of new design examples is supported by the digital production of forms, and three-dimensional models through varying geometric approaches. In this study, a design approach that uses computer aided architectural design to produce architectural forms will be suggested. This approach utilizes principles existing in the unique fractal dimension of elements based on a vocabulary relevant to a specific architectural language. By relying on the fractal dimension and features of an existing architectural pattern, this generative design approach supports creativity in the production of new forms. The proposed approach is evaluated as a creative tool in architectural design. The subject of architecture; buildings, spaces, surroundings, symbols of that particular society are also the elements of a meta-language which creates a fractal geometry based relation. It is possible to analyse this relation through a fractal geometry-based principle. In short, a fractal geometrical generative method is suggested. Also, recently-surfaced discussions about "Chaos Theory" and its effects on the design process via "Chaos and Self - Similarity" are studied. The significance of these different phenomena and disciplines upon architectural design are also studied for developing a possible creative tool.
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13

Dragisic, Maja, and Andjelka Bnin-Bninski. "The application models of the topological principle of continuous deformation in the architectural design process." Facta universitatis - series: Architecture and Civil Engineering 15, no. 3 (2017): 453–64. http://dx.doi.org/10.2298/fuace161115035d.

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Architecture and geometry share a mutual history, and their relationship precedes the introduction of digital and computer technologies in architectural theory and design. Geometry has always been directly related to the modalities of thinking in architecture through the problems of conceptualisation, representation, building, technology. Through the historical overview of these two disciplines, it is possible to perceive direct influences of geometry on the architectural creative concepts, formal characteristics of architectural works, structural aspects, and building methods in architecture. However, the focus of this paper is not on the representation of historical intertwining of these two disciplines, which is indisputable, it is on the attempt to represent one specific bond between topology and architecture, firstly through the explanation of the principle of continuous deformability, and secondly through the representation of the models through which the principle occurs in the architectural design process, as well. The first part of this work will introduce and analyse the transition of concepts of continuity and deformability, from mathematical topology through philosophy to architecture, while the second part of the work will explain two models in detail, formal and systematic, through which the principle of continuous deformation is applied in certain architectural design practices. Overall, this work deals with the interpretation of the principle of continuous deformation in architecture and it shows in which way the architectural discourse changes the meaning of a mathematical-philosophical notion and turns it into a design methodology of its own. The subtlety of the question Bernard Tschumi asks about space illustrates the need to thoroughly investigate interdisciplinary relation between architecture, philosophy, and mathematics: ?Is topology a mental construction toward a theory of space?? (Tschumi, 2004, p.49)
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14

Moloney, Jules, and Rajaa Issa. "Materials in Architectural Design Education Software: A Case Study." International Journal of Architectural Computing 1, no. 1 (January 2003): 46–58. http://dx.doi.org/10.1260/147807703322467423.

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Most CAAD software in use for architectural education relies heavily on abstract geometry manipulation to create architectural form. Building materials are usually applied as finishing textures to complement the visual effect of the geometry. This paper investigates the limitations of commonly used CAAD software in terms of encouraging an intuitive thinking about the physical characteristics of building materials in the context of the educational design studio. The importance of the link between representation and creativity is noted. In order to sample the current functionality of typical software used in architectural education a case study involving 80 first year architecture students is presented. These outcomes are discussed and the possibility for new or extended software features are suggested. The paper concludes with an argument for design software that redresses the balance between geometry and materials in architectural design education.
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15

Haklay, Gil, and Avi Gopher. "Geometry and Architectural Planning at Göbekli Tepe, Turkey." Cambridge Archaeological Journal 30, no. 2 (January 14, 2020): 343–57. http://dx.doi.org/10.1017/s0959774319000660.

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The site of Göbekli Tepe in southeastern Turkey keeps fascinating archaeologists as it is being exposed. The excavation since 1995 has been accompanied by a lively discussion about the meaning and implications of its remarkable early Neolithic megalithic architecture, unprecedented in its monumentality, complexity and symbolic content. The building history and the chronological relations between the different structures (enclosures), however, remain in many ways a challenge and open to further analysis. The study presented here is an attempt to contribute in this direction by applying a preliminary architectural formal analysis in order to reconstruct aspects of the architectural design processes involved in the construction of the monumental enclosures. This is done under the premise that such investigation would shed light on the chaîne opératoire of the enclosures' construction and their history, thus enabling a fresh look as well as an evaluation of past suggestions regarding these structures and the people who built them. Indeed, the results of the analysis brought to light an underlying geometric pattern which offers a new understanding of the assemblage of architectural remains indicating that three of the stone-built large enclosures were planned and initially built as a single project.
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16

Napong, Nophaket. "The Graph Geometry for Architectural Planning." Journal of Asian Architecture and Building Engineering 3, no. 1 (May 2004): 157–64. http://dx.doi.org/10.3130/jaabe.3.157.

