Application of Gireh on Free Surface Pattern with Recognition of Gireh Projection on Iranian Domes Surface in the Congruence Method
Subject Areas : Future ArchitectureAref Azizpour Shoubi 1 , َAhad NeJad Ebrahimi 2
1 - Tabriz Islamic Art University
2 - Tabriz Islamic Art University
Keywords: "Islamic Architecture and Surfaces", "Free Surface", "Gireh", "Dome", "Projection Method of Gireh",
Abstract :
Free surfaces are one of the requirements of contemporary architecture. Owing to the emergence of these surfaces, the configuration of Girehs in Islamic architecture became incompatible with them. The traditional structural principles of Girehs expand two-dimensionally, whereas free surfaces expand irregularly and three-dimensionally. Gireh-work is considered one of the original and identity-giving decorations in Islamic architecture. To identify and develop contemporary architecture and past architectural achievements, it is necessary to find a strategy for projecting Girehes on free surfaces based on historical authenticity. The Islamic architecture of Iran has had many valuable achievements that can be applied to contemporary architectural challenges. In Iranian Islamic architecture, the dome and Gireh decoration play a crucial role, so the Iranian architect has tried to match these two elements using the geometric features of the dome and Gireh. As part of a qualitative research process, two examples of Iranian domes have been selected and analyzed with a descriptive-analytical approach in order to answer the following question: how Gireh’s geometrical principles on domical surfaces can be applied to contemporary free surfaces? In order to project Gireh onto the dome, a network based on radial gore segments was used as part of the projection technique. Transferring Girehs based on this network causes congruence homogeneity. Topological models of free surfaces are based on NURBS lines, making it possible to discretize and define the points on them. This makes it possible to apply anisotropic congruence transformation to Gireh projections on free surfaces.
احمدی، زهرا. (1388). زمینه گرایی و معماری پایدار. مجموعه مقالات اولین همایش ملی معماری پایدار، همدان: دانشکده فنی حرفهای سما. https://civilica.com/doc/78814
امینپور، احمد؛ محمدرضا اولیا؛ رضا ابوئی؛ بیتا حاجبی (1395). ارائه دو روش جدید در ترسیم گره و مقایسه آنها. نشریه علمی-پژوهشی انجمن علمی معماری و شهرسازی ایران، شماره 11، 67-83. https://doi.org/10.30475/isau.2017.62018
بزنوال، رولان. (1379). فنآوری تاق در خاور کهن. ترجمه: محسن حبیبی، تهران: سازمان میراث فرهنگی کشور.
بونر، جی. 1400. الگوهای هندسی اسلامی؛ توسعه تاریخی و روشهای سنتی ساخت. ترجمه: احد نژادابراهیمی، عارف عزیزپورشوبی. تبریز: دانشگاه هنر اسلامی تبریز.
رضوانی، علیرضا. (1394). شبکههای فضایی و احجام هندسی. مشهد: دانشگاه آزاد اسلامی.
عزیزپور شوبی، عارف (1397). کاربست گره در سطوح آزاد با الگو برداری از گرههای بکار رفته در سطوح آزاد فضاهای مذهبی ایرانی اسلامی از دوره ایلخانی تا پایان قاجار. پایاننامه کارشناسی ارشد، دانشگاه هنر اسلامی تبریز. به راهنمایی احد نژادابراهیمی.
فیضی، محسن و مهدی خاک زند (1392). فرم، فضا و نظم در معماری ایران، تهران: انتشارات علم و صنعت.
گرینبرگ، ماروین ج (1389). هندسههای اقلیدسی و نااقلیدسی و بسط آن. ترجمه: محمد هادی شفیعیها .تهران: مرکز نشر دانشگاهی.
لیتربارو، دیوید ،و مصطفوی، محسن (1389). معماری سطوح. ترجمه: مصطفی کیانی. تهران: دانشگاه هنر.
منتظر, بهناز, و سلطان زاده, حسین. (1397). بازتاب نقش پنج ضلعی منتظم در نقوش هندسی معماری اسلامی ایران. مطالعات هنر اسلامی. 14(30). صص: 15- 40.