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17

Ajlouni, Rima. "Quasi-periodic Geometry for Architectural Acoustics." Enquiry A Journal for Architectural Research 15, no. 1 (December 18, 2018): 42–61. http://dx.doi.org/10.17831/enq:arcc.v15i1.453.

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The discovery of quasi-periodic atomic order in the crystalline state has uncovered an exciting new class of symmetries that has never been explored before. Because of their non-periodic translational order and self-similar properties, quasi-periodic structures offer unique opportunities for investigating questions related to their acoustical behavior. Their unique long-range non-periodic formations have the ability to diffuse and orchestrate the flow of sound energy in many unique ways; offering intriguing potential for innovating a new wave of optimized sound diffusers. One key limitation with available periodic diffusers is that their repeating logic creates repetitive energy loops, which significantly reduce their ability to uniformly disperse sound energy. Quasi-periodic geometry can mitigate such limitation. By encapsulating an infinite variety of distinct profiles in all directions, quasi-periodic surfaces can eliminate the formation of bundled or looped reflections; considerably enhancing the ability of the diffuser to uniformly disperse sound energy. To investigate this hypothesis, an experimental approach is used to simulate sound reflection patterns of the quasi-periodic surface profiles using a ray tracing method. Both qualitative and quantitative analyses are used to interpret the simulated results. The international Standards (ISO) metrics are used to validate the proposed approach and verify the results. Results show that the diffusion quality of the tested quasi-periodic surface is superior to the diffusion performance of the tested periodic surface.
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18

SEKI, Hiroki. "SURFACE GEOMETRY AND ARCHITECTURAL DESIGN ACTIVITIES." Journal of Architecture and Planning (Transactions of AIJ) 83, no. 751 (2018): 1687–94. http://dx.doi.org/10.3130/aija.83.1687.

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19

Liapi, Katherine A. "Geometry in Architectural Engineering Education Revisited." Journal of Architectural Engineering 8, no. 3 (September 2002): 80–88. http://dx.doi.org/10.1061/(asce)1076-0431(2002)8:3(80).

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20

Burry, Jane. "The Shifting Ground Of Architectural Geometry." Architectural Theory Review 15, no. 2 (August 2010): 187–200. http://dx.doi.org/10.1080/13264826.2010.495453.

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21

Pottmann, Helmut. "Architectural Geometry and Fabrication-Aware Design." Nexus Network Journal 15, no. 2 (April 27, 2013): 195–208. http://dx.doi.org/10.1007/s00004-013-0149-5.

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22

Papasterevski, Dimitar. "Architectural Term: Self – Similarity." South East European Journal of Architecture and Design 2020 (June 12, 2020): 1–4. http://dx.doi.org/10.3889/seejad.2020.10054.

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Architecture, as one of the oldest areas of human activity, describes several categories that seem to be effective today: firmitas, utilities, venustas. But on the other hand, almost every period re-examines and reinterprets these terms. What is happening today? Are there old provisions still? Can we create new ones or expand, modify or re-create them? This paper evaluates the term of the architectural theme to contribute to the creation of a kind of critical vocabulary of contemporary architecture in the context of understanding architectural thought. Different ways of understanding/interpreting an architectural term can lead us to a new and different way of understanding and comprehending architecture itself in a modern changing world. This paper considers the relationship between fractal geometry and architecture as they respond to complexity and order, through the architectural term “self-similarity”.
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23

de, Jorge-Huertas, and Jorge-Moreno de. "Palladio and the Mediterranean heritage the patio, atrium and portico as geometrical and well-being strategies." Spatium, no. 41 (2019): 1–13. http://dx.doi.org/10.2298/spat1941001j.

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Palladio?s heritage has aspects that are interrelated with the vernacular architectural heritage of the Mediterranean, and it entails a collective knowledge. The aim of this research is to analyse his work and its evolution over time, paying specific attention to three architectural design elements: the patio, the portico and the atrium in relation to their proportions and ratios. This work will highlight how geometry shapes the space and the form of these three elements, producing architecture for well-being. The main results may constitute a possible new frontier of research where these three design elements make a connection between interior and exterior spaces, strengthen a greater visibility of the geometry, create ?intermediate spaces? and enhance the idea of a ?Continuous Monument?. The paper will underline how mathematical factors such as proportions, ratios and constructive geometry, together with climatic reasons, are important in architecture for both its configuration and geometry and they are a constant in Palladio?s heritage and his Mediterranean cultural influence.
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Sasportas, Raphaël, and Feriel Mustapha. "Modular architecture shape design recursive algorithm." E3S Web of Conferences 170 (2020): 06006. http://dx.doi.org/10.1051/e3sconf/202017006006.

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The architecture and architectural shape of a building plays an important role in the interior housing design, many concepts have been developed to optimize this and to have a housing that reflects both visual and architectural comfort or even thermal one. The evolution of these houses however is not controlled, modular architecture has appeared because among its basic principles is being built from modules that can be assembled, then separately modified or even disassembled, the advantage of this typology of architecture is that it is fast in execution, light in installation and above all has very little impact on the environment in which it is part. These buildings are characterized by more dynamic geometries, which results in a very rich architectural language and an interesting sky line, however, to be able to project all the possibilities is a challenge in itself. In this article the discrete geometry is treated through the development of an algorithm that illustrates the process that allows to expose all possible cell combinations, the latter represents the basic module of modular architecture, the most attracting choices will be arranged to illustrate the formal and architectural optimization of a house. In this study the emphasis will be placed on the mathematical part in order to highlight the relationship between geometry and its influence on the final architectural rendering.
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Lee, Myung-Sik. "Application of Fractal Geometry to Architectural Design." Architectural research 16, no. 4 (December 30, 2014): 175–83. http://dx.doi.org/10.5659/aikar.2014.16.4.175.

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26

Vukmirovic, Srdjan, Mirjana Devetakovic, and Ljiljana Petrusevski. "Topology — Possibilities of application in architectural geometry." Pollack Periodica 7, Supplement 1 (January 2012): 29–42. http://dx.doi.org/10.1556/pollack.7.2012.s.3.

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27

Sturz, Yvonne R., Manfred Morari, and Roy S. Smith. "Control of an Architectural Cable Net Geometry." IEEE Transactions on Control Systems Technology 28, no. 4 (July 2020): 1378–92. http://dx.doi.org/10.1109/tcst.2019.2910449.

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28

Cheng, Irene. "Race and Architectural Geometry: Thomas Jefferson’s Octagons." J19: The Journal of Nineteenth-Century Americanists 3, no. 1 (2015): 121–30. http://dx.doi.org/10.1353/jnc.2015.0000.

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Kasap, Orkun. "Advances in Architectural Geometry (AAG) 2016 Symposium." Nexus Network Journal 19, no. 1 (February 10, 2017): 225–33. http://dx.doi.org/10.1007/s00004-017-0330-3.

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30

Shelden, Dennis R. "The long awaited arrival of architectural geometry." Computer-Aided Design 41, no. 7 (July 2009): 551–52. http://dx.doi.org/10.1016/j.cad.2009.03.002.

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31

Guitart, Miguel. "Limit Geometries of Architectural Filters: Precise Rationality and Poetic Emotion." ZARCH, no. 15 (January 27, 2021): 222–33. http://dx.doi.org/10.26754/ojs_zarch/zarch.2020154648.

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An architectural filter is a porous material construction that regulates transverse visual relationships, and establishes degrees of connection through the intervention of light and gaze. Filtering boundaries display variable proportions of mass and air, which are instrumental to the production of the spatial experience behind the mediation of matter and geometry. A filter's structural system synthesizes geometric relations with the capacity to cause architectural atmospheres, as a result of the active border that is technically precise and sensorially ambiguous at the same time. The text sustains that the emerging atmospheres behind the filter cannot take place without a previous, precise geometric production; the poetic dimension of filtering strategies originates from its capacity to transform the concrete geometry of its contour conditions and controlled material execution into an unexpected atmosphere of emotional and incommensurable qualities.
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32

Yuan, Cheng Zhi, and Zhong Yi. "A Study on the Application of Algorithmic Modelling in Architectural Space Design." Applied Mechanics and Materials 174-177 (May 2012): 1743–47. http://dx.doi.org/10.4028/www.scientific.net/amm.174-177.1743.