نژادابراهیمی، احد؛ و عزیزپور شوبی، عارف (1398). شناسایی گنبدهای گره دار در مساجد ایرانی. معماری سبز، شماره 15، 50 – 57.
نوایی، کامبیز و حاجیقاسمی، کامبیز. 1390. خشت و خیال. تهران: سروش.
Blaga, Paul A. (2005). Lectures on Classical Differential Geometry, Risoprint, Cluj-Napoca.
Bonner, Jay. (2018). Doing the Jitterbug with Islamic geometric patterns. J. Math. Arts. 3 (12) 128 -143. https://doi.org/10.1080/17513472.2018.1466431
Bonner, Jay, and Craig S. Kaplan. )2017(. “4 Computer Algorithms for Star Pattern Construction.” In Islamic Geometric Patterns, 549–73. New York, NY: Springer New York. https://doi.org/10.1007/978-1-4419-0217-7_4.
Broug, Eric. (2013). Islamic geometric design. London: Thames & Hudson.
Carmo, MP Do. )2016(. Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition. Mineola, New York: DOVER PUBLICATIONS, INC.
Dimcic, Milos; Knippers, Jan. 2011. Structural Optimization of Grid Shells Based on Genetic Algorithms. acadia 2011 _proceedings. https://elib.uni-stuttgart.de/handle/11682/98
Georg Glaeser & Franz Gruber. (2007). Developable surfaces in contemporary architecture, Journal of Mathematics and the Arts, 1:1, 59-71, http://dx.doi.org/10.1080/17513470701230004
Henriksson, Viktoria & Hult, Maria. (2015). Rationalizing freeform architecture; Surface discretization and multi-objective optimization. Master’s thesis in Structural Engineering and Building Technology, Department of Applied Mechanics. Gothenburg, Sweden: CHALMERS UNIVERSITY OF TECHNOLOGY. https://publications.lib.chalmers.se/records/fulltext/231658/231658.pdf
Jablan, Slavik Vlado. )2002(. Symmetry, Ornament and Modularity. Vol. 30. Series on Knots and Everything. Singapore: WORLD SCIENTIFIC. https://doi.org/10.1142/5031.
Kaplan, Craig S., and David H. Salesin. (2004). “Islamic Star Patterns in Absolute Geometry”. ACM Transactions on Graphics 23 (2): 97–119. https://doi.org/10.1145/990002.990003
Kasraei, Mohammad Hossein, Yahya Nourian, and Mohammadjavad Mahdavinejad. (2016). “Girih for Domes: Analysis of Three Iranian Domes.” Nexus Network Journal 18 (1): 311–21. https://doi.org/10.1007/s00004-015-0282-4.
Kızılörenli, Ecenur,& Maden, Feray. (2021). Tessellation in Architecture from Past to Present. IOP Conf. Series: Materials Science and Engineering. https://doi.org/10.1088/1757-899X/1203/3/032062
Khalilia, Ahmadreza; Hossein Soltanzadehb; Seyed Hadi Ghoddusifar. (2018). Algorithmic Comparison of "Shamsah" in Iranian Architecture, Carpet and Pottery. International Journal of Applied Arts Studies (IJAPAS)3(4): 7–22. https://journals.indexcopernicus.com/search/article?articleId=2213551
Necipoğlu, G., & Al-Asad, M. (1995). The Topkapı Scroll: Geometry and Ornament in Islamic Architecture, Topkapı Palace Museum Library MSNo Title. Los_Angeles: Getty Center for the History of Art and the Humanities. doi:9780892363353
Nejad Ebrahimi, Ahad, and Aref Azizpour Shoubi. )2020(. “The Projection Strategies of Gireh on the Iranian Historical Domes.” Mathematics Interdisciplinary Research 5 (3): 239–57. https://doi.org/10.22052/mir.2020.212903.1187.
Makovicky, Emil. )2016(. Symmetry: Through the Eyes of Old Masters. Berlin/Boston: Walter de Gruyter GmbH. https://doi.org/10.1080/0889311x.2017.1286333.
Sarhangi, Reza. )2012(. “Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs.” Nexus Network Journal 14 (2): 345–72. https://doi.org/10.1007/s00004-012-0117-5.