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The birth of algorithmic modelling has made architecture breaking through the constraints of traditional Euclidean geometry truly into "era of non-Euclidean geometry space". Algorithmic modelling often uses pure numbers, mathematical rules and algebraic expressions for generating architectural art works with different styles. Usually there are two ways for algorithmic modelling: language programming and graphical. This article has discussed the design significance and operation methods of algorithmic modelling in order to inspire architects a little.
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Katona, Vilmos. "Relief Method: The Analysis of Architectonic Façades by Fractal Geometry." Buildings 11, no. 1 (December 31, 2020): 16. http://dx.doi.org/10.3390/buildings11010016.

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This paper explores the working hypothesis that fractal patterns that closely match those found in nature are more likely to convey a strong sense of genius loci to humans by comparison with ‘Euclidean’ patterns that do not occur in nature frequently. A part of this survey is concerned with showing the pattern-conscious thinking, regarding the façade composition and material textures, of historical buildings compared to different ecological or geological scenes. We also examine the background of pattern-design from architectural theory, and extrapolate the matter to certain questions about spatial quality, tectonics, and the phenomenon of place. Our most important concern is an attempt to enhance architectural arguments regarding place and character with mathematical calculations. We introduce ‘relief method’ as a possible way to capture the haptic nature of architecture beyond the patterns of its two-dimensional projections. Through this approach, façades are considered as reliefs and pictures at the same time, thus reflecting the tension between their materiality and visual representation. Fractal geometry also helps to understand how architectonic layers define scale, and by which means architecture could be translated into the human level of physical existence.
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Dorji, Yonten, Bernhard Schuldt, Liane Neudam, Rinzin Dorji, Kali Middleby, Emilie Isasa, Klaus Körber, Christian Ammer, Peter Annighöfer, and Dominik Seidel. "Three-dimensional quantification of tree architecture from mobile laser scanning and geometry analysis." Trees 35, no. 4 (April 12, 2021): 1385–98. http://dx.doi.org/10.1007/s00468-021-02124-9.

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Abstract Key message Mobile laser scanning and geometrical analysis revealed relationships between tree geometry and seed dispersal mechanism, latitude of origin, as well as growth. Abstract The structure and dynamics of a forest are defined by the architecture and growth patterns of its individual trees. In turn, tree architecture and growth result from the interplay between the genetic building plans and environmental factors. We set out to investigate whether (1) latitudinal adaptations of the crown shape occur due to characteristic solar elevation angles at a species’ origin, (2) architectural differences in trees are related to seed dispersal strategies, and (3) tree architecture relates to tree growth performance. We used mobile laser scanning (MLS) to scan 473 trees and generated three-dimensional data of each tree. Tree architectural complexity was then characterized by fractal analysis using the box-dimension approach along with a topological measure of the top heaviness of a tree. The tree species studied originated from various latitudinal ranges, but were grown in the same environmental settings in the arboretum. We found that trees originating from higher latitudes had significantly less top-heavy geometries than those from lower latitudes. Therefore, to a certain degree, the crown shape of tree species seems to be determined by their original habitat. We also found that tree species with wind-dispersed seeds had a higher structural complexity than those with animal-dispersed seeds (p < 0.001). Furthermore, tree architectural complexity was positively related to the growth performance of the trees (p < 0.001). We conclude that the use of 3D data from MLS in combination with geometrical analysis, including fractal analysis, is a promising tool to investigate tree architecture.
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35

Luo, Yu. "The Traditional Elements and Modern Architectural Design." Advanced Materials Research 243-249 (May 2011): 6562–65. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.6562.

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Architecture is not only functional, economic, and technical and other physical characteristics, but also closely related to human behaviors. Therefore, it also has originality, visual aesthetics and function to beautify the living characteristics. To keep interest in the exterior, with a strong modern style of "purity, geometry and sculptural architecture", should not be the best way. It is worth to integrate the traditional elements, symbols, with modern forms and ideas together to form the environmental and architectural modes with the cultural heritage and modern atmosphere, and their cultural patterns. To create an architectural culture in modern buildings that could keep the traditional cultural spirit and sustainable development may be our target to continually pursue.
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Li, Zai Hui, Qing Hua Chang, and Yuan Shen. "Influence and Application of Topological Geometry in Architectural Design." Advanced Materials Research 374-377 (October 2011): 191–94. http://dx.doi.org/10.4028/www.scientific.net/amr.374-377.191.