Sarhangi, Reza. (2008). “Illustrating Abu Al-Wafā’ Būzjānī: Flat Images, Spherical Constructions.” Iranian Studies 41 (4): 511–23. https://doi.org/10.1080/00210860802246184.
Séquin, Carlo H. (2008). “Symmetry for Architectural Design.” In Advances in Architectural Geometry. Edited by Helmut Pottmann, Axel Kilian, and Michael Hofer, 13–16. Vienna, Austria: Printed in Austria. https://doi.org/ISBN 978-3-902233-03-5.
Shelden, Dennis R, and Andrew J Witt. (2011). “Continuity and Rupture.” Architectural Design 81 (4): 36–43. https://doi.org/10.1002/ad.1266.
Su, Buqing, and Ting-yüan. Liu. (1989). Computational Geometry--Curve and Surface Modeling. New York: Academic Press, INC.
Wallner, Johannes, & Pottmann, Helmut. (2011). Geometric computing for freeform architecture. Journal of Mathematics in Industry, 1:4. https://doi.org/10.1186/2190-5983-1-4
_||_Ahmadi, Zahra. 2018. Contextualism and sustainable architecture (in Persian). Proceedings of the first national conference on sustainable architecture, Hamedan: Sama Technical Vocational College. https://civilica.com/doc/78814
Azizpour Shoubi. 2019. The Application of gireh (Islamic geometry pattern) in free surface with pattern recognition of used geometry pattern in domes surface of Iranian Islamic religious space in period from ilkhanid to end of Qajar (in Persian). Master thesis of Islamic Architecture, Faculty of Architecture & Urbanism, Tabriz Islamic Art University. Under supervision: Dr. Ahad Nezhad Ebrahimi
Aminppour, A & Olia, M.R & Abuee, R & Hajebi, B. (2016). The Presentation of Two New Methods in Drawing Girih: A Comparison Study (in Persian). Journal of Iranian Architecture & Urbanism (JIAU), 7(1), 67-83. https://doi.org/10.30475/isau.2017.62018
Besenval, Roland. (2000). Arch technology in the ancient east (in Persian). Translated Mohsen Habibi, Tehran: Iran's Cultural Heritage Organization.
Blaga, Paul A. (2005). Lectures on Classical Differential Geometry, Risoprint, Cluj-Napoca.
Bonner, Jay. (2018). Doing the Jitterbug with Islam-ic geometric patterns, J. Math. Arts. 3 (12) 128 -143. https://doi.org/10.1080/17513472.2018.1466431
Bonner, J. (2021). Islamic Geometric Patterns (in Persian). Translated Ahad Nejad Ebrahimi & Aref Azizpour Shoubi, Tabriz: Islamic Art University.
Bonner, Jay, and Craig S. Kaplan. )2017(. “4 Computer Algorithms for Star Pattern Construction.” In Islamic Geometric Patterns, 549–73. New York, NY: Springer New York. https://doi.org/10.1007/978-1-4419-0217-7_4.
Broug, Eric. (2013). Islamic geometric design. London: thames & Hudson.
Carmo, MP Do. )2016(. Differential Geometry of Curves and Surfaces. Revised and Updated Second Edition. Mineola, New York: DOVER PUBLICATIONS, INC.
Dimcic, Milos; Knippers, Jan. 2011. Structural Optimization of Grid Shells Based on Genetic Algorithms. acadia 2011 _proceedings. https://elib.uni-stuttgart.de/handle/11682/98
Faizi, Mohsen and Mehdi Khakzand (2012). Form, space and order in Iranian architecture (in Persian). Tehran: Elam and Sanat Publications.
Georg Glaeser & Franz Gruber. (2007). Developable surfaces in contemporary architecture, Journal of Mathematics and the Arts, 1:1, 59-71, http://dx.doi.org/10.1080/17513470701230004
Greenberg, M. J. (2009). Euclidean and Non-Euclidean Geometries: Developmentand History (in Persian). Translated by Mohammad Hadi Shafia. Tehran: University Publication Center.
HENRIKSSON, VIKTORIA & HULT, MARIA. (2015). Rationalizing freeform architecture; Surface discretization and multi-objective optimization. Master’s thesis in Structural Engineering and Building Technology, Department of Applied Mechanics. Gothenburg, Sweden: CHALMERS UNIVERSITY OF TECHNOLOGY
Jablan, Slavik Vlado. )2002(. Symmetry, Ornament and Modularity. Vol. 30. Series on Knots and Everything. Singapore: WORLD SCIENTIFIC. https://doi.org/10.1142/5031.