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Topology geometry was established in the nineteenth century. It has long been widely used in architectural design. This article makes a brief introduction of topology geometry, discusses the main research objectives and the spatial characteristics in topology, and takes some good cases in architectural design.
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Datta, Sambit, and David Beynon. "A Computational Approach to the Reconstruction of Surface Geometry from Early Temple Superstructures." International Journal of Architectural Computing 3, no. 4 (December 2005): 471–86. http://dx.doi.org/10.1260/147807705777781068.

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Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing “best-fit” constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.
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Petrović, Milica. "Universal Language of Geometry: Geometrical Grid – The Nature of Space." AM Journal of Art and Media Studies, no. 16 (September 5, 2018): 69. http://dx.doi.org/10.25038/am.v0i16.255.

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The space of an artistic plane, as well as architectural space, has certain regularities, which different theories explain in various ways. Geometric regularities in space are visible through the theoretical and practical work of artists and architects. For centuries, ever since Vitruvius, theorists have been looking for valid criteria to analyze the beauty of architecture. Iosif Brodsky goes as far as to say that beauty is the purpose of evolution, while other authors define geometry as the source of all beauty. Based on these hypotheses, in the 20th century the words of the architect Buckminster Fuller must be highlighted. He says that geometry is the essence of everything that surrounds us. The importance of geometry in space conception and its analysis are stated throughout this paper. Article received: March 29, 2018; Article accepted: April 10, 2018; Published online: September 15, 2018; Scholarly analysis or debateHow to cite this article: Petrović, Milica. "Universal Language of Geometry: Geometrical Grid – The Nature of Space." AM Journal of Art and Media Studies 16 (2018): 69−84. doi: 10.25038/am.v0i16.255
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39

Teddy, Livian, Gagoek Hardiman, N. Nuroji, and Sri Tudjono. "Method of Buildings Structural Vulnerability and Geometry Form Designs Evaluation Towards Earthquakes With The SVA Architectural Design." Journal of Architectural Design and Urbanism 2, no. 2 (April 26, 2020): 53–66. http://dx.doi.org/10.14710/jadu.v2i2.7577.

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In the process of architectural design, there is no special method employed by architects to evaluate buildings’ structural vulnerability and building geometry form designs towards earthquakes. Therefore, the alternative is adapting the existing method called SVA-Retrofit. JBDPA and Matsutaro Seki developed this method, and then the author adapted this method now called SVA Architectural Design. In the process of adaptation, deep literature review was conducted in order to acquire the adaptation results of the SVA-Architectural Design. These results can furthermore be an early prediction of structural vulnerability toward earthquakes that eventually leads to finding solutions for building designs or conducting detailed analysis done by structure experts.
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Almajidia, Basim Hassan, and Shams Ameer Kafi. "Digital Architecture Void Formation In Digital Architecture Interfaces." Al-Qadisiyah Journal for Engineering Sciences 13, no. 2 (July 1, 2020): 109–24. http://dx.doi.org/10.30772/qjes.v13i2.657.

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In the last era of the digital revolution, architectural outputs with distinctive void formations appeared. The development in digital technologies, which adopts solid geometry in the formation of its interfaces. So the void became an integral part of the design at the level of three dimensions, to serves as a fourth dimension of architecture. By connecting architecture with the time, the limits of length, width, and height fade away and change from the limits of place to those of time, and this void shifts out from achieving the aesthetic needs to achieving functional and structural needs. The direct correlation of the architectural void with the process of forming the interfaces led it to be considered as a basic architectural formation unit, and in light of this, the research problem was presented as (insufficient knowledge about the importance and role of the three-dimensional architectural void and the mechanisms of its formation in the interfaces of contemporary digital architecture as a void that generates or creates the design within the needs of the designer and the receiver ). The aim of the research came to reveal the concept of architectural void at the three-dimensional level, as well as revealing strategies and mechanisms for shaping the void in the interfaces. The research adopted the descriptive and analytical research methodology in proposing theoretical knowledge extracted from previous studies of building the theoretical framework for the geometry terms which contains (strategies for forming digital void, characteristics of void in digital output, features of digital spatial structure), and applying it on contemporary architectural models with a qualitative measure that is aimed at knowing the effect of terms on the selected samples and the percentage of their effectiveness in the characteristics of the digital output, and verifying the main research hypothesis which stipulated the adoption of the strategy of forming the digital void to combine the mechanisms of digital formation that is used to create void formation to meet the needs in contemporary architecture. The results indicated that the disappearance of the boundaries between the interior and exterior over time led to the use of the void in the formation of the building’s outer mass at the three-dimensional level so that the formation of the mass is based on that void which is called (design-generating void) and the structure which is created by the void called (the spatial structure), as its formation depended on "geometry" and its methods of formation.
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41

Franklin, Geraint. "Sweet Geometry: Edward Reynolds at the Architectural Association, 1956–58." Architectural History 62 (2019): 171–203. http://dx.doi.org/10.1017/arh.2019.7.

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AbstractThis article considers the position of the Anglo-Portuguese architect Edward Reynolds (1926–59) in the British avant-garde of the 1950s. InModern Architecture: A Critical History(1980), Kenneth Frampton suggested that Reynolds's student projects at the Architectural Association in London ‘exerted a decisive influence on the development of Brutalism’. This article scrutinises that claim through the lens of Reynolds's interactions with his peers, including the so-called French House group, an informal network that included his tutors John Killick, James Gowan and Peter Smithson. Notable characteristics of Reynolds's work — chiefly the use of complex and irregular geometries to articulate patterns of activity and movement — are discussed, as are contemporary projects by other members of the group and trends such as the New Brutalism, biomimicry and the revival of pre-war strands of Modernism.
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Werner, Maike, Nicholas A. Kurniawan, and Carlijn V. C. Bouten. "Cellular Geometry Sensing at Different Length Scales and its Implications for Scaffold Design." Materials 13, no. 4 (February 21, 2020): 963. http://dx.doi.org/10.3390/ma13040963.

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Geometrical cues provided by the intrinsic architecture of tissues and implanted biomaterials have a high relevance in controlling cellular behavior. Knowledge of how cells sense and subsequently respond to complex geometrical cues of various sizes and origins is needed to understand the role of the architecture of the extracellular environment as a cell-instructive parameter. This is of particular interest in the field of tissue engineering, where the success of scaffold-guided tissue regeneration largely depends on the formation of new tissue in a native-like organization in order to ensure proper tissue function. A well-considered internal scaffold design (i.e., the inner architecture of the porous structure) can largely contribute to the desired cell and tissue organization. Advances in scaffold production techniques for tissue engineering purposes in the last years have provided the possibility to accurately create scaffolds with defined macroscale external and microscale internal architectures. Using the knowledge of how cells sense geometrical cues of different size ranges can drive the rational design of scaffolds that control cellular and tissue architecture. This concise review addresses the recently gained knowledge of the sensory mechanisms of cells towards geometrical cues of different sizes (from the nanometer to millimeter scale) and points out how this insight can contribute to informed architectural scaffold designs.
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Hassan, Soraya Masthura, and Armelia Dafrina. "PROPORSI PADA KARYA DESAIN BANGUNAN TADAO ANDO DALAM KONTEKS GEOMETRI." Jurnal Arsitektur ARCADE 2, no. 1 (March 31, 2018): 33. http://dx.doi.org/10.31848/arcade.v2i1.19.