Kaplan, Craig S., and David H. Salesin. (2004). Islamic Star Patterns in Absolute Geometry. ACM Transactions on Graphics 23 (2): 97–119. https://doi.org/10.1145/990002.990003
Kasraei, Mohammad Hossein, Yahya Nourian, and Mohammadjavad Mahdavinejad. (2016). Girih for Domes: Analysis of Three Iranian Domes. Nexus Network Journal 18 (1): 311–21. https://doi.org/10.1007/s00004-015-0282-4.
Kızılörenli, Ecenur,& Maden, Feray. (2021). Tessellation in Architecture from Past to Present. IOP Conf. Series: Materials Science and Engineering. https://doi.org/10.1088/1757-899X/1203/3/032062
Khalilia, Ahmadreza; Hossein Soltanzadehb; Seyed Hadi Ghoddusifar. (2018). Algorithmic Comparison of "Shamsah" in Iranian Architecture, Carpet and Pottery. International Journal of Applied Arts Studies 3(4),7–22.
Leatherbarrow, David; Mohsen Mostafavi. (2010). Surface Architecture (in Persian). Translated by
Mustafa Kiyani. Tehran: University of Art.
Navai, Kambiz; Haji Qassemi, Kambiz. 2011. Khesht-o Khial; An Interpretation of Iranian Islamic Architecture (In Persian). Tehran: Soroush.
Necipoğlu, G., & Al-Asad, M. (1995). The Topkapı Scroll: Geometry and Ornament in Islamic Architecture, Topkapı Palace Museum Library MSNo Title. Los_Angeles: Getty Center for the History of Art and the Humanities. doi:9780892363353
Nejad Ebrahimi, Ahad, and Aref Azizpour Shoubi. )2020(. The Projection Strategies of Gireh on the Iranian Historical Domes. Mathematics Interdisciplinary Research 5 (3): 239–57. https://doi.org/10.22052/mir.2020.212903.1187.
Nejad Ebrahimi, Ahad, and Aref Azizpour Shoubi. )2019). Identify domes with gireh in Iranian Mosques (In Persian). Green Architecture 2 (15), 45-53.
Makovicky, Emil. )2016(. Symmetry: Through the Eyes of Old Masters. Berlin/Boston: Walter de Gruyter GmbH. https://doi.org/10.1080/0889311x.2017.1286333.
Montazer, B., Soltan Zadeh, H. (2018). Reflecting the Regular Pentagon Role in Geometric Patterns of Islamic Architecture of Iran (in Persian), Islamic Art Studies, 14(30), pp. 15-40. https://www.doi.org/10.22034/ias.2018.91746
Rezvani, Alireza. 2015. Spatial networks and geometric volumes (in Persian). Mashhad: Azad University
Sarhangi, Reza. )2012(.Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs. Nexus Network Journal 14 (2): 345–72. https://doi.org/10.1007/s00004-012-0117-5.
Sarhangi, Reza. (2008). Illustrating Abu Al-Wafā’ Būzjānī: Flat Images, Spherical Constructions. Iranian Studies 41 (4): 511–23. https://doi.org/10.1080/00210860802246184.
Séquin, Carlo H. (2008). Symmetry for Architectural Design. In Advances in Architectural Geometry, edited by Helmut Pottmann, Axel Kilian, and Michael Hofer, 13–16. Vienna, Austria: Printed in Austria. https://doi.org/ISBN 978-3-902233-03-5.
Shelden, Dennis R, and Andrew J Witt. (2011). Continuity and Rupture. Architectural Design 81 (4): 36–43. https://doi.org/10.1002/ad.1266.
Su, Buqing, and Ting-yüan. Liu. (1989). Computational Geometry--Curve and Surface Modeling. New York: Academic Press, INC.
Wallner, Johannes, & Pottmann, Helmut. (2011). Geometric computing for freeform architecture. Journal of Mathematics in Industry, 1:4.
https://doi.org/10.1186/2190-59