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Abstract: Proportion is one of the elements in the most basic geometric context in the process of designing an architectural work and is also one of the creativity-triggering instruments for an architect. The proportion concerns the ratio - ratio - of the geometric shape within an architectural composition. This study examines the pattern of proportions by Ando in the process of architecture to create a building, which characterizes the architecture of an Ando during his career. In this research, the content analysis method is used at several stages of research that is in the stage of finding Tadao Ando geometry design concept which is done through the textual study from several written sources and on the study of the intertextual study of the whole research samples in the form of Tadao Ando's works. this precedent method will be used in the analysis of the formative study stage, where an analysis of the work drawings such as the floor plan is performed and appears using the general theory of proportion and geometry as the basis for searching for proportions in the geometrical context of Ando's works. From the findings the ratio of proportions can be summed up several things: the dimension of length is a multiple or a derivative of the dimensions of width, width: the length where a: (x) a and (x) a: (x) a, x is a multiplier unit (0.5, 1, 1.25, 1.5, 2, 3, and 4) Keywords: Proportion, Geometric, Tadao Ando Abstrak: Proporsi merupakan salah satu elemen dalam konteks geometri yang paling mendasar di dalam proses perancangan suatu karya arsitektur dan juga merupakan salah satu instrumen pemicu kreatifitas bagi seorang arsitek. Proporsi menyangkut perbandingan – rasio – dari bentuk geometri di dalam suatu komposisi arsitektur. Penelitian ini mengkaji pola proporsi yang dilakukan oleh Ando dalam proses berarsitektur guna menciptakan suatu bangunan, yang mencirikan arsitektur seorang Ando selama perjalanan karirnya. Pada penelitian ini, metode analisis isi digunakan pada beberapa tahap penelitian yaitu pada tahap menemukan konsep desain geometri Tadao Ando yang dilakukan melalui kajian tekstual dari beberapa sumber tertulis dan pada kajian intertekstual pendeskrisian secara keseluruhan sampel penelitian yang berupa bangunan-bangunan karya Tadao Ando. motede preseden ini akan digunakan pada analisis tahap kajian formatif, dimana dilakukan analsis pada gambar kerja seperti denah, dan tampak dengan menggunakan teori umum dari proporsi dan geometri sebagai dasar penulusuran untuk menemukan proporsi dalam konteks geometri pada karya-karya Ando. Dari temuan rasio proporsi dapat disimpulkan beberapa hal yaitu: dimensi panjang merupakan kelipatan atau turunan dari dimensi lebar, lebar : panjang dimana a : (x)a dan (x)a : (x)a, x adalah unit kelipatan (0.5, 1, 1.25, 1.5, 2, 3, dan 4) Kata Kunci: proporsi, geometri, tadao ando
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Nestorović, Miodrag, and Vladimir Mišković. "Advanced development of space structures in domains of 3D transformation." SAJ - Serbian Architectural Journal 3, no. 3 (2011): 116–39. http://dx.doi.org/10.5937/saj1102116n.

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The emergence of the new architectural solutions and structural forms of Mengeringhausen, Tsuboi, Safdie, Foster, Calatrava and other creators of magnificent structures, may be taken as an initiation and explosion of inventiveness which has continued up to till present. Consequently, the topic of this paper is to show a part of broad range of structural systems which have not been sufficiently disclosed in Serbia and surroundings, in spite of their attractiveness in contemporary architecture, in terms of space transformations, materialization and technology. The basic properties of all analyzed space structures lies in their geometric shape (Archimedean and Platonic polyhedra, polyhedron structures, and bionic of structures as well), which applies regularity, symmetry, speed of mounting, as well as modularity of the original matrices. Solutions and analyses shown deal with multifunctional space matrices, which make its potential very important both in architectural design and in structural theory. The topic of this paper is to consider the development of matrix structure in context of architectural forms in future, emphasizing the importance of structural geometry and its possible applications.
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Cahtarevic, Rada, and Adna Proho. "Geometric modeling and complexity - a conceptual approach in architectural design and education." Spatium, no. 42 (2019): 35–40. http://dx.doi.org/10.2298/spat1942035c.

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By encompassing abstraction and patterned information, the new fields of geometry and mathematical models of complex dynamic spatial systems provide a new method for spatial modeling. Different approaches to the application of spatial modeling in architectural design are possible, taking into consideration on the one hand the theoretical background and knowledge of geometry, and on the other, advanced computational techniques. The generative principles of complex dynamic spatial formation allow parallels between the differentiated representations and directions of approach to spatial organization. The integration of conceptual, theoretical and practical methods into complex dynamic geometric models in the preliminary phase of design could support the development of cognitive capabilities, internal representations and understanding of complex dynamic formative processes. The development of nonlinear, dynamic, complex spatial imaginative thinking corresponds with trends in contemporary computational design. The application of complex geometric modeling, including sophisticated mechanisms of human perception, intelligence and creativity, provides a synthesis of artificial and human potential.
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46

López-Chao, Vicente, and Antonio Amado Lorenzo. "Architectural Graphics Research: Topics and Trends through Cluster and Map Network Analyses." Symmetry 12, no. 12 (November 24, 2020): 1936. http://dx.doi.org/10.3390/sym12121936.

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Graphic representation is a fundamental language in architecture and engineering because it facilitates the communication of any type of information. Therefore, professionals and students need continuous and updated training, with scientific references being the best source of knowledge. However, accessing the latest findings is a complex process for people in the professional world or without an extensive research background since there are no specific filters in the databases, such as architectural graphics. This manuscript aims to define the research topics and trends in architectural graphics as a point of reference for novel professors and new researchers in graphics or drawing. A database on the Scopus-indexed scientific production of the professors of architectural graphics from public architecture schools in Spain has been developed. Furthermore, cluster and map network analyses have been performed using VOSviewer with different levels of co-occurrence to define what this group of academics investigates and how the issues are related. The results evidenced a structure in four categories: the philosophy and theory of architectural graphics, the theory of geometry in architectural heritage, the application of digital graphics in architecture education and urban design management. Research gaps are mentioned and a base framework for the future of research in architectural graphics is proposed.
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Weigand, Phil C. "The Architecture of the Teuchitlan Tradition of the Occidente of Mesoamerica." Ancient Mesoamerica 7, no. 1 (1996): 91–101. http://dx.doi.org/10.1017/s0956536100001310.

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AbstractThis study examines the geometry of the architecture of the Teuchitlan tradition of western Mexico. An argument will be made that these concentric circular buildings represent formal architectural planning and that they have cultural significance. The pattern dating from the Classic period (ca. a.d. 200–700) will be stressed.
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Arnold, Felix. "Mathematics and the Islamic Architecture of Córdoba." Arts 7, no. 3 (August 8, 2018): 35. http://dx.doi.org/10.3390/arts7030035.

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In 10th-century Córdoba, mathematics—and particularly geometry—was applied to architectural design in new ways, constituting a “mathematical turn” of Islamic architecture. In the mosque of Córdoba and in the palaces of Madīnat al-Zahrāʾ, geometry was employed in the design of ground plans, elevations, decorative patterns, and even to measure the human view. While Roman architects like Vitruvius had used mathematics to place each element of a building in its appropriate relation to all other elements of a building, the architects at Córdoba employed geometry to create a spatial web in which all parts are equal to each other and part of a single, unified space. The architects of Córdoba thus pointed the way to new possibilities of designing architecture, possibilities which were to be tested further by architects of Gothic and Renaissance architecture, though to different ends.
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Bnin-Bninski, Anđelka, and Maja Dragišić. "Scale on paper between technique and imagination: Example of Constant's drawing hypothesis." SAJ - Serbian Architectural Journal 8, no. 3 (2016): 322–39. http://dx.doi.org/10.5937/saj1603322b.

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The procedure of scaling is one of the elemental routines in architectural drawing. Along with paper as a fundamental drawing material, scale is the architectural convention that follows the emergence of drawing in architecture from the Renaissance. This analysis is questioning the scaling procedure through the position of drawing in the conception process. Current theoretical researches on architectural drawing are underlining the paradigm change that occurred as a sudden switch from handmade to computer generated drawing. This change consequently influenced notions of drawing materiality, relations to scale and geometry. Developing the argument of scaling as a dual action, technical and imaginative, Constant's New Babylon drawing work is taken as an example to problematize the architect-project-object relational chain.
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Costes, Evelyne, Colin Smith, Michael Renton, Yann Guédon, Przemyslaw Prusinkiewicz, and Christophe Godin. "MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models." Functional Plant Biology 35, no. 10 (2008): 936. http://dx.doi.org/10.1071/fp08081.

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Construction of tree architectural databases over years is time consuming and cannot easily capture event dynamics, especially when both tree topology and geometry are considered. The present project aimed to bring together models of topology and geometry in a single simulation such that the architecture of an apple tree may emerge from process interactions. This integration was performed using L-systems. A mixed approach was developed based on stochastic models to simulate plant topology and mechanistic model for the geometry. The succession of growth units (GUs) along axes and their branching structure were jointly modelled by a hierarchical hidden Markov model. A biomechanical model, derived from previous studies, was used to calculate stem form at the metamer scale, taking into account the intra-year dynamics of primary, secondary and fruit growth. Outputs consist of 3-D mock-ups – geometric models representing the progression of tree form over time. To asses these models, a sensitivity analysis was performed and descriptors were compared between simulated and digitised trees, including the total number of GUs in the entire tree, descriptors of shoot geometry (basal diameter, length), and descriptors of axis geometry (inclination, curvature). In conclusion, despite some limitations, MAppleT constitutes a useful tool for simulating development of apple trees in interaction with gravity.
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